Details

analyze469.0ms (6.5%)

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 31 to 25 computations (19.4% saved)

sample63.0ms (0.9%)

Algorithm

1×

intervals

Results

34.0ms	256×	body	128	valid
9.0ms	256×	pre	128	true

Compiler

Compiled 50 to 42 computations (16% saved)

simplify19.0ms (0.3%)

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 → 1

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

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.6b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (*.f32 2 PI.f32) u2)))
	13.9b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (sin.f32 (.f32 (*.f32 2 PI.f32) u2)))

Compiler

Compiled 77 to 67 computations (13% saved)

localize34.0ms (0.5%)

Local error

Found 4 expressions with local error:

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)

rewrite87.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

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))

Compiler

Compiled 1380 to 649 computations (53% saved)

series60.0ms (0.8%)

Error

0.5b

Counts

4 → 21

Calls

4 calls:

29.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (*.f32 2 PI.f32) u2)))
8.0ms	(sin.f32 (.f32 (.f32 2 PI.f32) u2))
6.0ms	(.f32 (.f32 2 PI.f32) u2)
6.0ms	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))

Compiler

Compiled 1130 to 910 computations (19.5% saved)

simplify130.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

778×	`fma-def_binary32`
424×	`*-commutative_binary32`
400×	`cancel-sign-sub-inv_binary32`
380×	`fma-neg_binary32`
340×	`sub-neg_binary32`

Counts

103 → 70

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	175	2028
1	378	1875
2	1134	1829
3	2127	1787
4	4292	1787
5	4627	1787
6	4913	1787

prune68.0ms (1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	54	16	70
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	56	16	72

Error

0.1b

Counts

72 → 16

Alt Table

Status	Error	Program
	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 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))) (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	2.9b	(exp.f32 (log.f32 (.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	0.9b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32)))) (cbrt.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32)))))) (cbrt.f32 (sin.f32 (.f32 (*.f32 2 PI.f32) u2))))
	0.7b	(.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))))))
	0.6b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))))))
	1.7b	(.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sqrt.f32 (.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (*.f32 u2 PI.f32))))))
	11.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))))))
	1.0b	(.f32 (.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cbrt.f32 (.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))))) (cbrt.f32 (.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	6.6b	(.f32 2 (.f32 u2 (*.f32 PI.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	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	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))))))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32)))) (cbrt.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))))) (cbrt.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))))))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 u2 PI.f32))) (cbrt.f32 (.f32 2 (.f32 u2 PI.f32)))) (cbrt.f32 (.f32 2 (*.f32 u2 PI.f32))))))
	1.7b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))))) (sqrt.f32 (sin.f32 (.f32 (.f32 2 PI.f32) u2))))

Compiler

Compiled 1778 to 1023 computations (42.5% saved)

localize43.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.3b	(log1p.f32 (expm1.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32)))))
0.3b	(expm1.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))))
0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))))))
0.4b	(*.f32 u2 PI.f32)

rewrite85.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

17×	`add-sqr-sqrt_binary32`
16×	`associate-l_binary32`
11×	`sqrt-prod_binary32`
11×	`*-un-lft-identity_binary32`
11×	`add-cube-cbrt_binary32`

Counts

4 → 73

Calls

4 calls:

5.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))))))
4.0ms	(*.f32 u2 PI.f32)
0.0ms	(expm1.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))))
0.0ms	(log1p.f32 (expm1.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32)))))

Compiler

Compiled 1379 to 681 computations (50.6% saved)

series91.0ms (1.3%)

Error

0.1b

Counts

4 → 24

Calls

4 calls:

41.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))))))
19.0ms	(log1p.f32 (expm1.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32)))))
10.0ms	(expm1.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))))
5.0ms	(*.f32 u2 PI.f32)

Compiler

Compiled 1354 to 1072 computations (20.8% saved)

simplify127.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

836×	`fma-neg_binary32`
443×	`distribute-rgt-neg-in_binary32`
416×	`distribute-lft-neg-in_binary32`
380×	`fma-def_binary32`
359×	`*-commutative_binary32`

Counts

97 → 71

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	177	1963
1	391	1782
2	1152	1728
3	2581	1704
4	4787	1704
5	5000	1704
6	4907	1704

