Details

analyze2.5s (2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
0%	74.9%	25.1%	2
18.7%	56.2%	25.1%	3
37.5%	37.5%	25.1%	4
42.1%	32.8%	25.1%	5
46.8%	28.1%	25.1%	6
48%	26.9%	25.1%	7
49.2%	25.8%	25.1%	8
49.5%	25.5%	25.1%	9
49.8%	25.2%	25.1%	10
49.8%	25.2%	25.1%	11
49.8%	25.1%	25.1%	12
49.9%	25%	25.1%	13
49.9%	25%	25.1%	14

Compiler

Compiled 127 to 112 computations (11.8% saved)

sample1.9s (1.5%)

Algorithm

1×

intervals

Results

1.7s	117×	body	8192	exit
148.0ms	256×	body	128	valid
8.0ms	375×	pre	128	true
1.0ms	2×	body	128	invalid

Compiler

Compiled 252 to 223 computations (11.5% saved)

simplify49.0ms (0%)

Algorithm

1×	egg-herbie

Rules

388×	`associate-+l+_binary64`
296×	`associate-+r+_binary64`
271×	`distribute-rgt-in_binary64`
266×	`distribute-lft-in_binary64`
224×	`associate-r_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	156
1	160	147
2	606	119
3	3454	115
4	4863	115
5	4787	115

prune12.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

1.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	1.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))) (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z))) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))
▶	1.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))

Status

Error

Program

1.7b

(*.f64 (/.f64 (PI.f64) (sin.f64 (*.f64 (PI.f64) z))) (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))) (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z))) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))

▶

1.7b

(*.f64 (/.f64 (PI.f64) (sin.f64 (*.f64 (PI.f64) z))) (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))

Compiler

Compiled 596 to 508 computations (14.8% saved)

localize59.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8))))
✓	1.0b	(sqrt.f64 (*.f64 (PI.f64) 2))
✓	2.8b	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2)))
✓	5.2b	(-.f64 (-.f64 1 z) 1)

series42.0ms (0%)

Counts

4 → 36

Calls

4 calls:

37.0ms	(.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8))))
3.0ms	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2)))
2.0ms	(-.f64 (-.f64 1 z) 1)
0.0ms	(sqrt.f64 (*.f64 (PI.f64) 2))

rewrite554.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

394×	`frac-add_binary64`
130×	`frac-times_binary64`
101×	`associate-*r/_binary64`
93×	`*-un-lft-identity_binary64`
58×	`flip-+_binary64`

Counts

4 → 249

Calls

4 calls:

222.0ms	(.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8))))
32.0ms	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2)))
11.0ms	(-.f64 (-.f64 1 z) 1)
2.0ms	(sqrt.f64 (*.f64 (PI.f64) 2))

simplify1.2s (1%)

Algorithm

1×	egg-herbie

Rules

891×	`fma-def_binary64`
392×	`*-commutative_binary64`
250×	`associate-l_binary64`
240×	`distribute-rgt-in_binary64`
224×	`distribute-lft-in_binary64`

Counts

285 → 390

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	833	76191
1	3546	71260
2	4930	71260

prune12.1s (9.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	1234	6	1240
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	1236	6	1242

