Details

analyze490.0ms (4.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 39 to 31 computations (20.5% saved)

sample2.6s (23.1%)

Results

2.5s	8256×	body	128	valid
1.0ms	4×	body	128	invalid

Compiler

Compiled 94 to 76 computations (19.1% saved)

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

40×	`fma-neg_binary32`
22×	`sub-neg_binary32`
17×	`cancel-sign-sub-inv_binary32`
15×	`fma-def_binary32`
11×	`*-commutative_binary32`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	26	21
2	38	21
3	46	21
4	56	21
5	67	21
6	82	21
7	106	21
8	119	21
9	125	21
10	144	21
11	140	21
12	167	21
13	180	21
14	184	21
15	185	21
16	163	21

prune5.0ms (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

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	13.4b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
▶	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))

Compiler

Compiled 90 to 77 computations (14.4% saved)

localize37.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
✓	0.2b	(sin.f32 (.f32 (.f32 2 (PI.f32)) u2))
✓	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
✓	0.4b	(.f32 (.f32 2 (PI.f32)) u2)

series168.0ms (1.5%)

Counts

4 → 52

Calls

4 calls:

150.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
11.0ms	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
3.0ms	(sin.f32 (.f32 (.f32 2 (PI.f32)) u2))
3.0ms	(.f32 (.f32 2 (PI.f32)) u2)

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`sqrt-prod_binary32`
18×	`add-sqr-sqrt_binary32`
14×	`associate-l_binary32`
13×	`*-un-lft-identity_binary32`
13×	`add-cube-cbrt_binary32`

Counts

4 → 82

Calls

4 calls:

6.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
4.0ms	(.f32 (.f32 2 (PI.f32)) u2)
3.0ms	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
1.0ms	(sin.f32 (.f32 (.f32 2 (PI.f32)) u2))

simplify143.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

553×	`cancel-sign-sub-inv_binary32`
510×	`fma-neg_binary32`
360×	`times-frac_binary32`
236×	`associate-l_binary32`
224×	`fma-def_binary32`

Counts

134 → 166

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	286	3674
1	776	3341
2	2559	3238
3	4483	3212
4	5079	3212

prune239.0ms (2.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	151	15	166
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	153	15	168

Error

0.0b

Counts

168 → 15

Alt Table

Status	Error	Program
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	1.6b	(-.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2 (.f32 u2 (PI.f32)) (.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 4/3 (pow.f32 (.f32 u2 (PI.f32)) 3) (.f32 8/315 (.f32 (pow.f32 u2 7) (pow.f32 (PI.f32) 7))))))
	13.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	1.3b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (sqrt.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))))
	1.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))
	0.7b	(.f32 (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	1.4b	(.f32 (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.7b	(.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))))
	0.7b	(.f32 (.f32 (fabs.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	5.1b	(.f32 2 (.f32 u2 (*.f32 (PI.f32) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	0.6b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.7b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (sqrt.f32 (.f32 (.f32 2 (PI.f32)) u2)) (sqrt.f32 (.f32 (.f32 2 (PI.f32)) u2)))))
	0.9b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
▶	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))) (.f32 2 (PI.f32))) (.f32 (*.f32 u2 u2) u2)))))

Compiler

Compiled 5304 to 3235 computations (39% saved)

localize63.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (.f32 u2 u2) u2)
✓	0.2b	(.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))) (.f32 2 (PI.f32))) (.f32 (.f32 u2 u2) u2))
✓	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))) (.f32 2 (PI.f32))) (.f32 (*.f32 u2 u2) u2)))))
✓	1.0b	(.f32 (.f32 2 (PI.f32)) (*.f32 2 (PI.f32)))

series167.0ms (1.5%)

Counts

4 → 44

Calls

4 calls:

149.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))) (.f32 2 (PI.f32))) (.f32 (*.f32 u2 u2) u2)))))
15.0ms	(.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))) (.f32 2 (PI.f32))) (.f32 (.f32 u2 u2) u2))
3.0ms	(.f32 (.f32 u2 u2) u2)
0.0ms	(.f32 (.f32 2 (PI.f32)) (*.f32 2 (PI.f32)))

rewrite131.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

817×	`pow1_binary32`
401×	`pow-prod-down_binary32`
218×	`add-cbrt-cube_binary32`
215×	`add-exp-log_binary32`
213×	`pow-prod-up_binary32`

Counts

4 → 312

Calls

4 calls:

39.0ms	(.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))) (.f32 2 (PI.f32))) (.f32 (.f32 u2 u2) u2))
8.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))) (.f32 2 (PI.f32))) (.f32 (*.f32 u2 u2) u2)))))
5.0ms	(.f32 (.f32 2 (PI.f32)) (*.f32 2 (PI.f32)))
5.0ms	(.f32 (.f32 u2 u2) u2)

simplify230.0ms (2%)

Algorithm

1×	egg-herbie

Rules

658×	`fma-def_binary32`
486×	`associate-l_binary32`
416×	`associate-r_binary32`
289×	`cancel-sign-sub-inv_binary32`
246×	`times-frac_binary32`

