Details

analyze2.3s (3.7%)

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)

sample55.5s (89.7%)

Results

51.4s	4007×	body	8192	exit
4.0s	8256×	body	128	valid
38.0ms	80×	body	128	invalid

Compiler

Compiled 378 to 334 computations (11.6% saved)

simplify26.0ms (0%)

Algorithm

1×	egg-herbie

Rules

343×	`associate-+l+_binary64`
293×	`associate-+r+_binary64`
271×	`distribute-rgt-in_binary64`
266×	`distribute-lft-in_binary64`
222×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	156
1	160	147
2	637	119
3	4406	115

Stop Event

1×	node limit

Counts

1 → 2

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

0.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	1.9b	(.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)))))
▶	0.6b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (/.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (-.f64 15/2 z)))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))))))

Status

Error

Program

1.9b

(*.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)))))

▶

0.6b

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

Compiler

Compiled 596 to 508 computations (14.8% saved)

localize48.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))
✓	1.0b	(/.f64 7713234287776531/10000000000000 (-.f64 3 z))
✓	1.0b	(sqrt.f64 (*.f64 (PI.f64) 2))
✓	1.2b	(/.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (-.f64 15/2 z)))

series23.0ms (0%)

Counts

4 → 28

Calls

4 calls:

19.0ms	(/.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (-.f64 15/2 z)))
2.0ms	(+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))
2.0ms	(/.f64 7713234287776531/10000000000000 (-.f64 3 z))
0.0ms	(sqrt.f64 (*.f64 (PI.f64) 2))

rewrite35.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

252×	`add-sqr-sqrt_binary64`
248×	`log1p-expm1-u_binary64`
248×	`expm1-log1p-u_binary64`
243×	`add-cbrt-cube_binary64`
242×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	48
1	520	48

Stop Event

1×	node limit

Counts

4 → 82

Calls

4 calls:

33.0ms	(+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))
33.0ms	(/.f64 7713234287776531/10000000000000 (-.f64 3 z))
33.0ms	(sqrt.f64 (*.f64 (PI.f64) 2))
33.0ms	(/.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (-.f64 15/2 z)))

simplify29.0ms (0%)

Algorithm

1×	egg-herbie

Rules

378×	`associate-r_binary64`
369×	`fma-def_binary64`
334×	`associate-+l+_binary64`
269×	`associate-l_binary64`
217×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	737
1	387	707
2	1216	701

Stop Event

1×	node limit

Counts

110 → 117

prune321.0ms (0.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	113	4	117
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	113	6	119

Error

0.3b

Counts

119 → 6

Alt Table

Status	Error	Program
	1.9b	(.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)))))
	3.0b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) 2))) 3) (/.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (-.f64 15/2 z)))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))))))
	1.5b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (exp.f64 (-.f64 (.f64 (-.f64 1/2 z) (log.f64 (-.f64 15/2 z))) (-.f64 15/2 z)))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))))))
▶	0.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 (log.f64 15/2) 2) (.f64 (pow.f64 z 2) (sqrt.f64 15/2))) (exp.f64 15/2))) (+.f64 (.f64 892/3375 (/.f64 (.f64 (pow.f64 z 3) (sqrt.f64 15/2)) (exp.f64 15/2))) (+.f64 (.f64 14/15 (/.f64 (.f64 z (sqrt.f64 15/2)) (exp.f64 15/2))) (+.f64 (.f64 127/225 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 15/2)) (exp.f64 15/2))) (+.f64 (.f64 7/15 (/.f64 (.f64 (pow.f64 (log.f64 15/2) 2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2))) (exp.f64 15/2))) (/.f64 (sqrt.f64 15/2) (exp.f64 15/2))))))) (+.f64 (.f64 14/15 (/.f64 (.f64 (log.f64 15/2) (.f64 (pow.f64 z 2) (sqrt.f64 15/2))) (exp.f64 15/2))) (+.f64 (.f64 1/6 (/.f64 (.f64 (pow.f64 (log.f64 15/2) 3) (.f64 (pow.f64 z 3) (sqrt.f64 15/2))) (exp.f64 15/2))) (+.f64 (.f64 127/225 (/.f64 (.f64 (log.f64 15/2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2))) (exp.f64 15/2))) (/.f64 (.f64 (log.f64 15/2) (.f64 z (sqrt.f64 15/2))) (exp.f64 15/2))))))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))))))
	1.2b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (/.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (-.f64 15/2 z)))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (fma.f64 7713234287776531/10000000000000 (/.f64 1 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))))))
✓	0.6b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (/.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (-.f64 15/2 z)))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))))))