Error

0.3b

Counts

1242 → 6

Alt Table

Status	Error	Program
	1.3b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (-.f64 (fma.f64 3264229102083425005530891465931403/2963520000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (.f64 z z) (sqrt.f64 15/2))))) (fma.f64 1106209385320415913103082059/8400000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (.f64 (sqrt.f64 2) (.f64 (.f64 z z) (sqrt.f64 15/2))) (pow.f64 (log.f64 15/2) 2)))) (fma.f64 1106209385320415913103082059/4200000000000000000000000 (.f64 (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (sqrt.f64 15/2))) (sqrt.f64 (PI.f64))) (.f64 2408637854869972117504576098451/3528000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 z (sqrt.f64 15/2))))))))) (fma.f64 1106209385320415913103082059/4200000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (.f64 z (sqrt.f64 15/2)) (log.f64 15/2))))) (fma.f64 1106209385320415913103082059/4200000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (log.f64 15/2) (.f64 (.f64 z z) (sqrt.f64 15/2)))))) (.f64 1479421971200822750497987168891/3528000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (log.f64 15/2) (.f64 (sqrt.f64 2) (.f64 (*.f64 z z) (sqrt.f64 15/2)))))))))))
	1.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (log.f64 (exp.f64 (+.f64 (-.f64 1 z) -1))) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
	1.4b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2) (-.f64 (-.f64 1 z) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2)))) (fma.f64 3764081837873279/25000000000000000000000 (.f64 (+.f64 (-.f64 1 z) 6) (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (.f64 (+.f64 1 (-.f64 1 z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (+.f64 (-.f64 1 z) 2) (+.f64 (-.f64 1 z) 3)))))) (.f64 (+.f64 (-.f64 1 z) 7) (fma.f64 (+.f64 (-.f64 1 z) 6) (fma.f64 -3464277381643003/25000000000000000 (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (.f64 (+.f64 1 (-.f64 1 z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (+.f64 (-.f64 1 z) 2) (+.f64 (-.f64 1 z) 3)))) (.f64 (+.f64 (-.f64 1 z) 5) (fma.f64 2501468655737381/200000000000000 (.f64 (.f64 (+.f64 1 (-.f64 1 z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (+.f64 (-.f64 1 z) 2) (+.f64 (-.f64 1 z) 3))) (.f64 (+.f64 (-.f64 1 z) 4) (fma.f64 (.f64 (+.f64 1 (-.f64 1 z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (+.f64 (-.f64 1 z) 2) -883075145810703/5000000000000) (.f64 (+.f64 (-.f64 1 z) 3) (fma.f64 (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000) (.f64 (+.f64 1 (-.f64 1 z)) 7713234287776531/10000000000000) (.f64 (fma.f64 (+.f64 1 (-.f64 1 z)) (+.f64 999999999999429700000000108414029999993130164299/1000000000000000000000000000000000000000000000000 (pow.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) 3)) (.f64 -3147848041806007/2500000000000 (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000))) (+.f64 (-.f64 1 z) 2))))))))) (.f64 2496092394504893/250000000000000000000 (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (.f64 (+.f64 1 (-.f64 1 z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (+.f64 (-.f64 1 z) 2) (+.f64 (-.f64 1 z) 3)))))))))) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (+.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (-.f64 (.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1)) (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))))) (+.f64 (-.f64 (-.f64 1 z) 1) 2)) (+.f64 (-.f64 (-.f64 1 z) 1) 3)) (+.f64 (-.f64 (-.f64 1 z) 1) 4)) (+.f64 (-.f64 (-.f64 1 z) 1) 5)) (+.f64 (-.f64 (-.f64 1 z) 1) 6)) (+.f64 (-.f64 (-.f64 1 z) 1) 7)) (+.f64 (-.f64 (-.f64 1 z) 1) 8))))
	1.0b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z))))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
	1.4b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (-.f64 1 z))) 1) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (pow.f64 9999999999998099/10000000000000000 3) (pow.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1)) 3)) (+.f64 (-.f64 (-.f64 1 z) 1) 2)) (.f64 (+.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (-.f64 (.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1)) (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))))) -3147848041806007/2500000000000)) (+.f64 (-.f64 (-.f64 1 z) 1) 3)) (.f64 (.f64 (+.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (-.f64 (.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1)) (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))))) (+.f64 (-.f64 (-.f64 1 z) 1) 2)) 7713234287776531/10000000000000)) (+.f64 (-.f64 (-.f64 1 z) 1) 4)) (.f64 (.f64 (.f64 (+.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (-.f64 (.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1)) (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))))) (+.f64 (-.f64 (-.f64 1 z) 1) 2)) (+.f64 (-.f64 (-.f64 1 z) 1) 3)) -883075145810703/5000000000000)) (+.f64 (-.f64 (-.f64 1 z) 1) 5)) (.f64 (.f64 (.f64 (.f64 (+.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (-.f64 (.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1)) (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))))) (+.f64 (-.f64 (-.f64 1 z) 1) 2)) (+.f64 (-.f64 (-.f64 1 z) 1) 3)) (+.f64 (-.f64 (-.f64 1 z) 1) 4)) 2501468655737381/200000000000000)) (+.f64 (-.f64 (-.f64 1 z) 1) 6)) (.f64 (.f64 (.f64 (.f64 (.f64 (+.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (-.f64 (.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1)) (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))))) (+.f64 (-.f64 (-.f64 1 z) 1) 2)) (+.f64 (-.f64 (-.f64 1 z) 1) 3)) (+.f64 (-.f64 (-.f64 1 z) 1) 4)) (+.f64 (-.f64 (-.f64 1 z) 1) 5)) -3464277381643003/25000000000000000)) (+.f64 (-.f64 (-.f64 1 z) 1) 7)) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (+.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (-.f64 (.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1)) (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))))) (+.f64 (-.f64 (-.f64 1 z) 1) 2)) (+.f64 (-.f64 (-.f64 1 z) 1) 3)) (+.f64 (-.f64 (-.f64 1 z) 1) 4)) (+.f64 (-.f64 (-.f64 1 z) 1) 5)) (+.f64 (-.f64 (-.f64 1 z) 1) 6)) 2496092394504893/250000000000000000000)) (+.f64 (-.f64 (-.f64 1 z) 1) 8)) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (+.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (-.f64 (.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1)) (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))))) (+.f64 (-.f64 (-.f64 1 z) 1) 2)) (+.f64 (-.f64 (-.f64 1 z) 1) 3)) (+.f64 (-.f64 (-.f64 1 z) 1) 4)) (+.f64 (-.f64 (-.f64 1 z) 1) 5)) (+.f64 (-.f64 (-.f64 1 z) 1) 6)) (+.f64 (-.f64 (-.f64 1 z) 1) 7)) 3764081837873279/25000000000000000000000))) (.f64 (.f64 (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (-.f64 1 1/2)) (exp.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2))) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (+.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (-.f64 (.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1)) (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))))) (+.f64 (-.f64 (-.f64 1 z) 1) 2)) (+.f64 (-.f64 (-.f64 1 z) 1) 3)) (+.f64 (-.f64 (-.f64 1 z) 1) 4)) (+.f64 (-.f64 (-.f64 1 z) 1) 5)) (+.f64 (-.f64 (-.f64 1 z) 1) 6)) (+.f64 (-.f64 (-.f64 1 z) 1) 7)) (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
▶	0.5b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2) (-.f64 1 z))) (fma.f64 3764081837873279/25000000000000000000000 (.f64 (+.f64 (-.f64 1 z) 6) (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))))))) (.f64 (+.f64 (-.f64 1 z) 7) (fma.f64 (+.f64 (-.f64 1 z) 6) (fma.f64 -3464277381643003/25000000000000000 (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))))) (.f64 (+.f64 (-.f64 1 z) 5) (fma.f64 2501468655737381/200000000000000 (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)))) (.f64 (+.f64 (-.f64 1 z) 4) (fma.f64 -883075145810703/5000000000000 (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (.f64 (+.f64 (-.f64 1 z) 3) (fma.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (.f64 (/.f64 -7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)))))))))) (.f64 2496092394504893/250000000000000000000 (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))))))))))) (.f64 (.f64 (sqrt.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2)) (exp.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2))) (.f64 (+.f64 (-.f64 1 z) 7) (.f64 (+.f64 (-.f64 1 z) 6) (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)))))))))))