prune75.0ms (1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	72	15	87

Error

0.1b

Counts

87 → 15

Alt Table

Status	Error	Program
	0.9b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32)))) (cbrt.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32)))))) (cbrt.f32 (sin.f32 (.f32 (*.f32 2 PI.f32) u2))))
	0.7b	(.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
▶	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))))))
	0.6b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))))))
	2.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 u2 (.f32 PI.f32 2) (fma.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 PI.f32 5)) (fma.f32 (pow.f32 u2 7) (.f32 (pow.f32 PI.f32 7) -8/315) (.f32 (pow.f32 (.f32 u2 PI.f32) 3) -4/3)))))
	11.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (sin.f32 (.f32 (*.f32 u2 PI.f32) 2)))))))
	1.7b	(.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sqrt.f32 (.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (*.f32 u2 PI.f32))))))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (.f32 (.f32 (cbrt.f32 (expm1.f32 (sin.f32 (.f32 (.f32 u2 PI.f32) 2)))) (cbrt.f32 (expm1.f32 (sin.f32 (.f32 (.f32 u2 PI.f32) 2))))) (cbrt.f32 (expm1.f32 (sin.f32 (.f32 (*.f32 u2 PI.f32) 2)))))))
	11.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))))))
	1.0b	(.f32 (.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cbrt.f32 (.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))))) (cbrt.f32 (.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	6.6b	(.f32 2 (.f32 u2 (*.f32 PI.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	2.9b	(exp.f32 (log.f32 (.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	1.7b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))))) (sqrt.f32 (sin.f32 (.f32 (.f32 2 PI.f32) u2))))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (sin.f32 (.f32 2 (.f32 (.f32 (cbrt.f32 u2) (cbrt.f32 u2)) (*.f32 PI.f32 (cbrt.f32 u2))))))))

Compiler

Compiled 1802 to 1068 computations (40.7% saved)

localize51.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.2b	(log1p.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))))
0.3b	(expm1.f32 (log1p.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32)))))
0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))))))
0.4b	(*.f32 u2 PI.f32)

rewrite76.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

17×	`add-sqr-sqrt_binary32`
16×	`associate-l_binary32`
11×	`sqrt-prod_binary32`
11×	`*-un-lft-identity_binary32`
11×	`add-cube-cbrt_binary32`

Counts

4 → 73

Calls

4 calls:

5.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))))))
3.0ms	(*.f32 u2 PI.f32)
1.0ms	(expm1.f32 (log1p.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32)))))
0.0ms	(log1p.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))))

Compiler

Compiled 1379 to 681 computations (50.6% saved)

series106.0ms (1.5%)

Error

0.1b

Counts

4 → 24

Calls

4 calls:

48.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))))))
24.0ms	(expm1.f32 (log1p.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32)))))
14.0ms	(log1p.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))))
5.0ms	(*.f32 u2 PI.f32)

Compiler

Compiled 1494 to 1199 computations (19.7% saved)

simplify111.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

772×	`fma-neg_binary32`
462×	`fma-def_binary32`
376×	`*-commutative_binary32`
304×	`cancel-sign-sub-inv_binary32`
276×	`sub-neg_binary32`

Counts

97 → 72

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	177	1968
1	392	1782
2	1242	1727
3	3424	1725
4	4793	1725
5	4924	1725

prune72.0ms (1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	72	15	87

Error

0.1b

Counts

87 → 15

Alt Table

Status	Error	Program
	2.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (exp.f32 (log.f32 (log1p.f32 (sin.f32 (.f32 (*.f32 u2 PI.f32) 2)))))))
	2.9b	(exp.f32 (log.f32 (.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	0.9b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32)))) (cbrt.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32)))))) (cbrt.f32 (sin.f32 (.f32 (*.f32 2 PI.f32) u2))))
	0.7b	(.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	0.6b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))))))
	2.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 u2 (.f32 PI.f32 2) (fma.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 PI.f32 5)) (fma.f32 (pow.f32 u2 7) (.f32 (pow.f32 PI.f32 7) -8/315) (.f32 (pow.f32 (.f32 u2 PI.f32) 3) -4/3)))))
	11.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (sin.f32 (.f32 (*.f32 u2 PI.f32) 2)))))))
	5.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (fma.f32 4/3 (pow.f32 (.f32 u2 PI.f32) 3) (.f32 (.f32 u2 PI.f32) (-.f32 2 (.f32 (.f32 u2 PI.f32) 2))))))
	1.7b	(.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sqrt.f32 (.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
▶	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (*.f32 u2 PI.f32))))))
	11.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))))))
	1.0b	(.f32 (.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cbrt.f32 (.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))))) (cbrt.f32 (.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	6.6b	(.f32 2 (.f32 u2 (*.f32 PI.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	1.7b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))))) (sqrt.f32 (sin.f32 (.f32 (.f32 2 PI.f32) u2))))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (sin.f32 (.f32 2 (.f32 (.f32 (cbrt.f32 u2) (cbrt.f32 u2)) (*.f32 PI.f32 (cbrt.f32 u2))))))))

Compiler

Compiled 1886 to 1094 computations (42% saved)

localize43.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.2b	(log1p.f32 (.f32 2 (.f32 u2 PI.f32)))
0.2b	(expm1.f32 (log1p.f32 (.f32 2 (.f32 u2 PI.f32))))
0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (*.f32 u2 PI.f32))))))
0.4b	(*.f32 u2 PI.f32)

rewrite77.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

17×	`add-sqr-sqrt_binary32`
16×	`associate-l_binary32`
11×	`sqrt-prod_binary32`
11×	`*-un-lft-identity_binary32`
11×	`add-cube-cbrt_binary32`

