Details

analyze3.0s (4.6%)

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)

sample57.2s (86.5%)

Results

52.8s	3916×	body	8192	exit
4.3s	8256×	body	128	valid
54.0ms	105×	body	128	invalid

Compiler

Compiled 378 to 334 computations (11.6% saved)

simplify47.0ms (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 (+.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 (.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)))))

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 (+.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 (*.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)))))

Compiler

Compiled 596 to 508 computations (14.8% saved)

localize47.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(+.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)))
✓	1.0b	(.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
✓	1.0b	(sqrt.f64 (*.f64 (PI.f64) 2))
✓	2.8b	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))

series31.0ms (0%)

Counts

4 → 36

Calls

4 calls:

26.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
3.0ms	(+.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)))
2.0ms	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))
0.0ms	(sqrt.f64 (*.f64 (PI.f64) 2))

rewrite50.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

411×	`log1p-expm1-u_binary64`
411×	`expm1-log1p-u_binary64`
402×	`add-log-exp_binary64`
400×	`add-exp-log_binary64`
370×	`pow1_binary64`

Counts

4 → 84

Calls

4 calls:

48.0ms	(+.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)))
48.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
48.0ms	(sqrt.f64 (*.f64 (PI.f64) 2))
48.0ms	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	90
1	862	90
2	5023	90
0	0	0
1	0	0

simplify63.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

618×	`*-commutative_binary64`
498×	`distribute-rgt-neg-in_binary64`
398×	`associate-+l+_binary64`
338×	`sub-neg_binary64`
274×	`associate-r_binary64`

Counts

120 → 120

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	156	1112
1	463	1108
2	1559	997
3	4023	997
4	5009	997

prune489.0ms (0.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	114	6	120
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	116	6	122

Error

0.3b

Counts

122 → 6

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 (fma.f64 (pow.f64 (cbrt.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z)))) 2) (cbrt.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)))))
	1.4b	(.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 7827144361880981797/30000000000000000 (.f64 z (+.f64 314207804027640689/720000000000000 (.f64 z 4708246094784852251/8640000000000000)))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))) (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z))) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))
▶	0.5b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (pow.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) 3) 1/3) (+.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)))))
	2.0b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (+.f64 (+.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (exp.f64 -15/2)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 15/2)) (.f64 14/15 (.f64 z (.f64 (sqrt.f64 2) (sqrt.f64 15/2)))))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (exp.f64 -15/2)) (+.f64 (.f64 127/225 (.f64 (.f64 z z) (.f64 (sqrt.f64 2) (sqrt.f64 15/2)))) (.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 z (.f64 z (sqrt.f64 15/2))) (pow.f64 (log.f64 15/2) 2))))))) (+.f64 (.f64 (.f64 (pow.f64 z 3) (.f64 (sqrt.f64 2) (sqrt.f64 15/2))) (+.f64 (.f64 (.f64 (exp.f64 -15/2) (pow.f64 (log.f64 15/2) 2)) (.f64 (sqrt.f64 (PI.f64)) 7/15)) (.f64 892/3375 (.f64 (sqrt.f64 (PI.f64)) (exp.f64 -15/2))))) (-.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (log.f64 15/2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2)))))) -127/225) (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 (.f64 (sqrt.f64 (PI.f64)) (exp.f64 -15/2)) (+.f64 (.f64 14/15 (.f64 (log.f64 15/2) (.f64 (.f64 z z) (.f64 (sqrt.f64 2) (sqrt.f64 15/2))))) (.f64 1/6 (.f64 (sqrt.f64 2) (.f64 (*.f64 (pow.f64 z 3) (sqrt.f64 15/2)) (pow.f64 (log.f64 15/2) 3)))))))))) (+.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)))))
	2.0b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (PI.f64)))) 3) (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)))))
	1.0b	(.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 (fma.f64 (sqrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (sqrt.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)))))

Compiler

Compiled 10980 to 8499 computations (22.6% saved)

localize53.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(pow.f64 (.f64 (.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) 3)
✓	1.0b	(sqrt.f64 (*.f64 2 (PI.f64)))
✓	2.0b	(pow.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) 3) 1/3)
	2.8b	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))

series941.0ms (1.4%)

Counts

3 → 24

Calls

3 calls:

846.0ms

(pow.f64 (pow.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) 3) 1/3)

95.0ms

(pow.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) 3)

0.0ms

(sqrt.f64 (*.f64 2 (PI.f64)))

rewrite79.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

200×	`add-sqr-sqrt_binary64`
199×	`log1p-expm1-u_binary64`
199×	`expm1-log1p-u_binary64`
190×	`add-log-exp_binary64`
189×	`add-cbrt-cube_binary64`

Counts

3 → 91

Calls

3 calls:

76.0ms

(pow.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) 3)

76.0ms

(sqrt.f64 (*.f64 2 (PI.f64)))