Compiler

Compiled 235304 to 201411 computations (14.4% saved)

localize65.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)))
✓	1.0b	(sqrt.f64 (*.f64 2 (PI.f64)))
✓	2.8b	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z))))
✓	5.2b	(+.f64 (-.f64 1 z) -1)

series7.0ms (0%)

Counts

4 → 36

Calls

4 calls:

3.0ms	(-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)))
3.0ms	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z))))
2.0ms	(+.f64 (-.f64 1 z) -1)
0.0ms	(sqrt.f64 (*.f64 2 (PI.f64)))

rewrite96.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

313×	`*-un-lft-identity_binary64`
114×	`prod-diff_binary64`
111×	`distribute-lft-out_binary64`
98×	`add-sqr-sqrt_binary64`
91×	`times-frac_binary64`

Counts

4 → 229

Calls

4 calls:

38.0ms	(-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)))
19.0ms	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z))))
6.0ms	(+.f64 (-.f64 1 z) -1)
2.0ms	(sqrt.f64 (*.f64 2 (PI.f64)))

simplify258.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

418×	`fma-neg_binary64`
207×	`cancel-sign-sub-inv_binary64`
203×	`fma-def_binary64`
194×	`distribute-rgt-in_binary64`
180×	`distribute-lft-in_binary64`

Counts

265 → 246

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	398	15013
1	1092	7179
2	3235	6134
3	4513	6134
4	4693	6134

prune32.9s (26.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	1329	2	1331
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	1331	6	1337