Compiler

Compiled 10679 to 8333 computations (22% saved)

localize97.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(/.f64 (sqrt.f64 15/2) (exp.f64 15/2))
	1.0b	(sqrt.f64 (*.f64 (PI.f64) 2))
✓	1.0b	(pow.f64 (log.f64 15/2) 3)
✓	1.0b	(pow.f64 (log.f64 15/2) 2)

series0.0ms (0%)

Counts

3 → 0

Calls

3 calls:

0.0ms	(pow.f64 (log.f64 15/2) 2)
0.0ms	(/.f64 (sqrt.f64 15/2) (exp.f64 15/2))
0.0ms	(pow.f64 (log.f64 15/2) 3)

rewrite42.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

775×	`log1p-expm1-u_binary64`
775×	`expm1-log1p-u_binary64`
151×	`log1p-udef_binary64`
90×	`add-sqr-sqrt_binary64`
88×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	212	20
2	2238	20

Stop Event

1×	node limit

Counts

3 → 72

Calls

3 calls:

41.0ms	(/.f64 (sqrt.f64 15/2) (exp.f64 15/2))
41.0ms	(pow.f64 (log.f64 15/2) 3)
41.0ms	(pow.f64 (log.f64 15/2) 2)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

72 → 72

prune717.0ms (1.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	109	8	117

Error

0.3b

Counts

117 → 8

Alt Table

Status	Error	Program
	3.0b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) 2))) 3) (/.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (-.f64 15/2 z)))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.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 (sqrt.f64 (.f64 (PI.f64) 2)) (-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 (log.f64 15/2) 2) (.f64 (pow.f64 z 2) (sqrt.f64 15/2))) (exp.f64 15/2))) (+.f64 (.f64 892/3375 (/.f64 (.f64 (pow.f64 z 3) (sqrt.f64 15/2)) (exp.f64 15/2))) (+.f64 (.f64 14/15 (/.f64 (.f64 z (sqrt.f64 15/2)) (exp.f64 15/2))) (+.f64 (.f64 127/225 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 15/2)) (exp.f64 15/2))) (+.f64 (.f64 7/15 (/.f64 (.f64 (pow.f64 (log.f64 15/2) 2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2))) (exp.f64 15/2))) (exp.f64 (-.f64 (log.f64 (sqrt.f64 15/2)) 15/2))))))) (+.f64 (.f64 14/15 (/.f64 (.f64 (log.f64 15/2) (.f64 (pow.f64 z 2) (sqrt.f64 15/2))) (exp.f64 15/2))) (+.f64 (.f64 1/6 (/.f64 (.f64 (pow.f64 (log.f64 15/2) 3) (.f64 (pow.f64 z 3) (sqrt.f64 15/2))) (exp.f64 15/2))) (+.f64 (.f64 127/225 (/.f64 (.f64 (log.f64 15/2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2))) (exp.f64 15/2))) (/.f64 (.f64 (log.f64 15/2) (.f64 z (sqrt.f64 15/2))) (exp.f64 15/2))))))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))))))
	1.9b	(.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)))))
	1.5b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (exp.f64 (-.f64 (.f64 (-.f64 1/2 z) (log.f64 (-.f64 15/2 z))) (-.f64 15/2 z)))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))))))
	1.3b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 (log.f64 15/2) 2) (.f64 (pow.f64 z 2) (sqrt.f64 15/2))) (exp.f64 15/2))) (+.f64 (.f64 892/3375 (/.f64 (.f64 (pow.f64 z 3) (sqrt.f64 15/2)) (exp.f64 15/2))) (+.f64 (.f64 14/15 (/.f64 (.f64 z (sqrt.f64 15/2)) (exp.f64 15/2))) (+.f64 (.f64 127/225 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 15/2)) (exp.f64 15/2))) (+.f64 (.f64 7/15 (/.f64 (.f64 (pow.f64 (log.f64 15/2) 2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2))) (exp.f64 15/2))) (.f64 (/.f64 1 (sqrt.f64 (exp.f64 15/2))) (/.f64 (sqrt.f64 15/2) (sqrt.f64 (exp.f64 15/2))))))))) (+.f64 (.f64 14/15 (/.f64 (.f64 (log.f64 15/2) (.f64 (pow.f64 z 2) (sqrt.f64 15/2))) (exp.f64 15/2))) (+.f64 (.f64 1/6 (/.f64 (.f64 (pow.f64 (log.f64 15/2) 3) (.f64 (pow.f64 z 3) (sqrt.f64 15/2))) (exp.f64 15/2))) (+.f64 (.f64 127/225 (/.f64 (.f64 (log.f64 15/2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2))) (exp.f64 15/2))) (/.f64 (.f64 (log.f64 15/2) (*.f64 z (sqrt.f64 15/2))) (exp.f64 15/2))))))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))))))
✓	0.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 (log.f64 15/2) 2) (.f64 (pow.f64 z 2) (sqrt.f64 15/2))) (exp.f64 15/2))) (+.f64 (.f64 892/3375 (/.f64 (.f64 (pow.f64 z 3) (sqrt.f64 15/2)) (exp.f64 15/2))) (+.f64 (.f64 14/15 (/.f64 (.f64 z (sqrt.f64 15/2)) (exp.f64 15/2))) (+.f64 (.f64 127/225 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 15/2)) (exp.f64 15/2))) (+.f64 (.f64 7/15 (/.f64 (.f64 (pow.f64 (log.f64 15/2) 2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2))) (exp.f64 15/2))) (/.f64 (sqrt.f64 15/2) (exp.f64 15/2))))))) (+.f64 (.f64 14/15 (/.f64 (.f64 (log.f64 15/2) (.f64 (pow.f64 z 2) (sqrt.f64 15/2))) (exp.f64 15/2))) (+.f64 (.f64 1/6 (/.f64 (.f64 (pow.f64 (log.f64 15/2) 3) (.f64 (pow.f64 z 3) (sqrt.f64 15/2))) (exp.f64 15/2))) (+.f64 (.f64 127/225 (/.f64 (.f64 (log.f64 15/2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2))) (exp.f64 15/2))) (/.f64 (.f64 (log.f64 15/2) (.f64 z (sqrt.f64 15/2))) (exp.f64 15/2))))))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))))))
▶	1.2b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (/.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (-.f64 15/2 z)))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (fma.f64 7713234287776531/10000000000000 (/.f64 1 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))))))
✓	0.6b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (/.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (-.f64 15/2 z)))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))))))

Compiler

Compiled 23627 to 20737 computations (12.2% saved)

localize49.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (/.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (-.f64 15/2 z)))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (fma.f64 7713234287776531/10000000000000 (/.f64 1 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))))))
✓	1.0b	(.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (/.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (-.f64 15/2 z)))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (fma.f64 7713234287776531/10000000000000 (/.f64 1 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z))))))))
	1.0b	(sqrt.f64 (*.f64 (PI.f64) 2))
	1.2b	(/.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (-.f64 15/2 z)))

series89.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

47.0ms

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

42.0ms

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

rewrite50.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

695×	`log1p-expm1-u_binary64`
695×	`expm1-log1p-u_binary64`
99×	`expm1-udef_binary64`
99×	`log1p-udef_binary64`
89×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	219
1	1446	219