76.0ms

(pow.f64 (pow.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) 3) 1/3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	64
1	431	64
2	4888	64
3	4962	64
0	0	0
1	0	0

simplify88.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

768×	`associate-r_binary64`
603×	`associate-l_binary64`
453×	`cancel-sign-sub-inv_binary64`
337×	`unswap-sqr_binary64`
325×	`*-commutative_binary64`

Counts

115 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	239	2806
1	823	2751
2	3817	2554
3	5312	2554

prune396.0ms (0.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	147	7	154

Error

0.3b

Counts

154 → 7

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 (fma.f64 (pow.f64 (cbrt.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z)))) 2) (cbrt.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)))))
	1.4b	(.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 7827144361880981797/30000000000000000 (.f64 z (+.f64 314207804027640689/720000000000000 (.f64 z 4708246094784852251/8640000000000000)))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))) (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z))) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))
	1.0b	(.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 (fma.f64 (sqrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (sqrt.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)))))
▶	0.5b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3/2) (pow.f64 (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (+.f64 z -15/2))) 3)) 1/3) (+.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)))))
	1.2b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (pow.f64 (-.f64 (+.f64 (.f64 14/5 (.f64 (sqrt.f64 (pow.f64 (PI.f64) 3)) (.f64 (pow.f64 (exp.f64 -15/2) 3) (.f64 (pow.f64 (sqrt.f64 2) 3) (.f64 z (pow.f64 (sqrt.f64 15/2) 3)))))) (.f64 (.f64 (pow.f64 (exp.f64 -15/2) 3) (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 (sqrt.f64 15/2) 3))) (sqrt.f64 (pow.f64 (PI.f64) 3)))) (.f64 3 (.f64 (sqrt.f64 (pow.f64 (PI.f64) 3)) (.f64 (pow.f64 (exp.f64 -15/2) 3) (.f64 (pow.f64 (sqrt.f64 2) 3) (.f64 (log.f64 15/2) (*.f64 z (pow.f64 (sqrt.f64 15/2) 3)))))))) 1/3) (+.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)))))
	2.1b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (pow.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) 3) 1/3) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 904338909853211/2500000000000 z 479507597606835099/10000000000000000) (/.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)))))
	2.0b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (PI.f64)))) 3) (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)))))

Compiler

Compiled 15861 to 12631 computations (20.4% saved)

localize54.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(*.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (+.f64 z -15/2)))
✓	1.0b	(pow.f64 (*.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (+.f64 z -15/2))) 3)
✓	2.0b	(pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3/2) (pow.f64 (*.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (+.f64 z -15/2))) 3)) 1/3)
	2.8b	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))

series1.3s (2%)

Counts

3 → 36

Calls

3 calls:

1.2s

(pow.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) 3/2) (pow.f64 (*.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (+.f64 z -15/2))) 3)) 1/3)

36.0ms

(pow.f64 (*.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (+.f64 z -15/2))) 3)

10.0ms

(*.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (+.f64 z -15/2)))

rewrite68.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

377×	`log1p-udef_binary64`
220×	`add-sqr-sqrt_binary64`
220×	`log1p-expm1-u_binary64`
220×	`expm1-log1p-u_binary64`
211×	`add-cbrt-cube_binary64`

Counts

3 → 48

Calls

3 calls:

67.0ms

(*.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (+.f64 z -15/2)))

67.0ms

(pow.f64 (*.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (+.f64 z -15/2))) 3)

67.0ms

(pow.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) 3/2) (pow.f64 (*.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (+.f64 z -15/2))) 3)) 1/3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	72
1	475	66
2	4650	66
3	5139	66
0	0	0
1	0	0

simplify83.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

634×	`associate-l_binary64`
426×	`cancel-sign-sub-inv_binary64`
421×	`*-commutative_binary64`
410×	`fma-def_binary64`
267×	`associate-+r+_binary64`

Counts

84 → 77

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	367	3269
1	1118	3261
2	3681	3201
3	5054	3201

prune383.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	116	6	122

Error

0.3b

Counts

122 → 6

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 (fma.f64 (pow.f64 (cbrt.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z)))) 2) (cbrt.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)))))
	1.4b	(.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 7827144361880981797/30000000000000000 (.f64 z (+.f64 314207804027640689/720000000000000 (.f64 z 4708246094784852251/8640000000000000)))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))) (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z))) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))
▶	1.0b	(.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 (fma.f64 (sqrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (sqrt.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)))))
✓	0.5b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3/2) (pow.f64 (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (+.f64 z -15/2))) 3)) 1/3) (+.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)))))
	1.2b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (pow.f64 (-.f64 (+.f64 (.f64 14/5 (.f64 (sqrt.f64 (pow.f64 (PI.f64) 3)) (.f64 (pow.f64 (exp.f64 -15/2) 3) (.f64 (pow.f64 (sqrt.f64 2) 3) (.f64 z (pow.f64 (sqrt.f64 15/2) 3)))))) (.f64 (.f64 (pow.f64 (exp.f64 -15/2) 3) (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 (sqrt.f64 15/2) 3))) (sqrt.f64 (pow.f64 (PI.f64) 3)))) (.f64 3 (.f64 (sqrt.f64 (pow.f64 (PI.f64) 3)) (.f64 (pow.f64 (exp.f64 -15/2) 3) (.f64 (pow.f64 (sqrt.f64 2) 3) (.f64 (log.f64 15/2) (*.f64 z (pow.f64 (sqrt.f64 15/2) 3)))))))) 1/3) (+.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)))))
	2.1b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3/2) (pow.f64 (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (+.f64 z -15/2))) 3)) 1/3) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 904338909853211/2500000000000 z 479507597606835099/10000000000000000) (/.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)))))