Error

0.3b

Counts

1337 → 6

Alt Table

Status	Error	Program
	1.4b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2) (-.f64 (-.f64 1 z) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2)))) (fma.f64 3764081837873279/25000000000000000000000 (.f64 (+.f64 (-.f64 1 z) 6) (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (.f64 (+.f64 1 (-.f64 1 z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (+.f64 (-.f64 1 z) 2) (+.f64 (-.f64 1 z) 3)))))) (.f64 (+.f64 (-.f64 1 z) 7) (fma.f64 (+.f64 (-.f64 1 z) 6) (fma.f64 -3464277381643003/25000000000000000 (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (.f64 (+.f64 1 (-.f64 1 z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (+.f64 (-.f64 1 z) 2) (+.f64 (-.f64 1 z) 3)))) (.f64 (+.f64 (-.f64 1 z) 5) (fma.f64 2501468655737381/200000000000000 (.f64 (.f64 (+.f64 1 (-.f64 1 z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (+.f64 (-.f64 1 z) 2) (+.f64 (-.f64 1 z) 3))) (.f64 (+.f64 (-.f64 1 z) 4) (fma.f64 (.f64 (+.f64 1 (-.f64 1 z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (+.f64 (-.f64 1 z) 2) -883075145810703/5000000000000) (.f64 (+.f64 (-.f64 1 z) 3) (fma.f64 (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000) (.f64 (+.f64 1 (-.f64 1 z)) 7713234287776531/10000000000000) (.f64 (fma.f64 (+.f64 1 (-.f64 1 z)) (+.f64 999999999999429700000000108414029999993130164299/1000000000000000000000000000000000000000000000000 (pow.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) 3)) (.f64 -3147848041806007/2500000000000 (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000))) (+.f64 (-.f64 1 z) 2))))))))) (.f64 2496092394504893/250000000000000000000 (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (.f64 (+.f64 1 (-.f64 1 z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (+.f64 (-.f64 1 z) 2) (+.f64 (-.f64 1 z) 3)))))))))) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (+.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (-.f64 (.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1)) (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))))) (+.f64 (-.f64 (-.f64 1 z) 1) 2)) (+.f64 (-.f64 (-.f64 1 z) 1) 3)) (+.f64 (-.f64 (-.f64 1 z) 1) 4)) (+.f64 (-.f64 (-.f64 1 z) 1) 5)) (+.f64 (-.f64 (-.f64 1 z) 1) 6)) (+.f64 (-.f64 (-.f64 1 z) 1) 7)) (+.f64 (-.f64 (-.f64 1 z) 1) 8))))
▶	1.0b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z))))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
	1.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2) (-.f64 1 z))) (fma.f64 3764081837873279/25000000000000000000000 (.f64 (+.f64 (-.f64 1 z) 6) (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))))))) (.f64 (+.f64 (-.f64 1 z) 7) (fma.f64 (+.f64 (-.f64 1 z) 6) (fma.f64 -3464277381643003/25000000000000000 (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))))) (.f64 (+.f64 (-.f64 1 z) 5) (fma.f64 2501468655737381/200000000000000 (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)))) (.f64 (+.f64 (-.f64 1 z) 4) (fma.f64 -883075145810703/5000000000000 (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (.f64 (+.f64 (-.f64 1 z) 3) (fma.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (.f64 (/.f64 -7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)))))))))) (.f64 2496092394504893/250000000000000000000 (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))))))))))) (.f64 (.f64 (sqrt.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2)) (exp.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2))) (.f64 (+.f64 (-.f64 1 z) 7) (.f64 (+.f64 (-.f64 1 z) 6) (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (fma.f64 (*.f64 z z) 264902633081502703/540000000000000 (fma.f64 z 4968593293387813/18000000000000 -6274711494956025703/30000000000000000))))))))))
	2.4b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (PI.f64)))) (cbrt.f64 (sqrt.f64 (.f64 2 (PI.f64))))) (cbrt.f64 (sqrt.f64 (.f64 2 (PI.f64))))) (pow.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2) (-.f64 1 z))) (fma.f64 3764081837873279/25000000000000000000000 (.f64 (+.f64 (-.f64 1 z) 6) (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))))))) (.f64 (+.f64 (-.f64 1 z) 7) (fma.f64 (+.f64 (-.f64 1 z) 6) (fma.f64 -3464277381643003/25000000000000000 (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))))) (.f64 (+.f64 (-.f64 1 z) 5) (fma.f64 2501468655737381/200000000000000 (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)))) (.f64 (+.f64 (-.f64 1 z) 4) (fma.f64 -883075145810703/5000000000000 (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (.f64 (+.f64 (-.f64 1 z) 3) (fma.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (.f64 (/.f64 -7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)))))))))) (.f64 2496092394504893/250000000000000000000 (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))))))))))) (.f64 (.f64 (sqrt.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2)) (exp.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2))) (.f64 (+.f64 (-.f64 1 z) 7) (.f64 (+.f64 (-.f64 1 z) 6) (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)))))))))))
	1.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (log.f64 (exp.f64 (+.f64 (-.f64 1 z) -1))) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
✓	0.5b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2) (-.f64 1 z))) (fma.f64 3764081837873279/25000000000000000000000 (.f64 (+.f64 (-.f64 1 z) 6) (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))))))) (.f64 (+.f64 (-.f64 1 z) 7) (fma.f64 (+.f64 (-.f64 1 z) 6) (fma.f64 -3464277381643003/25000000000000000 (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))))) (.f64 (+.f64 (-.f64 1 z) 5) (fma.f64 2501468655737381/200000000000000 (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)))) (.f64 (+.f64 (-.f64 1 z) 4) (fma.f64 -883075145810703/5000000000000 (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (.f64 (+.f64 (-.f64 1 z) 3) (fma.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (.f64 (/.f64 -7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)))))))))) (.f64 2496092394504893/250000000000000000000 (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))))))))))) (.f64 (.f64 (sqrt.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2)) (exp.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2))) (.f64 (+.f64 (-.f64 1 z) 7) (.f64 (+.f64 (-.f64 1 z) 6) (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)))))))))))