Counts

356 → 227

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	334	8080
1	709	5417
2	2752	5379
3	4306	5370
4	4931	5370
5	4949	5370

prune341.0ms (3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	223	4	227
Fresh	5	9	14
Picked	1	0	1
Done	0	0	0
Total	229	13	242

Error

0.0b

Counts

242 → 13

Alt Table

Status	Error	Program
	0.7b	(.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))))
▶	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 (PI.f32) 4)))) (.f32 2 (PI.f32))) (.f32 (.f32 u2 u2) u2)))))
	1.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))
	0.7b	(.f32 (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	0.9b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	1.4b	(.f32 (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 8 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))))))) (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 8 (*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))))))))
	0.9b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (sin.f32 (cbrt.f32 (.f32 8 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)))))) (cbrt.f32 (sin.f32 (cbrt.f32 (.f32 8 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)))))))) (cbrt.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))) (.f32 2 (PI.f32))) (.f32 (*.f32 u2 u2) u2))))))
	2.1b	(fma.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))) -6004799503160661/4503599627370496 (fma.f32 2 (.f32 u2 (.f32 (PI.f32) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 4803839602528529/18014398509481984 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (*.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	13.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.7b	(.f32 (.f32 (fabs.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	0.6b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.7b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (sqrt.f32 (.f32 (.f32 2 (PI.f32)) u2)) (sqrt.f32 (.f32 (.f32 2 (PI.f32)) u2)))))

Compiler

Compiled 8864 to 4974 computations (43.9% saved)

localize77.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f32 (.f32 u2 u2) u2)
✓	0.2b	(.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 (PI.f32) 4)))) (.f32 2 (PI.f32))) (.f32 (*.f32 u2 u2) u2))
✓	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 (PI.f32) 4)))) (.f32 2 (PI.f32))) (.f32 (.f32 u2 u2) u2)))))
✓	1.0b	(.f32 (PI.f32) (.f32 (PI.f32) 4))

series163.0ms (1.4%)

Counts

3 → 32

Calls

3 calls:

150.0ms

(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2)))))

13.0ms

(*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2))

0.0ms

(*.f32 (PI.f32) (*.f32 (PI.f32) 4))

rewrite60.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-cbrt-cube_binary32`
46×	`add-exp-log_binary32`
46×	`pow1_binary32`
31×	`cbrt-unprod_binary32`
31×	`prod-exp_binary32`

Counts

3 → 90

Calls

3 calls:

40.0ms

(*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2))

7.0ms

(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2)))))

4.0ms

(*.f32 (PI.f32) (*.f32 (PI.f32) 4))

simplify127.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

637×	`fma-def_binary32`
394×	`associate-l_binary32`
345×	`associate-r_binary32`
289×	`cancel-sign-sub-inv_binary32`
275×	`fma-neg_binary32`

Counts

122 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	280	4368
1	694	3239
2	2340	3110
3	4692	3108
4	4979	3108

prune239.0ms (2.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	164	4	168
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	168	13	181

Error

0.0b

Counts

181 → 13

Alt Table

Status	Error	Program
	0.7b	(.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))))
	1.3b	(.f32 (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 (PI.f32) 4)))) (.f32 2 (PI.f32))) (.f32 (.f32 u2 u2) u2)))))) (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 (PI.f32) 4)))) (.f32 2 (PI.f32))) (.f32 (*.f32 u2 u2) u2)))))))
▶	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 (PI.f32) 4)))) (.f32 2 (PI.f32))) (pow.f32 u2 3)))))
	13.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	1.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))
	0.7b	(.f32 (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	0.9b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (sin.f32 (cbrt.f32 (.f32 8 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)))))) (cbrt.f32 (sin.f32 (cbrt.f32 (.f32 8 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)))))))) (cbrt.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))) (.f32 2 (PI.f32))) (.f32 (*.f32 u2 u2) u2))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (cbrt.f32 (.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 (PI.f32) 4)))) (.f32 2 (PI.f32))) (.f32 (.f32 u2 u2) u2))))))
	2.1b	(fma.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))) -6004799503160661/4503599627370496 (fma.f32 2 (.f32 u2 (.f32 (PI.f32) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 4803839602528529/18014398509481984 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (*.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.7b	(.f32 (.f32 (fabs.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	0.6b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	1.3b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (sin.f32 (cbrt.f32 (.f32 8 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))))))) (sqrt.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 (PI.f32) 4)))) (.f32 2 (PI.f32))) (.f32 (*.f32 u2 u2) u2))))))

Compiler

Compiled 6746 to 3972 computations (41.1% saved)

localize71.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(sin.f32 (cbrt.f32 (.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (pow.f32 u2 3))))
✓	0.2b	(.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (pow.f32 u2 3))
✓	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 (PI.f32) 4)))) (.f32 2 (PI.f32))) (pow.f32 u2 3)))))
	1.0b	(.f32 (PI.f32) (.f32 (PI.f32) 4))

series166.0ms (1.5%)