Stop Event

1×	node limit

Counts

2 → 21

Calls

2 calls:

49.0ms

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

49.0ms

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

simplify65.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

374×	`cancel-sign-sub-inv_binary64`
276×	`associate-r_binary64`
261×	`fma-def_binary64`
209×	`*-commutative_binary64`
189×	`associate-*r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	227	3151
1	793	3080
2	3390	2711

Stop Event

1×	node limit

Counts

45 → 52

prune238.0ms (0.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	3	2	5
Picked	1	0	1
Done	1	1	2
Total	97	9	106

Error

0.1b

Counts

106 → 9

Alt Table

Status	Error	Program
	1.2b	(-.f64 (fma.f64 1106209385320415913103082059/25200000000000000000000000 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 (PI.f64) 5/2)) (/.f64 (exp.f64 15/2) (.f64 (sqrt.f64 15/2) z))) (+.f64 (.f64 (sqrt.f64 (PI.f64)) (+.f64 (.f64 1106209385320415913103082059/8400000000000000000000000 (/.f64 (.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 15/2) z)) (pow.f64 (log.f64 15/2) 2)) (exp.f64 15/2))) (.f64 2408637854869972117504576098451/3528000000000000000000000000 (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 15/2)) (exp.f64 15/2))))) (.f64 (sqrt.f64 (PI.f64)) (+.f64 (.f64 3264229102083425005530891465931403/2963520000000000000000000000000 (.f64 (/.f64 (sqrt.f64 2) (exp.f64 15/2)) (.f64 (sqrt.f64 15/2) z))) (.f64 1106209385320415913103082059/4200000000000000000000000 (/.f64 (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 15/2)) z) (exp.f64 15/2))))))) (+.f64 (.f64 1106209385320415913103082059/4200000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (/.f64 (.f64 (.f64 (sqrt.f64 2) (sqrt.f64 15/2)) (log.f64 15/2)) (exp.f64 15/2)))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (/.f64 (sqrt.f64 2) (exp.f64 15/2)) (.f64 (sqrt.f64 15/2) (.f64 z (log.f64 15/2))))) 2408637854869972117504576098451/3528000000000000000000000000)))
✓	0.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 (log.f64 15/2) 2) (.f64 (pow.f64 z 2) (sqrt.f64 15/2))) (exp.f64 15/2))) (+.f64 (.f64 892/3375 (/.f64 (.f64 (pow.f64 z 3) (sqrt.f64 15/2)) (exp.f64 15/2))) (+.f64 (.f64 14/15 (/.f64 (.f64 z (sqrt.f64 15/2)) (exp.f64 15/2))) (+.f64 (.f64 127/225 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 15/2)) (exp.f64 15/2))) (+.f64 (.f64 7/15 (/.f64 (.f64 (pow.f64 (log.f64 15/2) 2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2))) (exp.f64 15/2))) (/.f64 (sqrt.f64 15/2) (exp.f64 15/2))))))) (+.f64 (.f64 14/15 (/.f64 (.f64 (log.f64 15/2) (.f64 (pow.f64 z 2) (sqrt.f64 15/2))) (exp.f64 15/2))) (+.f64 (.f64 1/6 (/.f64 (.f64 (pow.f64 (log.f64 15/2) 3) (.f64 (pow.f64 z 3) (sqrt.f64 15/2))) (exp.f64 15/2))) (+.f64 (.f64 127/225 (/.f64 (.f64 (log.f64 15/2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2))) (exp.f64 15/2))) (/.f64 (.f64 (log.f64 15/2) (.f64 z (sqrt.f64 15/2))) (exp.f64 15/2))))))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))))))
▶	1.0b	(pow.f64 (.f64 (.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (/.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (-.f64 15/2 z))))) (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (fma.f64 7713234287776531/10000000000000 (/.f64 1 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z))))))) 1)
	1.5b	(-.f64 (+.f64 (.f64 1106209385320415913103082059/4200000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 15/2)) (.f64 (exp.f64 15/2) z)))) (.f64 2408637854869972117504576098451/3528000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 15/2)) (exp.f64 15/2))))) (.f64 1106209385320415913103082059/4200000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (/.f64 (.f64 (sqrt.f64 2) (*.f64 (log.f64 15/2) (sqrt.f64 15/2))) (exp.f64 15/2)))))
	1.9b	(.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)))))
	1.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (pow.f64 (/.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (-.f64 15/2 z))) 3) 1/3)) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (fma.f64 7713234287776531/10000000000000 (/.f64 1 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))))))
	1.5b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (exp.f64 (-.f64 (.f64 (-.f64 1/2 z) (log.f64 (-.f64 15/2 z))) (-.f64 15/2 z)))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))))))
	44.0b	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (/.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (-.f64 15/2 z))))) (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (fma.f64 7713234287776531/10000000000000 (/.f64 1 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z))))))) (.f64 (.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (/.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (-.f64 15/2 z))))) (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (fma.f64 7713234287776531/10000000000000 (/.f64 1 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))))) (.f64 (.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (/.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (-.f64 15/2 z))))) (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (fma.f64 7713234287776531/10000000000000 (/.f64 1 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))))))
	1.4b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (+.f64 (.f64 (sqrt.f64 (PI.f64)) (+.f64 (.f64 2408637854869972117504576098451/3528000000000000000000000000 (.f64 (/.f64 (sqrt.f64 2) (exp.f64 15/2)) (.f64 (sqrt.f64 15/2) z))) (.f64 3264229102083425005530891465931403/2963520000000000000000000000000 (/.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 15/2) (.f64 z z))) (exp.f64 15/2))))) (-.f64 (.f64 (sqrt.f64 (PI.f64)) (+.f64 (.f64 1106209385320415913103082059/4200000000000000000000000 (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 15/2)) (exp.f64 15/2))) (.f64 1106209385320415913103082059/8400000000000000000000000 (.f64 (/.f64 (sqrt.f64 2) (exp.f64 15/2)) (.f64 (sqrt.f64 15/2) (.f64 (.f64 z z) (pow.f64 (log.f64 15/2) 2))))))) (fma.f64 1106209385320415913103082059/4200000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (/.f64 (sqrt.f64 2) (exp.f64 15/2)) (.f64 (sqrt.f64 15/2) (.f64 z (log.f64 15/2))))) (.f64 (/.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (log.f64 15/2) (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 15/2) (.f64 z z))))) (exp.f64 15/2)) 2408637854869972117504576098451/3528000000000000000000000000)))))