Compiler

Compiled 509039 to 431172 computations (15.3% saved)

localize49.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z))))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8))))
	1.0b	(sqrt.f64 (*.f64 (PI.f64) 2))
✓	1.1b	(+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z))))
	5.2b	(-.f64 (-.f64 1 z) 1)

series37.0ms (0%)

Counts

2 → 24

Calls

2 calls:

33.0ms

(*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z))))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8))))

3.0ms

(+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z))))

rewrite409.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

295×	`frac-add_binary64`
114×	`frac-times_binary64`
101×	`*-un-lft-identity_binary64`
89×	`associate-*r/_binary64`
50×	`flip-+_binary64`

Counts

2 → 183

Calls

2 calls:

177.0ms

(*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z))))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8))))

27.0ms

(+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z))))

simplify1.1s (0.9%)

Algorithm

1×	egg-herbie

Rules

845×	`fma-def_binary64`
334×	`*-commutative_binary64`
208×	`associate-l_binary64`
201×	`distribute-rgt-in_binary64`
187×	`distribute-lft-in_binary64`

Counts

207 → 279

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	687	61158
1	3023	59797
2	4878	59777
3	4973	59777

prune5.1s (4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	1062	1	1063
Fresh	1	3	4
Picked	0	1	1
Done	1	0	1
Total	1064	5	1069