Compiler

Compiled 13365 to 10765 computations (19.5% saved)

localize50.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(+.f64 (+.f64 (fma.f64 (sqrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (sqrt.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)))
	1.0b	(.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
	1.0b	(sqrt.f64 (*.f64 (PI.f64) 2))
✓	2.3b	(fma.f64 (sqrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (sqrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))

series21.0ms (0%)

Counts

2 → 24

Calls

2 calls:

11.0ms

(fma.f64 (sqrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (sqrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))

10.0ms

(+.f64 (+.f64 (fma.f64 (sqrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (sqrt.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)))

rewrite76.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

273×	`log1p-expm1-u_binary64`
273×	`expm1-log1p-u_binary64`
267×	`add-log-exp_binary64`
266×	`add-exp-log_binary64`
264×	`add-cbrt-cube_binary64`

Counts

2 → 43

Calls

2 calls:

75.0ms

(+.f64 (+.f64 (fma.f64 (sqrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (sqrt.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)))

75.0ms

(fma.f64 (sqrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (sqrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	56
1	574	56
2	4921	56
3	4710	56
0	0	0
1	0	0

simplify54.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

955×	`fma-def_binary64`
665×	`fma-neg_binary64`
429×	`associate-/r*_binary64`
289×	`associate-/l/_binary64`
235×	`associate-+l+_binary64`

Counts

67 → 73

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	72	426
1	198	282
2	472	274
3	1130	258
4	2412	256
5	4835	252
6	4984	252

prune281.0ms (0.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	115	6	121

Error

0.3b

Counts

121 → 6

Alt Table

Status	Error	Program
	1.6b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 2 (PI.f64))) 2) 1/2) (pow.f64 (cbrt.f64 (.f64 2 (PI.f64))) 1/2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 (sqrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (sqrt.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)))))
	1.4b	(.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 (fma.f64 z (fma.f64 z 4708246094784852251/8640000000000000 314207804027640689/720000000000000) 7827144361880981797/30000000000000000) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))) (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z))) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))
✓	1.0b	(.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 (fma.f64 (sqrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (sqrt.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)))))
✓	0.5b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3/2) (pow.f64 (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (+.f64 z -15/2))) 3)) 1/3) (+.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)))))
	2.1b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3/2) (pow.f64 (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (exp.f64 (+.f64 z -15/2))) 3)) 1/3) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 904338909853211/2500000000000 z 479507597606835099/10000000000000000) (/.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)))))
	2.1b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (exp.f64 (+.f64 (+.f64 z -15/2) (log.f64 (.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)))))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 (sqrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (sqrt.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)))))

Compiler

Compiled 10133 to 7851 computations (22.5% saved)

regimes894.0ms (1.4%)

Accuracy

Total 0.2b remaining (39.6%)

Threshold costs 0.2b (39.6%)

Counts

132 → 1

Compiler

Compiled 22296 to 18408 computations (17.4% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

19×	`+-commutative_binary64`
11×	`sub-neg_binary64`
7×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	123
1	92	123
2	105	123
3	107	123
4	108	123
5	107	123

end355.0ms (0.5%)

Compiler: Compiled 634 to 521 computations (17.8% saved)

Details

analyze3.0s (4.6%)

sample57.2s (86.5%)

simplify47.0ms (0.1%)

prune12.0ms (0%)

localize47.0ms (0.1%)

series31.0ms (0%)

rewrite50.0ms (0.1%)

simplify63.0ms (0.1%)

prune489.0ms (0.7%)

localize53.0ms (0.1%)

series941.0ms (1.4%)

rewrite79.0ms (0.1%)

simplify88.0ms (0.1%)

prune396.0ms (0.6%)

localize54.0ms (0.1%)

series1.3s (2%)

rewrite68.0ms (0.1%)

simplify83.0ms (0.1%)

prune383.0ms (0.6%)

localize50.0ms (0.1%)

series21.0ms (0%)

rewrite76.0ms (0.1%)

simplify54.0ms (0.1%)

prune281.0ms (0.4%)

regimes894.0ms (1.4%)

simplify5.0ms (0%)

end355.0ms (0.5%)

Profiling