Details

analyze408.0ms (6.4%)

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)

sample2.1s (32.5%)

Results

2.1s	8256×	body	128	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 78 to 62 computations (20.5% saved)

preprocess36.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

104×	`fma-neg_binary32`
95×	`fma-def_binary32`
60×	`sub-neg_binary32`
45×	`cancel-sign-sub-inv_binary32`
30×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	88
1	59	84
2	98	84
3	124	84
4	155	84
5	191	84
6	231	84
7	319	84
8	490	84
9	531	84
10	585	84
11	635	84
12	726	84
13	773	84
14	791	84
15	794	84
0	3	3

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 16 to 14 computations (12.5% saved)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

40×	`fma-neg_binary32`
22×	`sub-neg_binary32`
17×	`cancel-sign-sub-inv_binary32`
13×	`fma-def_binary32`
10×	`*-commutative_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	26	21
2	39	21
3	49	21
4	60	21
5	74	21
6	92	21
7	119	21
8	149	21
9	162	21
10	184	21
11	206	21
12	245	21
13	262	21
14	268	21
15	269	21

Stop Event

1×

saturated

Counts

1 → 2

prune9.0ms (0.1%)

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	12.7b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
▶	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))

Compiler

Compiled 90 to 77 computations (14.4% saved)

localize31.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series166.0ms (2.6%)

Counts

4 → 32

Calls

15 calls:

67.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))	u2	inf
58.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))	u2	-inf
10.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))	u1	0
7.0ms	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))	u1	inf
5.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))	u1	inf

rewrite55.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

679×	`prod-diff_binary32`
204×	`expm1-udef_binary32`
204×	`log1p-udef_binary32`
132×	`add-sqr-sqrt_binary32`
124×	`expm1-log1p-u_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	45
1	266	37
2	3275	37

Stop Event

1×	node limit

Counts

4 → 96

simplify52.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

538×	`cancel-sign-sub-inv_binary32`
348×	`times-frac_binary32`
276×	`associate-*l/_binary32`
247×	`associate-/r*_binary32`
214×	`associate-/l*_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	179	1948
1	571	1783
2	2097	1637

Stop Event

1×	node limit

Counts

128 → 144

prune191.0ms (3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	132	12	144
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	134	12	146

Error

0.1b

Counts

146 → 12

Alt Table

Status	Error	Program
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (+.f32 1 (expm1.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2)))))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 1 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (neg.f32 (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))) (fma.f32 (neg.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (log.f32 (pow.f32 (exp.f32 u2) (PI.f32))))))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (.f32 (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2))) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (fma.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) u2))) (sin.f32 (.f32 (PI.f32) u2)) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2))))
	8.5b	(.f32 (.f32 (cbrt.f32 (log1p.f32 u1)) (cbrt.f32 (sqrt.f32 (log1p.f32 u1)))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))
	2.0b	(-.f32 (.f32 (fma.f32 (.f32 2/3 (pow.f32 u2 4)) (pow.f32 (PI.f32) 4) 1) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2 (.f32 (.f32 u2 u2) (pow.f32 (PI.f32) 2)) (.f32 4/45 (*.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6))))))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (+.f32 (cos.f32 (.f32 (PI.f32) u2)) (sin.f32 (.f32 (PI.f32) u2))) (-.f32 (cos.f32 (.f32 (PI.f32) u2)) (sin.f32 (.f32 (PI.f32) u2)))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
	15.3b	(sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))
	8.5b	(.f32 (pow.f32 (pow.f32 (log1p.f32 u1) 1/4) 2) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
▶	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (pow.f32 (cbrt.f32 (*.f32 (PI.f32) u2)) 3))))
	9.8b	(exp.f32 (log.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))

Compiler

Compiled 5104 to 3184 computations (37.6% saved)

localize45.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(cbrt.f32 (*.f32 (PI.f32) u2))
✓	0.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (pow.f32 (cbrt.f32 (*.f32 (PI.f32) u2)) 3))))
	0.3b	(*.f32 (PI.f32) u2)
✓	0.7b	(pow.f32 (cbrt.f32 (*.f32 (PI.f32) u2)) 3)

series159.0ms (2.5%)

Counts

3 → 20

Calls

12 calls:

54.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (pow.f32 (cbrt.f32 (*.f32 (PI.f32) u2)) 3))))	u2	inf
53.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (pow.f32 (cbrt.f32 (*.f32 (PI.f32) u2)) 3))))	u2	-inf
17.0ms	(pow.f32 (cbrt.f32 (*.f32 (PI.f32) u2)) 3)	u2	-inf
8.0ms	(cbrt.f32 (*.f32 (PI.f32) u2))	u2	-inf
5.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (pow.f32 (cbrt.f32 (*.f32 (PI.f32) u2)) 3))))	u1	0

rewrite50.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

995×	`prod-diff_binary32`
148×	`add-sqr-sqrt_binary32`
143×	`expm1-log1p-u_binary32`
142×	`log1p-expm1-u_binary32`
138×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	33
1	326	29
2	3711	29

Stop Event

1×	node limit

Counts

3 → 74

simplify39.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

528×	`fma-def_binary32`
364×	`associate-l_binary32`
359×	`associate-r_binary32`
294×	`cancel-sign-sub-inv_binary32`
258×	`associate-+l+_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	1250
1	357	1178
2	1217	1078

Stop Event

1×	node limit

Counts

94 → 100

prune179.0ms (2.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	115	12	127

Error

0.1b

Counts

127 → 12

Alt Table

Status	Error	Program
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (+.f32 1 (expm1.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2)))))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (log.f32 (pow.f32 (exp.f32 u2) (PI.f32))))))
▶	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (.f32 (pow.f32 (cbrt.f32 u2) 2) (.f32 (cbrt.f32 u2) (PI.f32))))))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (.f32 (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2))) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (fma.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) u2))) (sin.f32 (.f32 (PI.f32) u2)) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2))))
	8.5b	(.f32 (.f32 (cbrt.f32 (log1p.f32 u1)) (cbrt.f32 (sqrt.f32 (log1p.f32 u1)))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))
	12.7b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	2.0b	(-.f32 (.f32 (fma.f32 (.f32 2/3 (pow.f32 u2 4)) (pow.f32 (PI.f32) 4) 1) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2 (.f32 (.f32 u2 u2) (pow.f32 (PI.f32) 2)) (.f32 4/45 (*.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6))))))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (+.f32 (cos.f32 (.f32 (PI.f32) u2)) (sin.f32 (.f32 (PI.f32) u2))) (-.f32 (cos.f32 (.f32 (PI.f32) u2)) (sin.f32 (.f32 (PI.f32) u2)))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
	8.5b	(.f32 (pow.f32 (pow.f32 (log1p.f32 u1) 1/4) 2) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
✓	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (pow.f32 (cbrt.f32 (*.f32 (PI.f32) u2)) 3))))
	9.8b	(exp.f32 (log.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))

Compiler

Compiled 3386 to 2096 computations (38.1% saved)

localize44.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (.f32 (pow.f32 (cbrt.f32 u2) 2) (.f32 (cbrt.f32 u2) (PI.f32))))))
✓	0.3b	(.f32 (pow.f32 (cbrt.f32 u2) 2) (.f32 (cbrt.f32 u2) (PI.f32)))
✓	0.4b	(*.f32 (cbrt.f32 u2) (PI.f32))
✓	0.5b	(pow.f32 (cbrt.f32 u2) 2)

series221.0ms (3.5%)

Counts

4 → 32

Calls

15 calls:

58.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (.f32 (pow.f32 (cbrt.f32 u2) 2) (.f32 (cbrt.f32 u2) (PI.f32))))))	u2	-inf
53.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (.f32 (pow.f32 (cbrt.f32 u2) 2) (.f32 (cbrt.f32 u2) (PI.f32))))))	u2	inf
50.0ms	(.f32 (pow.f32 (cbrt.f32 u2) 2) (.f32 (cbrt.f32 u2) (PI.f32)))	u2	-inf
20.0ms	(pow.f32 (cbrt.f32 u2) 2)	u2	-inf
10.0ms	(*.f32 (cbrt.f32 u2) (PI.f32))	u2	-inf

rewrite50.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

245×	`expm1-udef_binary32`
245×	`log1p-udef_binary32`
174×	`fma-def_binary32`
158×	`add-sqr-sqrt_binary32`
153×	`associate-r_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	39
1	327	35
2	3980	35