Error

0.3b

Counts

1069 → 5

Alt Table

Status	Error	Program
▶	0.5b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 15/2) (-.f64 1 z))) (fma.f64 3764081837873279/25000000000000000000000 (.f64 (+.f64 (-.f64 1 z) 6) (.f64 (+.f64 (-.f64 1 z) 5) (-.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))))) (.f64 (+.f64 (-.f64 1 z) 7) (fma.f64 (+.f64 (-.f64 1 z) 6) (fma.f64 -3464277381643003/25000000000000000 (-.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (.f64 (+.f64 (-.f64 1 z) 5) (-.f64 (.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3)))) (/.f64 (/.f64 6257345435636579942128840739161/40000000000000000000000000000 (+.f64 (-.f64 1 z) 4)) (+.f64 (-.f64 1 z) 4))))) (.f64 2496092394504893/250000000000000000000 (.f64 (+.f64 (-.f64 1 z) 5) (-.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))))))))) (.f64 (.f64 (sqrt.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 15/2)) (exp.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 15/2))) (.f64 (+.f64 (-.f64 1 z) 7) (.f64 (+.f64 (-.f64 1 z) 6) (*.f64 (+.f64 (-.f64 1 z) 5) (-.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4)))))))))
	1.4b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2) (-.f64 (-.f64 1 z) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2)))) (fma.f64 3764081837873279/25000000000000000000000 (.f64 (+.f64 (-.f64 1 z) 6) (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (.f64 (+.f64 1 (-.f64 1 z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (+.f64 (-.f64 1 z) 2) (+.f64 (-.f64 1 z) 3)))))) (.f64 (+.f64 (-.f64 1 z) 7) (fma.f64 (+.f64 (-.f64 1 z) 6) (fma.f64 -3464277381643003/25000000000000000 (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (.f64 (+.f64 1 (-.f64 1 z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (+.f64 (-.f64 1 z) 2) (+.f64 (-.f64 1 z) 3)))) (.f64 (+.f64 (-.f64 1 z) 5) (fma.f64 2501468655737381/200000000000000 (.f64 (.f64 (+.f64 1 (-.f64 1 z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (+.f64 (-.f64 1 z) 2) (+.f64 (-.f64 1 z) 3))) (.f64 (+.f64 (-.f64 1 z) 4) (fma.f64 (.f64 (+.f64 1 (-.f64 1 z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (+.f64 (-.f64 1 z) 2) -883075145810703/5000000000000) (.f64 (+.f64 (-.f64 1 z) 3) (fma.f64 (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000) (.f64 (+.f64 1 (-.f64 1 z)) 7713234287776531/10000000000000) (.f64 (fma.f64 (+.f64 1 (-.f64 1 z)) (+.f64 999999999999429700000000108414029999993130164299/1000000000000000000000000000000000000000000000000 (pow.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) 3)) (.f64 -3147848041806007/2500000000000 (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000))) (+.f64 (-.f64 1 z) 2))))))))) (.f64 2496092394504893/250000000000000000000 (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (.f64 (+.f64 1 (-.f64 1 z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (+.f64 (-.f64 1 z) 2) (+.f64 (-.f64 1 z) 3)))))))))) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (+.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (-.f64 (.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1)) (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))))) (+.f64 (-.f64 (-.f64 1 z) 1) 2)) (+.f64 (-.f64 (-.f64 1 z) 1) 3)) (+.f64 (-.f64 (-.f64 1 z) 1) 4)) (+.f64 (-.f64 (-.f64 1 z) 1) 5)) (+.f64 (-.f64 (-.f64 1 z) 1) 6)) (+.f64 (-.f64 (-.f64 1 z) 1) 7)) (+.f64 (-.f64 (-.f64 1 z) 1) 8))))
✓	1.0b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z))))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
	1.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2) (-.f64 1 z))) (fma.f64 3764081837873279/25000000000000000000000 (.f64 (+.f64 (-.f64 1 z) 6) (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))))))) (.f64 (+.f64 (-.f64 1 z) 7) (fma.f64 (+.f64 (-.f64 1 z) 6) (fma.f64 -3464277381643003/25000000000000000 (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))))) (.f64 (+.f64 (-.f64 1 z) 5) (fma.f64 2501468655737381/200000000000000 (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)))) (.f64 (+.f64 (-.f64 1 z) 4) (fma.f64 -883075145810703/5000000000000 (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (.f64 (+.f64 (-.f64 1 z) 3) (fma.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (.f64 (/.f64 -7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)))))))))) (.f64 2496092394504893/250000000000000000000 (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))))))))))) (.f64 (.f64 (sqrt.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2)) (exp.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2))) (.f64 (+.f64 (-.f64 1 z) 7) (.f64 (+.f64 (-.f64 1 z) 6) (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (fma.f64 (*.f64 z z) 264902633081502703/540000000000000 (fma.f64 z 4968593293387813/18000000000000 -6274711494956025703/30000000000000000))))))))))
	2.4b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (PI.f64)))) (cbrt.f64 (sqrt.f64 (.f64 2 (PI.f64))))) (cbrt.f64 (sqrt.f64 (.f64 2 (PI.f64))))) (pow.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2) (-.f64 1 z))) (fma.f64 3764081837873279/25000000000000000000000 (.f64 (+.f64 (-.f64 1 z) 6) (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))))))) (.f64 (+.f64 (-.f64 1 z) 7) (fma.f64 (+.f64 (-.f64 1 z) 6) (fma.f64 -3464277381643003/25000000000000000 (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))))) (.f64 (+.f64 (-.f64 1 z) 5) (fma.f64 2501468655737381/200000000000000 (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)))) (.f64 (+.f64 (-.f64 1 z) 4) (fma.f64 -883075145810703/5000000000000 (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (.f64 (+.f64 (-.f64 1 z) 3) (fma.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (.f64 (/.f64 -7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)))))))))) (.f64 2496092394504893/250000000000000000000 (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))))))))))) (.f64 (.f64 (sqrt.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2)) (exp.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2))) (.f64 (+.f64 (-.f64 1 z) 7) (.f64 (+.f64 (-.f64 1 z) 6) (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)))))))))))