Compiler

Compiled 10585 to 8356 computations (21.1% saved)

localize52.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (fma.f64 7713234287776531/10000000000000 (/.f64 1 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z))))))
✓	1.0b	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (fma.f64 7713234287776531/10000000000000 (/.f64 1 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))))
	1.0b	(sqrt.f64 (*.f64 (PI.f64) 2))
	1.2b	(/.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (-.f64 15/2 z)))

series6.0ms (0%)

Counts

2 → 24

Calls

2 calls:

3.0ms

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

3.0ms

(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (fma.f64 7713234287776531/10000000000000 (/.f64 1 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))))

rewrite49.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

522×	`log1p-expm1-u_binary64`
522×	`expm1-log1p-u_binary64`
456×	`pow1_binary64`
109×	`unpow-prod-down_binary64`
93×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	112
1	1078	112

Stop Event

1×	node limit

Counts

2 → 53

Calls

2 calls:

48.0ms

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

47.0ms

(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (fma.f64 7713234287776531/10000000000000 (/.f64 1 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))))

simplify34.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

612×	`associate-/r*_binary64`
562×	`fma-def_binary64`
388×	`times-frac_binary64`
308×	`associate-/l/_binary64`
233×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	282
1	161	278
2	392	272
3	1064	258
4	2764	258

