Details

analyze2.8s (3.4%)

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)

sample59.7s (71.1%)

Results

54.7s	3913×	body	8192	exit
4.9s	8256×	body	128	valid
50.0ms	93×	body	128	invalid

Compiler

Compiled 378 to 334 computations (11.6% saved)

simplify51.0ms (0.1%)

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)

localize58.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(.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))))
✓	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)

series39.0ms (0%)

Counts

4 → 36

Calls

4 calls:

34.0ms	(.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))))
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))

rewrite94.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64`
40×	`add-sqr-sqrt_binary64`
27×	`prod-diff_binary64`
24×	`add-cube-cbrt_binary64`
14×	`add-log-exp_binary64`

Counts

4 → 125

Calls

4 calls:

43.0ms	(.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))))
30.0ms	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2)))
8.0ms	(-.f64 (-.f64 1 z) 1)
2.0ms	(sqrt.f64 (*.f64 (PI.f64) 2))

simplify133.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

397×	`associate-r_binary64`
385×	`fma-neg_binary64`
333×	`associate-l_binary64`
318×	`cancel-sign-sub-inv_binary64`
290×	`times-frac_binary64`

Counts

161 → 202

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	324	3671
1	896	2770
2	3137	2758
3	4901	2758
4	4836	2758

prune3.1s (3.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	1046	6	1052
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	1048	6	1054

Error

0.9b

Counts

1054 → 6

Alt Table

Status	Error	Program
	2.0b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) 2))) (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) 2)))) (cbrt.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)))))
	32.4b	(.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 (fma.f64 (+.f64 1 (sqrt.f64 z)) (-.f64 1 (sqrt.f64 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)))))
	1.9b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (-.f64 (fma.f64 127/225 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (.f64 z z) (.f64 (sqrt.f64 2) (sqrt.f64 15/2))))) (fma.f64 1/2 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (.f64 z (.f64 z (sqrt.f64 15/2))) (pow.f64 (log.f64 15/2) 2))))) (fma.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (sqrt.f64 15/2))) (.f64 14/15 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 z (.f64 (sqrt.f64 2) (sqrt.f64 15/2))))))))) (fma.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (.f64 z (.f64 (sqrt.f64 2) (sqrt.f64 15/2))) (log.f64 15/2))) (.f64 14/15 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (log.f64 15/2) (.f64 (.f64 z z) (.f64 (sqrt.f64 2) (sqrt.f64 15/2))))))))) (+.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	(.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 (fma.f64 (-.f64 2 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 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000))) (/.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)))))
	1.2b	(.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 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 2076511864126339/4000000000000 (.f64 z 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)))))
	2.1b	(.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 (fma.f64 (*.f64 (cbrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1)))) (cbrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))))) (cbrt.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 141720 to 119230 computations (15.9% saved)

localize66.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(.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))))
	1.0b	(sqrt.f64 (*.f64 (PI.f64) 2))
✓	2.4b	(fma.f64 (-.f64 2 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)))
	5.2b	(-.f64 (-.f64 1 z) 1)

series8.0ms (0%)

Counts

1 → 12

Calls

1 calls:

8.0ms

(fma.f64 (-.f64 2 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)))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma.f64 (-.f64 2 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)))

simplify80.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

778×	`fma-def_binary64`
624×	`distribute-rgt-in_binary64`
591×	`distribute-lft-in_binary64`
152×	`associate-*l/_binary64`
152×	`fma-neg_binary64`

Counts

22 → 32

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	686
1	151	587
2	394	550
3	1199	543
4	4811	543
5	4937	543

prune4.5s (5.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	864	3	867
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	868	5	873

