Details

analyze438.0ms (5.6%)

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 (26.8%)

Results

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

Compiler

Compiled 78 to 62 computations (20.5% saved)

preprocess36.0ms (0.5%)

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)

simplify14.0ms (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

prune5.0ms (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
▶	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.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 (*.f32 2 (PI.f32)) u2)))

Compiler

Compiled 90 to 77 computations (14.4% saved)

localize33.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series160.0ms (2%)

Counts

4 → 32

Calls

15 calls:

64.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))	u2	inf
60.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))	u2	-inf
7.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))	u1	inf
5.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))	u1	0
4.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))	u1	-inf

rewrite64.0ms (0.8%)

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

simplify51.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

538×	`cancel-sign-sub-inv_binary32`
348×	`times-frac_binary32`
276×	`associate-*l/_binary32`
247×	`associate-/r*_binary32`
218×	`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

prune192.0ms (2.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	133	11	144
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	135	11	146

Error

0.1b

Counts

146 → 11

Alt Table

Status	Error	Program
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (exp.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))) 1))
	2.9b	(+.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) (.f32 (pow.f32 (PI.f32) 2) (.f32 (*.f32 u2 u2) -2)))))
	8.6b	(.f32 (.f32 (cbrt.f32 (log1p.f32 u1)) (cbrt.f32 (sqrt.f32 (log1p.f32 u1)))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))
	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 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1))) (fma.f32 (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) 1 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1))))
	8.7b	(pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))) 3)
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.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 (exp.f32 (log1p.f32 (*.f32 (PI.f32) u2))) 1))))
	10.5b	(exp.f32 (log.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
▶	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))

Compiler

Compiled 4916 to 3096 computations (37% saved)

localize67.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 2)
✓	0.3b	(-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))
	0.4b	(*.f32 (PI.f32) u2)
✓	0.6b	(pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)

series21.0ms (0.3%)

Counts

3 → 24

Calls

9 calls:

4.0ms	(-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))	u2	0
3.0ms	(pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)	u2	0
3.0ms	(-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))	u2	-inf
2.0ms	(-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))	u2	inf
2.0ms	(pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 2)	u2	0

rewrite109.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

897×	`expm1-log1p-u_binary32`
725×	`prod-diff_binary32`
204×	`egg-rr`
102×	`add-sqr-sqrt_binary32`
101×	`log1p-expm1-u_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	42
1	212	30
2	2620	30

Stop Event

1×	node limit

Counts

3 → 204

simplify39.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

838×	`fma-neg_binary32`
536×	`distribute-rgt-neg-in_binary32`
511×	`distribute-lft-neg-in_binary32`
367×	`unswap-sqr_binary32`
337×	`associate-r_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	53	489
1	166	477
2	530	471
3	2603	471

Stop Event

1×	node limit

Counts

228 → 231

prune555.0ms (7.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	255	6	261
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	260	12	272

Error

0.1b

Counts

272 → 12

Alt Table

Status	Error	Program
	8.6b	(.f32 (.f32 (cbrt.f32 (log1p.f32 u1)) (cbrt.f32 (sqrt.f32 (log1p.f32 u1)))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))
	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)) 4)) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 4))) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 4)) (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 4))) (fma.f32 (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 3)) (sin.f32 (.f32 (PI.f32) u2)) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
▶	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2))) (.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2))) (sin.f32 (*.f32 (PI.f32) u2))))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (pow.f32 (cos.f32 (log.f32 (pow.f32 (exp.f32 u2) (PI.f32)))) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (-.f32 (exp.f32 (log1p.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2))) 1) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 6) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 6)) (/.f32 1 (+.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 4)))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (log.f32 (pow.f32 (exp.f32 u2) (PI.f32)))) 2)))
	8.7b	(pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))) 3)
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (-.f32 (exp.f32 (log1p.f32 (*.f32 (PI.f32) u2))) 1))))
	2.9b	(+.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) (.f32 (pow.f32 (PI.f32) 2) (.f32 (*.f32 u2 u2) -2)))))