Stop Event

1×	node limit

Counts

77 → 80

prune295.0ms (0.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	122	4	126
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	126	9	135

Error

0.0b

Counts

135 → 9

Alt Table

Status	Error	Program
	1.0b	(pow.f64 (.f64 (.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (-.f64 15/2 z))) 2)) (cbrt.f64 (/.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (-.f64 15/2 z))))))) (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (fma.f64 7713234287776531/10000000000000 (/.f64 1 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z))))))) 1)
	1.1b	(pow.f64 (.f64 (.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (/.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (-.f64 15/2 z))))) (fma.f64 z 102757979785251069442117317613/235200000000000000000000000 (fma.f64 z (.f64 z (fma.f64 z 4027292589444183035165374538123333/6638284800000000000000000000000 64608921419941589693928044520019/118540800000000000000000000000)) 1106209385320415913103082059/4200000000000000000000000))) 1)
	1.9b	(.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)))))
	0.9b	(pow.f64 (.f64 (.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 2)) (/.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (-.f64 15/2 z))))) (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (fma.f64 7713234287776531/10000000000000 (/.f64 1 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z))))))) 1)
	1.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (pow.f64 (/.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (-.f64 15/2 z))) 3) 1/3)) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (fma.f64 7713234287776531/10000000000000 (/.f64 1 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))))))
	1.5b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (exp.f64 (-.f64 (.f64 (-.f64 1/2 z) (log.f64 (-.f64 15/2 z))) (-.f64 15/2 z)))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))))))
	0.4b	(pow.f64 (.f64 (.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (exp.f64 (-.f64 (.f64 (-.f64 1/2 z) (log.f64 (-.f64 15/2 z))) (-.f64 15/2 z))))) (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (fma.f64 7713234287776531/10000000000000 (/.f64 1 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z))))))) 1)
✓	0.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 (log.f64 15/2) 2) (.f64 (pow.f64 z 2) (sqrt.f64 15/2))) (exp.f64 15/2))) (+.f64 (.f64 892/3375 (/.f64 (.f64 (pow.f64 z 3) (sqrt.f64 15/2)) (exp.f64 15/2))) (+.f64 (.f64 14/15 (/.f64 (.f64 z (sqrt.f64 15/2)) (exp.f64 15/2))) (+.f64 (.f64 127/225 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 15/2)) (exp.f64 15/2))) (+.f64 (.f64 7/15 (/.f64 (.f64 (pow.f64 (log.f64 15/2) 2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2))) (exp.f64 15/2))) (/.f64 (sqrt.f64 15/2) (exp.f64 15/2))))))) (+.f64 (.f64 14/15 (/.f64 (.f64 (log.f64 15/2) (.f64 (pow.f64 z 2) (sqrt.f64 15/2))) (exp.f64 15/2))) (+.f64 (.f64 1/6 (/.f64 (.f64 (pow.f64 (log.f64 15/2) 3) (.f64 (pow.f64 z 3) (sqrt.f64 15/2))) (exp.f64 15/2))) (+.f64 (.f64 127/225 (/.f64 (.f64 (log.f64 15/2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2))) (exp.f64 15/2))) (/.f64 (.f64 (log.f64 15/2) (.f64 z (sqrt.f64 15/2))) (exp.f64 15/2))))))) (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 3 z)) (/.f64 -883075145810703/5000000000000 (-.f64 4 z)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 5 z)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))))))
	1.4b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (+.f64 (.f64 (sqrt.f64 (PI.f64)) (+.f64 (.f64 2408637854869972117504576098451/3528000000000000000000000000 (.f64 (/.f64 (sqrt.f64 2) (exp.f64 15/2)) (.f64 (sqrt.f64 15/2) z))) (.f64 3264229102083425005530891465931403/2963520000000000000000000000000 (/.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 15/2) (.f64 z z))) (exp.f64 15/2))))) (-.f64 (.f64 (sqrt.f64 (PI.f64)) (+.f64 (.f64 1106209385320415913103082059/4200000000000000000000000 (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 15/2)) (exp.f64 15/2))) (.f64 1106209385320415913103082059/8400000000000000000000000 (.f64 (/.f64 (sqrt.f64 2) (exp.f64 15/2)) (.f64 (sqrt.f64 15/2) (.f64 (.f64 z z) (pow.f64 (log.f64 15/2) 2))))))) (fma.f64 1106209385320415913103082059/4200000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (/.f64 (sqrt.f64 2) (exp.f64 15/2)) (.f64 (sqrt.f64 15/2) (.f64 z (log.f64 15/2))))) (.f64 (/.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (log.f64 15/2) (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 15/2) (.f64 z z))))) (exp.f64 15/2)) 2408637854869972117504576098451/3528000000000000000000000000)))))