Error

0.3b

Counts

873 → 5

Alt Table

Status	Error	Program
	2.0b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) 2))) (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) 2)))) (cbrt.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	(.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 (fma.f64 (-.f64 2 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 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (fma.f64 (*.f64 (cbrt.f64 (-.f64 1 z)) (cbrt.f64 (-.f64 1 z))) (cbrt.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	(.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 (fma.f64 (.f64 (cbrt.f64 (-.f64 1 z)) (cbrt.f64 (-.f64 1 z))) (cbrt.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 (fma.f64 (-.f64 2 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 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000))) (/.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 (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 (expm1.f64 (log1p.f64 (fma.f64 (-.f64 2 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 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000))) (/.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)))))
	2.1b	(.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 (fma.f64 (*.f64 (cbrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1)))) (cbrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))))) (cbrt.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 140045 to 117219 computations (16.3% saved)

localize67.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(sqrt.f64 (*.f64 (PI.f64) 2))
	2.4b	(fma.f64 (-.f64 2 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)))
✓	3.4b	(expm1.f64 (log1p.f64 (fma.f64 (-.f64 2 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)))))
	5.2b	(-.f64 (-.f64 1 z) 1)

series4.0ms (0%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(expm1.f64 (log1p.f64 (fma.f64 (-.f64 2 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)))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 11

Calls

1 calls:

0.0ms

(expm1.f64 (log1p.f64 (fma.f64 (-.f64 2 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)))))

simplify104.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

934×	`fma-neg_binary64`
592×	`fma-def_binary64`
408×	`distribute-rgt-in_binary64`
375×	`distribute-lft-in_binary64`
258×	`associate-l_binary64`

Counts

23 → 34

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	713
1	146	614
2	360	574
3	1012	567
4	3606	567
5	4973	567
6	5295	567

prune4.5s (5.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	849	1	850
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	849	6	855

Error

0.3b

Counts

855 → 6

Alt Table

Status	Error	Program
	1.4b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.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 (expm1.f64 (log1p.f64 (fma.f64 (-.f64 2 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 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000))) (/.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)))))
	2.0b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) 2))) (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) 2)))) (cbrt.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	(.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 (fma.f64 (-.f64 2 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 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (fma.f64 (*.f64 (cbrt.f64 (-.f64 1 z)) (cbrt.f64 (-.f64 1 z))) (cbrt.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	(.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 (fma.f64 (.f64 (cbrt.f64 (-.f64 1 z)) (cbrt.f64 (-.f64 1 z))) (cbrt.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 (fma.f64 (-.f64 2 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 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000))) (/.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 (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 (expm1.f64 (log1p.f64 (fma.f64 (-.f64 2 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 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000))) (/.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)))))
	2.1b	(.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 (fma.f64 (*.f64 (cbrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1)))) (cbrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))))) (cbrt.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 138522 to 116227 computations (16.1% saved)

localize72.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(sqrt.f64 (*.f64 (PI.f64) 2))
	2.4b	(fma.f64 (-.f64 2 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)))
	5.2b	(-.f64 (-.f64 1 z) 1)
✓	5.2b	(fma.f64 (*.f64 (cbrt.f64 (-.f64 1 z)) (cbrt.f64 (-.f64 1 z))) (cbrt.f64 (-.f64 1 z)) -1)

series107.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

107.0ms

(fma.f64 (*.f64 (cbrt.f64 (-.f64 1 z)) (cbrt.f64 (-.f64 1 z))) (cbrt.f64 (-.f64 1 z)) -1)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (*.f64 (cbrt.f64 (-.f64 1 z)) (cbrt.f64 (-.f64 1 z))) (cbrt.f64 (-.f64 1 z)) -1)

simplify62.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

464×	`unswap-sqr_binary64`
454×	`fma-neg_binary64`
349×	`neg-mul-1_binary64`
312×	`cancel-sign-sub-inv_binary64`
260×	`associate-l_binary64`

Counts

22 → 26

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	38	310
1	85	240
2	175	190
3	473	162
4	1925	150
5	4364	147
6	4910	147

prune3.6s (4.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	757	0	757
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	757	6	763