Compiler

Compiled 11660 to 4380 computations (62.4% saved)

localize54.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2))) (.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2))) (sin.f32 (.f32 (PI.f32) u2)))))
	0.4b	(*.f32 (PI.f32) u2)
✓	0.4b	(.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2))) (.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2))) (sin.f32 (*.f32 (PI.f32) u2))))
✓	0.4b	(.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2))) (sin.f32 (*.f32 (PI.f32) u2)))

series27.0ms (0.3%)

Counts

3 → 32

Calls

9 calls:

5.0ms	(.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2))) (sin.f32 (*.f32 (PI.f32) u2)))	u2	0
4.0ms	(.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2))) (sin.f32 (*.f32 (PI.f32) u2)))	u2	-inf
3.0ms	(-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2))) (.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2))) (sin.f32 (.f32 (PI.f32) u2)))))	u2	0
3.0ms	(.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2))) (sin.f32 (*.f32 (PI.f32) u2)))	u2	inf
3.0ms	(.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2))) (.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2))) (sin.f32 (*.f32 (PI.f32) u2))))	u2	0

rewrite81.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

552×	`log-prod_binary32`
254×	`fma-def_binary32`
200×	`expm1-udef_binary32`
200×	`log1p-udef_binary32`
194×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	62
1	255	30
2	3090	30

Stop Event

1×	node limit

Counts

3 → 194

simplify38.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

662×	`fma-neg_binary32`
493×	`distribute-rgt-neg-in_binary32`
488×	`distribute-lft-neg-in_binary32`
373×	`unswap-sqr_binary32`
314×	`associate-r_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	59	584
1	166	576
2	472	554
3	2263	554

Stop Event

1×	node limit

Counts

226 → 213

prune657.0ms (8.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	269	4	273
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	271	14	285

Error

0.1b

Counts

285 → 14

Alt Table

Status	Error	Program
	8.6b	(.f32 (.f32 (cbrt.f32 (log1p.f32 u1)) (cbrt.f32 (sqrt.f32 (log1p.f32 u1)))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))
	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)) 4)) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 4))) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 4)) (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 4))) (fma.f32 (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 3)) (sin.f32 (.f32 (PI.f32) u2)) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (pow.f32 (cos.f32 (log.f32 (pow.f32 (exp.f32 u2) (PI.f32)))) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (-.f32 (exp.f32 (log1p.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2))) 1) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 6) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 6)) (/.f32 1 (+.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 4)))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (log.f32 (pow.f32 (exp.f32 u2) (PI.f32)))) 2)))
	8.7b	(pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))) 3)
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (pow.f32 (cbrt.f32 (sin.f32 (*.f32 (PI.f32) u2))) 2) 3)))
▶	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 (.f32 (neg.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2)))) (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2)))) (sin.f32 (.f32 (PI.f32) u2)) (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)))
	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (+.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (cbrt.f32 (exp.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))))) (log.f32 (cbrt.f32 (exp.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 (-.f32 (exp.f32 (log1p.f32 (*.f32 (PI.f32) u2))) 1))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (/.f32 1 (/.f32 1 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))))
	2.9b	(+.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) (.f32 (pow.f32 (PI.f32) 2) (.f32 (*.f32 u2 u2) -2)))))

Compiler

Compiled 9349 to 3829 computations (59% saved)

localize60.0ms (0.8%)

Local error

Found 4 expressions with local error:

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

series14.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

4.0ms	(fma.f32 (.f32 (neg.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2)))) (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2)))) (sin.f32 (.f32 (PI.f32) u2)) (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 2))	u2	0
3.0ms	(fma.f32 (.f32 (neg.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2)))) (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2)))) (sin.f32 (.f32 (PI.f32) u2)) (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 2))	u2	-inf
3.0ms	(fma.f32 (.f32 (neg.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2)))) (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2)))) (sin.f32 (.f32 (PI.f32) u2)) (pow.f32 (cos.f32 (*.f32 (PI.f32) u2)) 2))	u2	inf
2.0ms	(.f32 (neg.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2)))) (sqrt.f32 (sin.f32 (*.f32 (PI.f32) u2))))	u2	0
1.0ms	(.f32 (neg.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2)))) (sqrt.f32 (sin.f32 (*.f32 (PI.f32) u2))))	u2	-inf

rewrite47.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

826×	`log1p-expm1-u_binary32`
826×	`expm1-log1p-u_binary32`
302×	`prod-diff_binary32`
118×	`add-sqr-sqrt_binary32`
109×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	37
1	244	29
2	2894	29

Stop Event

1×	node limit

Counts

2 → 40

simplify31.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

737×	`fma-neg_binary32`
440×	`distribute-rgt-neg-in_binary32`
427×	`distribute-lft-neg-in_binary32`
396×	`associate-r_binary32`
375×	`associate-l_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	458
1	189	454
2	559	450
3	2639	450

Stop Event

1×	node limit

Counts

64 → 60

prune370.0ms (4.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	148	14	162

Error

0.1b

Counts

162 → 14

Alt Table

Status	Error	Program
	8.6b	(.f32 (.f32 (cbrt.f32 (log1p.f32 u1)) (cbrt.f32 (sqrt.f32 (log1p.f32 u1)))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))
	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)) 4)) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 4))) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 4)) (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 4))) (fma.f32 (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 3)) (sin.f32 (.f32 (PI.f32) u2)) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (pow.f32 (cos.f32 (log.f32 (pow.f32 (exp.f32 u2) (PI.f32)))) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (-.f32 (exp.f32 (log1p.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2))) 1) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 6) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 6)) (/.f32 1 (+.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 4)))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (log.f32 (pow.f32 (exp.f32 u2) (PI.f32)))) 2)))
	8.7b	(pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))) 3)
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (pow.f32 (cbrt.f32 (sin.f32 (*.f32 (PI.f32) u2))) 2) 3)))
✓	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 (.f32 (neg.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2)))) (sqrt.f32 (sin.f32 (.f32 (PI.f32) u2)))) (sin.f32 (.f32 (PI.f32) u2)) (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)))
	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (+.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (cbrt.f32 (exp.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))))) (log.f32 (cbrt.f32 (exp.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 (-.f32 (exp.f32 (log1p.f32 (*.f32 (PI.f32) u2))) 1))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (/.f32 1 (/.f32 1 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))))
	2.9b	(+.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) (.f32 (pow.f32 (PI.f32) 2) (.f32 (*.f32 u2 u2) -2)))))

Compiler

Compiled 4868 to 1664 computations (65.8% saved)

regimes2.3s (29.7%)

Accuracy

Total 0.2b remaining (70.4%)

Threshold costs 0.2b (70.4%)

Counts

195 → 1

Compiler

Compiled 56430 to 40794 computations (27.7% 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

end234.0ms (3%)

Stop Event

1×

fuel

Compiler

Compiled 427 to 318 computations (25.5% 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

analyze438.0ms (5.6%)

sample2.1s (26.8%)

preprocess36.0ms (0.5%)

simplify14.0ms (0.2%)

prune5.0ms (0.1%)

localize33.0ms (0.4%)

series160.0ms (2%)

rewrite64.0ms (0.8%)

simplify51.0ms (0.7%)

prune192.0ms (2.5%)

localize67.0ms (0.9%)

series21.0ms (0.3%)

rewrite109.0ms (1.4%)

simplify39.0ms (0.5%)

prune555.0ms (7.1%)

localize54.0ms (0.7%)

series27.0ms (0.3%)

rewrite81.0ms (1%)

simplify38.0ms (0.5%)

prune657.0ms (8.4%)

localize60.0ms (0.8%)

series14.0ms (0.2%)

rewrite47.0ms (0.6%)

simplify31.0ms (0.4%)

prune370.0ms (4.7%)

regimes2.3s (29.7%)

simplify2.0ms (0%)

end234.0ms (3%)

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