Counts

4 → 73

Calls

4 calls:

6.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (*.f32 u2 PI.f32))))))
3.0ms	(*.f32 u2 PI.f32)
0.0ms	(log1p.f32 (.f32 2 (.f32 u2 PI.f32)))
0.0ms	(expm1.f32 (log1p.f32 (.f32 2 (.f32 u2 PI.f32))))

Compiler

Compiled 1369 to 671 computations (51% saved)

series121.0ms (1.7%)

Error

0.1b

Counts

4 → 28

Calls

4 calls:

58.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (*.f32 u2 PI.f32))))))
22.0ms	(expm1.f32 (log1p.f32 (.f32 2 (.f32 u2 PI.f32))))
14.0ms	(log1p.f32 (.f32 2 (.f32 u2 PI.f32)))
5.0ms	(*.f32 u2 PI.f32)

Compiler

Compiled 2319 to 1888 computations (18.6% saved)

simplify78.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

918×	`associate-/l*_binary32`
454×	`fma-def_binary32`
365×	`cancel-sign-sub-inv_binary32`
181×	`fma-neg_binary32`
175×	`associate-r_binary32`

Counts

101 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	232	2470
1	561	2176
2	2043	2053
3	5500	2053

prune76.0ms (1.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	75	15	90

Error

0.1b

Counts

90 → 15

Alt Table

Status	Error	Program
	2.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (exp.f32 (log.f32 (log1p.f32 (sin.f32 (.f32 (*.f32 u2 PI.f32) 2)))))))
	2.9b	(exp.f32 (log.f32 (.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	0.9b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32)))) (cbrt.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32)))))) (cbrt.f32 (sin.f32 (.f32 (*.f32 2 PI.f32) u2))))
	0.7b	(.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	0.6b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))))))
	2.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 u2 (.f32 PI.f32 2) (fma.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 PI.f32 5)) (fma.f32 (pow.f32 u2 7) (.f32 (pow.f32 PI.f32 7) -8/315) (.f32 (pow.f32 (.f32 u2 PI.f32) 3) -4/3)))))
	11.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (sin.f32 (.f32 (*.f32 u2 PI.f32) 2)))))))
	5.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (fma.f32 4/3 (pow.f32 (.f32 u2 PI.f32) 3) (.f32 (.f32 u2 PI.f32) (-.f32 2 (.f32 (.f32 u2 PI.f32) 2))))))
	1.7b	(.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sqrt.f32 (.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	11.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))))))
	1.0b	(.f32 (.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cbrt.f32 (.f32 (sin.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))))) (cbrt.f32 (.f32 (sin.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	6.6b	(.f32 2 (.f32 u2 (*.f32 PI.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (sqrt.f32 u2) (.f32 PI.f32 (sqrt.f32 u2))))))))
	1.7b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (sin.f32 (.f32 (.f32 u2 PI.f32) 2)))) (sqrt.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 u2 PI.f32)))))))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (sin.f32 (.f32 2 (.f32 (.f32 (cbrt.f32 u2) (cbrt.f32 u2)) (*.f32 PI.f32 (cbrt.f32 u2))))))))

Compiler

Compiled 1775 to 959 computations (46% saved)

regimes2.9s (40.1%)

Accuracy

Total 0.5b remaining (85%)

Threshold costs 0.5b (85%)

Compiler

Compiled 56669 to 45923 computations (19% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-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	16	26
1	25	26
2	29	26
3	31	26
4	31	26

end1.0ms (0%)

Compiler: Compiled 18 to 16 computations (11.1% saved)

sample2.1s (29.7%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
263.0ms	8000×	pre	128	true
0.0ms	4×	pre	128	false

Compiler

Compiled 432 to 330 computations (23.6% 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

analyze469.0ms (6.5%)

sample63.0ms (0.9%)

simplify19.0ms (0.3%)

prune4.0ms (0.1%)

localize34.0ms (0.5%)

rewrite87.0ms (1.2%)

series60.0ms (0.8%)

simplify130.0ms (1.8%)

prune68.0ms (1%)

localize43.0ms (0.6%)

rewrite85.0ms (1.2%)

series91.0ms (1.3%)

simplify127.0ms (1.8%)

prune75.0ms (1%)

localize51.0ms (0.7%)

rewrite76.0ms (1.1%)

series106.0ms (1.5%)

simplify111.0ms (1.6%)

prune72.0ms (1%)

localize43.0ms (0.6%)

rewrite77.0ms (1.1%)

series121.0ms (1.7%)

simplify78.0ms (1.1%)

prune76.0ms (1.1%)

regimes2.9s (40.1%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample2.1s (29.7%)

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