Counts

3 → 44

Calls

3 calls:

149.0ms

(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (pow.f32 u2 3)))))

13.0ms

(*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (pow.f32 u2 3))

4.0ms

(sin.f32 (cbrt.f32 (*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (pow.f32 u2 3))))

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-exp-log_binary32`
19×	`prod-exp_binary32`
15×	`associate-r_binary32`
15×	`add-sqr-sqrt_binary32`
14×	`associate-l_binary32`

Counts

3 → 75

Calls

3 calls:

17.0ms

(*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (pow.f32 u2 3))

7.0ms

(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (pow.f32 u2 3)))))

2.0ms

(sin.f32 (cbrt.f32 (*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (pow.f32 u2 3))))

simplify157.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

738×	`fma-def_binary32`
377×	`log-prod_binary32`
375×	`associate-l_binary32`
352×	`cancel-sign-sub-inv_binary32`
330×	`associate-r_binary32`

Counts

119 → 150

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	273	4395
1	699	3355
2	2405	3335
3	4597	3335
4	4974	3335
5	5040	3335

prune237.0ms (2.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	169	3	172
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	173	12	185

Error

0.0b

Counts

185 → 12

Alt Table

Status	Error	Program
	13.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.6b	(.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (cbrt.f32 (.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (pow.f32 u2 3))))))
	1.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))
	0.7b	(.f32 (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	1.3b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (sin.f32 (cbrt.f32 (.f32 8 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))))))) (sqrt.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (pow.f32 u2 3))))))
	0.8b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (sin.f32 (cbrt.f32 (.f32 8 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)))))) (cbrt.f32 (sin.f32 (cbrt.f32 (.f32 8 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)))))))) (cbrt.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 (PI.f32) 4)))) (.f32 2 (PI.f32))) (pow.f32 u2 3))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (cbrt.f32 (.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 (PI.f32) 4)))) (.f32 2 (PI.f32))) (.f32 (.f32 u2 u2) u2))))))
	2.1b	(fma.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))) -6004799503160661/4503599627370496 (fma.f32 2 (.f32 u2 (.f32 (PI.f32) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 4803839602528529/18014398509481984 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (*.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5))))))
	1.3b	(.f32 (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 (PI.f32) 4)))) (.f32 2 (PI.f32))) (.f32 (.f32 u2 u2) u2)))))) (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 (PI.f32) 4)))) (.f32 2 (PI.f32))) (.f32 (*.f32 u2 u2) u2)))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.7b	(.f32 (.f32 (fabs.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	0.6b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))

Compiler

Compiled 6079 to 3922 computations (35.5% saved)

regimes5.0s (44.4%)

Accuracy

Total 0.4b remaining (88.6%)

Threshold costs 0.4b (88.6%)

Counts

331 → 1

Compiler

Compiled 98702 to 78822 computations (20.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary32`
2×	`+-commutative_binary32`
2×	`sub-neg_binary32`
2×	`neg-sub0_binary32`
2×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	45
1	36	45
2	40	45
3	42	45
4	42	45

end273.0ms (2.4%)

Compiler: Compiled 492 to 357 computations (27.4% saved)

Iter	Nodes	Cost
0	14	22
1	26	21
2	38	21
3	46	21
4	56	21
5	67	21
6	82	21
7	106	21
8	119	21
9	125	21
10	144	21
11	140	21
12	167	21
13	180	21
14	184	21
15	185	21
16	163	21

Iter	Nodes	Cost
0	14	22
1	26	21
2	38	21
3	46	21
4	56	21
5	67	21
6	82	21
7	106	21
8	119	21
9	125	21
10	144	21
11	140	21
12	167	21
13	180	21
14	184	21
15	185	21
16	163	21

Details

analyze490.0ms (4.4%)

sample2.6s (23.1%)

simplify16.0ms (0.1%)

prune5.0ms (0%)

localize37.0ms (0.3%)

series168.0ms (1.5%)

rewrite18.0ms (0.2%)

simplify143.0ms (1.3%)

prune239.0ms (2.1%)

localize63.0ms (0.6%)

series167.0ms (1.5%)

rewrite131.0ms (1.2%)

simplify230.0ms (2%)

prune341.0ms (3%)

localize77.0ms (0.7%)

series163.0ms (1.4%)

rewrite60.0ms (0.5%)

simplify127.0ms (1.1%)

prune239.0ms (2.1%)

localize71.0ms (0.6%)

series166.0ms (1.5%)

rewrite32.0ms (0.3%)

simplify157.0ms (1.4%)

prune237.0ms (2.1%)

regimes5.0s (44.4%)

simplify3.0ms (0%)

end273.0ms (2.4%)

Profiling

Iter	Nodes	Cost
0	14	22
1	26	21
2	38	21
3	46	21
4	56	21
5	67	21
6	82	21
7	106	21
8	119	21
9	125	21
10	144	21
11	140	21
12	167	21
13	180	21
14	184	21
15	185	21
16	163	21