Error

0.3b

Counts

763 → 6

Alt Table

Status	Error	Program
	1.4b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.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 (expm1.f64 (log1p.f64 (fma.f64 (-.f64 2 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 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000))) (/.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)))))
	2.0b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) 2))) (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) 2)))) (cbrt.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	(.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 (fma.f64 (-.f64 2 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 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (fma.f64 (*.f64 (cbrt.f64 (-.f64 1 z)) (cbrt.f64 (-.f64 1 z))) (cbrt.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	(.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 (fma.f64 (.f64 (cbrt.f64 (-.f64 1 z)) (cbrt.f64 (-.f64 1 z))) (cbrt.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 (fma.f64 (-.f64 2 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 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000))) (/.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 (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 (expm1.f64 (log1p.f64 (fma.f64 (-.f64 2 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 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000))) (/.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)))))
	2.1b	(.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 (fma.f64 (*.f64 (cbrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1)))) (cbrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))))) (cbrt.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 128898 to 107584 computations (16.5% saved)

regimes4.2s (5%)

Accuracy

Total 0.4b remaining (56.8%)

Threshold costs 0.4b (56.8%)

Counts

426 → 1

Compiler

Compiled 123356 to 107852 computations (12.6% saved)

simplify45.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

117×	`cancel-sign-sub-inv_binary64`
107×	`distribute-rgt-neg-in_binary64`
69×	`distribute-lft-neg-in_binary64`
61×	`distribute-neg-in_binary64`
60×	`distribute-lft-neg-out_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	73	237
1	112	237
2	127	235
3	140	235
4	150	235
5	162	235
6	169	235
7	174	235
8	186	235
9	194	235
10	207	235
11	222	235
12	240	235
13	268	235
14	302	235
15	350	235
16	408	235
17	466	235
18	522	235
19	568	235
20	608	235
21	637	235
22	655	235
23	664	235
24	666	235
25	646	235

end609.0ms (0.7%)

Compiler: Compiled 1224 to 1074 computations (12.3% saved)

Iter	Nodes	Cost
0	73	237
1	112	237
2	127	235
3	140	235
4	150	235
5	162	235
6	169	235
7	174	235
8	186	235
9	194	235
10	207	235
11	222	235
12	240	235
13	268	235
14	302	235
15	350	235
16	408	235
17	466	235
18	522	235
19	568	235
20	608	235
21	637	235
22	655	235
23	664	235
24	666	235
25	646	235

Iter	Nodes	Cost
0	73	237
1	112	237
2	127	235
3	140	235
4	150	235
5	162	235
6	169	235
7	174	235
8	186	235
9	194	235
10	207	235
11	222	235
12	240	235
13	268	235
14	302	235
15	350	235
16	408	235
17	466	235
18	522	235
19	568	235
20	608	235
21	637	235
22	655	235
23	664	235
24	666	235
25	646	235

Details

analyze2.8s (3.4%)

sample59.7s (71.1%)

simplify51.0ms (0.1%)

prune12.0ms (0%)

localize58.0ms (0.1%)

series39.0ms (0%)

rewrite94.0ms (0.1%)

simplify133.0ms (0.2%)

prune3.1s (3.7%)

localize66.0ms (0.1%)

series8.0ms (0%)

rewrite1.0ms (0%)

simplify80.0ms (0.1%)

prune4.5s (5.3%)

localize67.0ms (0.1%)

series4.0ms (0%)

rewrite1.0ms (0%)

simplify104.0ms (0.1%)

prune4.5s (5.4%)

localize72.0ms (0.1%)

series107.0ms (0.1%)

rewrite1.0ms (0%)

simplify62.0ms (0.1%)

prune3.6s (4.3%)

regimes4.2s (5%)

simplify45.0ms (0.1%)

end609.0ms (0.7%)

Profiling

Iter	Nodes	Cost
0	73	237
1	112	237
2	127	235
3	140	235
4	150	235
5	162	235
6	169	235
7	174	235
8	186	235
9	194	235
10	207	235
11	222	235
12	240	235
13	268	235
14	302	235
15	350	235
16	408	235
17	466	235
18	522	235
19	568	235
20	608	235
21	637	235
22	655	235
23	664	235
24	666	235
25	646	235