Compiler

Compiled 11053 to 8644 computations (21.8% saved)

regimes1.1s (1.8%)

Accuracy

Total 0.4b remaining (88.1%)

Threshold costs 0.4b (88.1%)

Counts

192 → 1

Compiler

Compiled 33408 to 27822 computations (16.7% saved)

simplify24.0ms (0%)

Algorithm

1×	egg-herbie

Rules

132×	`cancel-sign-sub-inv_binary64`
93×	`distribute-rgt-neg-in_binary64`
61×	`distribute-lft-neg-out_binary64`
60×	`sub-neg_binary64`
59×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	118
1	89	118
2	109	118
3	120	118
4	147	118
5	169	118
6	183	118
7	197	118
8	216	118
9	236	118
10	267	118
11	313	118
12	365	118
13	420	118
14	505	118
15	608	118
16	715	118
17	806	118
18	853	118
19	863	118

Stop Event

1×

saturated

end641.0ms (1%)

Compiler: Compiled 1032 to 868 computations (15.9% saved)

Iter	Nodes	Cost
0	61	118
1	89	118
2	109	118
3	120	118
4	147	118
5	169	118
6	183	118
7	197	118
8	216	118
9	236	118
10	267	118
11	313	118
12	365	118
13	420	118
14	505	118
15	608	118
16	715	118
17	806	118
18	853	118
19	863	118

Iter	Nodes	Cost
0	61	118
1	89	118
2	109	118
3	120	118
4	147	118
5	169	118
6	183	118
7	197	118
8	216	118
9	236	118
10	267	118
11	313	118
12	365	118
13	420	118
14	505	118
15	608	118
16	715	118
17	806	118
18	853	118
19	863	118

Details

analyze2.3s (3.7%)

sample55.5s (89.7%)

simplify26.0ms (0%)

prune12.0ms (0%)

localize48.0ms (0.1%)

series23.0ms (0%)

rewrite35.0ms (0.1%)

simplify29.0ms (0%)

prune321.0ms (0.5%)

localize97.0ms (0.2%)

series0.0ms (0%)

rewrite42.0ms (0.1%)

simplify7.0ms (0%)

prune717.0ms (1.2%)

localize49.0ms (0.1%)

series89.0ms (0.1%)

rewrite50.0ms (0.1%)

simplify65.0ms (0.1%)

prune238.0ms (0.4%)

localize52.0ms (0.1%)

series6.0ms (0%)

rewrite49.0ms (0.1%)

simplify34.0ms (0.1%)

prune295.0ms (0.5%)

regimes1.1s (1.8%)

simplify24.0ms (0%)

end641.0ms (1%)

Profiling

Iter	Nodes	Cost
0	61	118
1	89	118
2	109	118
3	120	118
4	147	118
5	169	118
6	183	118
7	197	118
8	216	118
9	236	118
10	267	118
11	313	118
12	365	118
13	420	118
14	505	118
15	608	118
16	715	118
17	806	118
18	853	118
19	863	118