Compiler

Compiled 190725 to 161618 computations (15.3% saved)

localize62.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(*.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))))
	1.0b	(sqrt.f64 (*.f64 2 (PI.f64)))
✓	1.1b	(+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))
	5.2b	(-.f64 (-.f64 1 z) 1)

series7.0ms (0%)

Counts

2 → 24

Calls

2 calls:

4.0ms

(*.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))))

3.0ms

(+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))

rewrite170.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

223×	`*-un-lft-identity_binary64`
125×	`distribute-lft-out_binary64`
85×	`frac-add_binary64`
43×	`flip-+_binary64`
43×	`flip3-+_binary64`

Counts

2 → 152

Calls

2 calls:

101.0ms

(*.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))))

25.0ms

(+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))

simplify306.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

813×	`distribute-rgt-in_binary64`
798×	`distribute-lft-in_binary64`
261×	`fma-def_binary64`
81×	`*-commutative_binary64`
53×	`associate-*l/_binary64`

Counts

176 → 184

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	278	20228
1	1122	19399
2	4941	19399

prune7.6s (6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	721	1	722
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	723	4	727

Error

0.3b

Counts

727 → 4

Alt Table

Status	Error	Program
	0.5b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 15/2) (-.f64 1 z))) (fma.f64 3764081837873279/25000000000000000000000 (.f64 (+.f64 (-.f64 1 z) 6) (.f64 (+.f64 (-.f64 1 z) 5) (-.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))))) (.f64 (+.f64 (-.f64 1 z) 7) (fma.f64 (+.f64 (-.f64 1 z) 6) (fma.f64 -3464277381643003/25000000000000000 (-.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (.f64 (+.f64 (-.f64 1 z) 5) (-.f64 (cbrt.f64 (pow.f64 (.f64 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) 9999999999998099/10000000000000000) (/.f64 7713234287776531/10000000000000 (+.f64 2 (-.f64 1 z)))) (/.f64 -883075145810703/5000000000000 (+.f64 3 (-.f64 1 z)))) (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) 9999999999998099/10000000000000000) (/.f64 7713234287776531/10000000000000 (+.f64 2 (-.f64 1 z)))) (/.f64 -883075145810703/5000000000000 (+.f64 3 (-.f64 1 z))))) 3)) (/.f64 (/.f64 6257345435636579942128840739161/40000000000000000000000000000 (+.f64 (-.f64 1 z) 4)) (+.f64 (-.f64 1 z) 4))))) (.f64 2496092394504893/250000000000000000000 (.f64 (+.f64 (-.f64 1 z) 5) (-.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))))))))) (.f64 (.f64 (sqrt.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 15/2)) (exp.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 15/2))) (.f64 (+.f64 (-.f64 1 z) 7) (.f64 (+.f64 (-.f64 1 z) 6) (*.f64 (+.f64 (-.f64 1 z) 5) (-.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4)))))))))
	1.4b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2) (-.f64 (-.f64 1 z) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2)))) (fma.f64 3764081837873279/25000000000000000000000 (.f64 (+.f64 (-.f64 1 z) 6) (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (.f64 (+.f64 1 (-.f64 1 z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (+.f64 (-.f64 1 z) 2) (+.f64 (-.f64 1 z) 3)))))) (.f64 (+.f64 (-.f64 1 z) 7) (fma.f64 (+.f64 (-.f64 1 z) 6) (fma.f64 -3464277381643003/25000000000000000 (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (.f64 (+.f64 1 (-.f64 1 z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (+.f64 (-.f64 1 z) 2) (+.f64 (-.f64 1 z) 3)))) (.f64 (+.f64 (-.f64 1 z) 5) (fma.f64 2501468655737381/200000000000000 (.f64 (.f64 (+.f64 1 (-.f64 1 z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (+.f64 (-.f64 1 z) 2) (+.f64 (-.f64 1 z) 3))) (.f64 (+.f64 (-.f64 1 z) 4) (fma.f64 (.f64 (+.f64 1 (-.f64 1 z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (+.f64 (-.f64 1 z) 2) -883075145810703/5000000000000) (.f64 (+.f64 (-.f64 1 z) 3) (fma.f64 (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000) (.f64 (+.f64 1 (-.f64 1 z)) 7713234287776531/10000000000000) (.f64 (fma.f64 (+.f64 1 (-.f64 1 z)) (+.f64 999999999999429700000000108414029999993130164299/1000000000000000000000000000000000000000000000000 (pow.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) 3)) (.f64 -3147848041806007/2500000000000 (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000))) (+.f64 (-.f64 1 z) 2))))))))) (.f64 2496092394504893/250000000000000000000 (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (.f64 (+.f64 1 (-.f64 1 z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (+.f64 (-.f64 1 z) 2) (+.f64 (-.f64 1 z) 3)))))))))) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (+.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (-.f64 (.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1)) (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))))) (+.f64 (-.f64 (-.f64 1 z) 1) 2)) (+.f64 (-.f64 (-.f64 1 z) 1) 3)) (+.f64 (-.f64 (-.f64 1 z) 1) 4)) (+.f64 (-.f64 (-.f64 1 z) 1) 5)) (+.f64 (-.f64 (-.f64 1 z) 1) 6)) (+.f64 (-.f64 (-.f64 1 z) 1) 7)) (+.f64 (-.f64 (-.f64 1 z) 1) 8))))
✓	1.0b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z))))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
	2.4b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (PI.f64)))) (cbrt.f64 (sqrt.f64 (.f64 2 (PI.f64))))) (cbrt.f64 (sqrt.f64 (.f64 2 (PI.f64))))) (pow.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2) (-.f64 1 z))) (fma.f64 3764081837873279/25000000000000000000000 (.f64 (+.f64 (-.f64 1 z) 6) (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))))))) (.f64 (+.f64 (-.f64 1 z) 7) (fma.f64 (+.f64 (-.f64 1 z) 6) (fma.f64 -3464277381643003/25000000000000000 (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))))) (.f64 (+.f64 (-.f64 1 z) 5) (fma.f64 2501468655737381/200000000000000 (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)))) (.f64 (+.f64 (-.f64 1 z) 4) (fma.f64 -883075145810703/5000000000000 (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (.f64 (+.f64 (-.f64 1 z) 3) (fma.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (.f64 (/.f64 -7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)))))))))) (.f64 2496092394504893/250000000000000000000 (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))))))))))) (.f64 (.f64 (sqrt.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2)) (exp.f64 (+.f64 (+.f64 (-.f64 1 z) -1) 15/2))) (.f64 (+.f64 (-.f64 1 z) 7) (.f64 (+.f64 (-.f64 1 z) 6) (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (-.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (+.f64 1 (-.f64 1 z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)))))))))))