Stop Event

1×	node limit

Counts

4 → 64

simplify34.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

528×	`fma-def_binary32`
364×	`associate-l_binary32`
359×	`associate-r_binary32`
294×	`cancel-sign-sub-inv_binary32`
258×	`associate-+l+_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	1310
1	357	1238
2	1217	1138

Stop Event

1×	node limit

Counts

96 → 91

prune125.0ms (2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	91	12	103

Error

0.1b

Counts

103 → 12

Alt Table

Status	Error	Program
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (+.f32 1 (expm1.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2)))))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (log.f32 (pow.f32 (exp.f32 u2) (PI.f32))))))
✓	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (.f32 (pow.f32 (cbrt.f32 u2) 2) (.f32 (cbrt.f32 u2) (PI.f32))))))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (.f32 (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2))) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (fma.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) u2))) (sin.f32 (.f32 (PI.f32) u2)) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2))))
	8.5b	(.f32 (.f32 (cbrt.f32 (log1p.f32 u1)) (cbrt.f32 (sqrt.f32 (log1p.f32 u1)))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))
	12.7b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	2.0b	(-.f32 (.f32 (fma.f32 (.f32 2/3 (pow.f32 u2 4)) (pow.f32 (PI.f32) 4) 1) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2 (.f32 (.f32 u2 u2) (pow.f32 (PI.f32) 2)) (.f32 4/45 (*.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6))))))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (+.f32 (cos.f32 (.f32 (PI.f32) u2)) (sin.f32 (.f32 (PI.f32) u2))) (-.f32 (cos.f32 (.f32 (PI.f32) u2)) (sin.f32 (.f32 (PI.f32) u2)))))
▶	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
	8.5b	(.f32 (pow.f32 (pow.f32 (log1p.f32 u1) 1/4) 2) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
✓	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (pow.f32 (cbrt.f32 (*.f32 (PI.f32) u2)) 3))))
	9.8b	(exp.f32 (log.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))

Compiler

Compiled 2959 to 1877 computations (36.6% saved)

localize43.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

series303.0ms (4.8%)

Counts

4 → 56

Calls

15 calls:

88.0ms	(log1p.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))	u2	inf
82.0ms	(log1p.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))))	u2	-inf
53.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))	u2	inf
51.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))	u2	-inf
6.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))	u1	inf

rewrite48.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

500×	`prod-diff_binary32`
211×	`expm1-udef_binary32`
211×	`log1p-udef_binary32`
136×	`add-sqr-sqrt_binary32`
130×	`expm1-log1p-u_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	51
1	282	47
2	3370	47

Stop Event

1×	node limit

Counts

4 → 70

simplify42.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-def_binary32`
522×	`associate-l_binary32`
486×	`associate-r_binary32`
404×	`cancel-sign-sub-inv_binary32`
171×	`associate-/r*_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	1713
1	436	1637
2	1472	1525

Stop Event

1×	node limit

Counts

126 → 115

prune142.0ms (2.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	110	5	115
Fresh	2	7	9
Picked	1	0	1
Done	1	1	2
Total	114	13	127