Compiler

Compiled 253479 to 214058 computations (15.6% saved)

regimes12.4s (9.9%)

Accuracy

Total 0.2b remaining (38.6%)

Threshold costs 0.2b (38.6%)

Counts

860 → 1

Compiler

Compiled 389024 to 337238 computations (13.3% saved)

simplify16.0ms (0%)

Algorithm

1×	egg-herbie

Rules

24×	`*-commutative_binary64`
15×	`+-commutative_binary64`
5×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	529
1	109	529
2	116	529
3	122	529
4	126	529
5	128	529
6	129	529
7	127	529

end13.0ms (0%)

Compiler: Compiled 353 to 301 computations (14.7% saved)

sample46.9s (37.3%)

Algorithm

1×

intervals

Results

42.7s	3790×	body	8192	exit
2.8s	8000×	body	128	valid
170.0ms	11886×	pre	128	true
35.0ms	96×	body	128	invalid

Compiler

Compiled 1716 to 1477 computations (13.9% saved)

Details

analyze2.5s (2%)

sample1.9s (1.5%)

simplify49.0ms (0%)

prune12.0ms (0%)

localize59.0ms (0%)

series42.0ms (0%)

rewrite554.0ms (0.4%)

simplify1.2s (1%)

prune12.1s (9.6%)

localize65.0ms (0.1%)

series7.0ms (0%)

rewrite96.0ms (0.1%)

simplify258.0ms (0.2%)

prune32.9s (26.1%)

localize49.0ms (0%)

series37.0ms (0%)

rewrite409.0ms (0.3%)

simplify1.1s (0.9%)

prune5.1s (4%)

localize62.0ms (0%)

series7.0ms (0%)

rewrite170.0ms (0.1%)

simplify306.0ms (0.2%)

prune7.6s (6%)

regimes12.4s (9.9%)

simplify16.0ms (0%)

end13.0ms (0%)

sample46.9s (37.3%)

Profiling