Error

0.1b

Counts

127 → 13

Alt Table

Status	Error	Program
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (+.f32 (cos.f32 (.f32 (PI.f32) u2)) (sin.f32 (.f32 (PI.f32) u2))) (-.f32 (cos.f32 (.f32 (PI.f32) u2)) (sin.f32 (.f32 (PI.f32) u2)))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (/.f32 (fma.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1) -1) (+.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))) 1) 1)))
✓	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (.f32 (pow.f32 (cbrt.f32 u2) 2) (.f32 (cbrt.f32 u2) (PI.f32))))))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (.f32 (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2))) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (fma.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) u2))) (sin.f32 (.f32 (PI.f32) u2)) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2))))
	8.5b	(.f32 (.f32 (cbrt.f32 (log1p.f32 u1)) (cbrt.f32 (sqrt.f32 (log1p.f32 u1)))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))
	2.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (pow.f32 (sqrt.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))) 2)))
	1.0b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 (sqrt.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (.f32 u2 2))) 1)) (sqrt.f32 (+.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))) 1)) -1))
	0.5b	(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cos.f32 (log.f32 (pow.f32 (pow.f32 (exp.f32 u2) 2) (PI.f32)))))))
	2.0b	(-.f32 (.f32 (fma.f32 (.f32 2/3 (pow.f32 u2 4)) (pow.f32 (PI.f32) 4) 1) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2 (.f32 (.f32 u2 u2) (pow.f32 (PI.f32) 2)) (.f32 4/45 (*.f32 (pow.f32 u2 6) (pow.f32 (PI.f32) 6))))))
	1.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (-.f32 (exp.f32 (log1p.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2)))))) 1)))
	8.5b	(.f32 (pow.f32 (pow.f32 (log1p.f32 u1) 1/4) 2) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (+.f32 1 (expm1.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2)))))))
	9.8b	(exp.f32 (log.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))

Compiler

Compiled 3222 to 2136 computations (33.7% saved)

regimes1.6s (24.8%)

Accuracy

Total 0.2b remaining (70%)

Threshold costs 0.2b (70%)

Counts

141 → 1

Compiler

Compiled 30318 to 24932 computations (17.8% saved)

simplify2.0ms (0%)

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	15	25
1	24	25
2	28	25
3	30	25

Stop Event

1×

saturated

end231.0ms (3.6%)

Stop Event

1×

fuel

Compiler

Compiled 378 to 294 computations (22.2% saved)

Iter	Nodes	Cost
0	30	88
1	59	84
2	98	84
3	124	84
4	155	84
5	191	84
6	231	84
7	319	84
8	490	84
9	531	84
10	585	84
11	635	84
12	726	84
13	773	84
14	791	84
15	794	84
0	3	3

Iter	Nodes	Cost
0	14	22
1	26	21
2	39	21
3	49	21
4	60	21
5	74	21
6	92	21
7	119	21
8	149	21
9	162	21
10	184	21
11	206	21
12	245	21
13	262	21
14	268	21
15	269	21

Iter	Nodes	Cost
0	30	88
1	59	84
2	98	84
3	124	84
4	155	84
5	191	84
6	231	84
7	319	84
8	490	84
9	531	84
10	585	84
11	635	84
12	726	84
13	773	84
14	791	84
15	794	84
0	3	3

Iter	Nodes	Cost
0	14	22
1	26	21
2	39	21
3	49	21
4	60	21
5	74	21
6	92	21
7	119	21
8	149	21
9	162	21
10	184	21
11	206	21
12	245	21
13	262	21
14	268	21
15	269	21

Details

analyze408.0ms (6.4%)

sample2.1s (32.5%)

preprocess36.0ms (0.6%)

simplify12.0ms (0.2%)

prune9.0ms (0.1%)

localize31.0ms (0.5%)

series166.0ms (2.6%)

rewrite55.0ms (0.9%)

simplify52.0ms (0.8%)

prune191.0ms (3%)

localize45.0ms (0.7%)

series159.0ms (2.5%)

rewrite50.0ms (0.8%)

simplify39.0ms (0.6%)

prune179.0ms (2.8%)

localize44.0ms (0.7%)

series221.0ms (3.5%)

rewrite50.0ms (0.8%)

simplify34.0ms (0.5%)

prune125.0ms (2%)

localize43.0ms (0.7%)

series303.0ms (4.8%)

rewrite48.0ms (0.8%)

simplify42.0ms (0.7%)

prune142.0ms (2.2%)

regimes1.6s (24.8%)

simplify2.0ms (0%)

end231.0ms (3.6%)

Profiling

Iter	Nodes	Cost
0	30	88
1	59	84
2	98	84
3	124	84
4	155	84
5	191	84
6	231	84
7	319	84
8	490	84
9	531	84
10	585	84
11	635	84
12	726	84
13	773	84
14	791	84
15	794	84
0	3	3

Iter	Nodes	Cost
0	14	22
1	26	21
2	39	21
3	49	21
4	60	21
5	74	21
6	92	21
7	119	21
8	149	21
9	162	21
10	184	21
11	206	21
12	245	21
13	262	21
14	268	21
15	269	21