Details

analyze101.0ms (1.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	1.5%	98.5%	0
0%	1.5%	98.5%	1
0%	1.5%	98.5%	2
0.8%	0.8%	98.5%	3
0.8%	0.8%	98.5%	4
1.2%	0.4%	98.5%	5
1.2%	0.4%	98.5%	6
1.4%	0.2%	98.5%	7
1.4%	0.2%	98.5%	8
1.4%	0.1%	98.5%	9
1.4%	0.1%	98.5%	10
1.5%	0%	98.5%	11
1.5%	0%	98.5%	12
1.5%	0%	98.5%	13
1.5%	0%	98.5%	14

Compiler

Compiled 27 to 21 computations (22.2% saved)

sample1.5s (27.5%)

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 54 to 42 computations (22.2% saved)

preprocess116.0ms (2.1%)

Algorithm

2×	egg-herbie

Rules

870×	`fma-neg_binary32`
458×	`fma-def_binary32`
424×	`distribute-rgt-in_binary32`
319×	`unsub-neg_binary32`
236×	`distribute-lft-in_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	28
1	38	22
2	71	22
3	124	22
4	168	22
5	229	22
6	300	22
7	411	22
8	688	22
9	961	22
10	1098	22
11	1295	22
12	1509	22
13	1759	22
14	1826	22
15	1856	22
16	1935	22
17	2367	22
18	3640	22
19	3914	22
20	4066	22
21	4096	22
22	4116	22
23	4116	22
24	4525	22
25	4742	22
26	4782	22
27	4806	22
28	4822	22
29	4822	22
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify18.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

175×	`fma-neg_binary32`
152×	`fma-def_binary32`
46×	`cancel-sign-sub-inv_binary32`
46×	`sub-neg_binary32`
30×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	24	11
2	41	11
3	70	11
4	97	11
5	127	11
6	167	11
7	241	11
8	359	11
9	435	11
10	511	11
11	603	11
12	741	11
13	853	11
14	866	11

Stop Event

1×

saturated

Counts

1 → 2

prune8.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))

Compiler

Compiled 37 to 29 computations (21.6% saved)

localize17.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f32 (*.f32 u -4))
✓	0.2b	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))

series244.0ms (4.4%)

Counts

2 → 36

Calls

9 calls:

98.0ms	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))	s	0
69.0ms	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))	s	inf
68.0ms	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))	s	-inf
4.0ms	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))	u	-inf
1.0ms	(.f32 (log1p.f32 (.f32 u -4)) (neg.f32 s))	u	inf

rewrite38.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

591×	`expm1-log1p-u_binary32`
590×	`log1p-expm1-u_binary32`
334×	`log-prod_binary32`
143×	`prod-diff_binary32`
125×	`expm1-udef_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	162	15
2	1949	15

Stop Event

1×	node limit

Counts

2 → 42

simplify37.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

836×	`fma-neg_binary32`
526×	`fma-def_binary32`
364×	`sub-neg_binary32`
212×	`associate-+l+_binary32`
186×	`unsub-neg_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	106	726
1	336	675
2	1065	632
3	3590	624

Stop Event

1×	node limit

Counts

78 → 91

prune60.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	83	8	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	8	92

Error

0.1b

Counts

92 → 8

Alt Table

Status	Error	Program
	12.1b	(.f32 (-.f32 (log1p.f32 (pow.f32 (.f32 u -4) 3)) (log.f32 (+.f32 1 (-.f32 (.f32 (.f32 u u) 16) (*.f32 u -4))))) (neg.f32 s))
	2.4b	(.f32 (neg.f32 (+.f32 (.f32 64 (pow.f32 u 4)) (+.f32 (.f32 64/3 (pow.f32 u 3)) (+.f32 (.f32 8 (pow.f32 u 2)) (*.f32 4 u))))) (neg.f32 s))
	2.3b	(+.f32 (.f32 s (fma.f32 4 u (.f32 64 (pow.f32 u 4)))) (.f32 s (.f32 (.f32 u u) (+.f32 8 (.f32 u 64/3)))))
	2.4b	(.f32 (fma.f32 u (-.f32 -4 (.f32 u 8)) (fma.f32 (pow.f32 u 4) -64 (*.f32 (pow.f32 u 3) -64/3))) (neg.f32 s))
▶	0.2b	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 3)) (neg.f32 s))
	2.4b	(+.f32 (.f32 8 (.f32 s (pow.f32 u 2))) (+.f32 (.f32 64/3 (.f32 s (pow.f32 u 3))) (+.f32 (.f32 64 (.f32 s (pow.f32 u 4))) (.f32 4 (.f32 s u)))))
	11.4b	(*.f32 (log.f32 (fma.f32 u -4 1)) (neg.f32 s))
	0.7b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))

Compiler

Compiled 1640 to 1182 computations (27.9% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log1p.f32 (*.f32 u -4))
✓	0.1b	(cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 3))
✓	0.2b	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 3)) (neg.f32 s))
✓	0.6b	(pow.f32 (log1p.f32 (*.f32 u -4)) 3)

series298.0ms (5.3%)

Counts

3 → 48

Calls

12 calls:

106.0ms	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 3)) (neg.f32 s))	s	0
82.0ms	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 3)) (neg.f32 s))	s	-inf
76.0ms	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 3)) (neg.f32 s))	s	inf
18.0ms	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 3)) (neg.f32 s))	u	0
5.0ms	(pow.f32 (log1p.f32 (*.f32 u -4)) 3)	u	-inf

rewrite50.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

758×	`expm1-log1p-u_binary32`
757×	`log1p-expm1-u_binary32`
143×	`prod-diff_binary32`
99×	`add-sqr-sqrt_binary32`
93×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	223	24
2	2449	24

Stop Event

1×	node limit

Counts

3 → 59

simplify57.0ms (1%)

Algorithm

1×	egg-herbie

Rules

441×	`fma-def_binary32`
434×	`times-frac_binary32`
339×	`associate-+r+_binary32`
272×	`sub-neg_binary32`
252×	`+-commutative_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	287	1975
1	999	1880
2	3830	1866

Stop Event

1×	node limit

Counts

107 → 130

prune147.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	172	2	174
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	173	9	182

Error

0.1b

Counts

182 → 9

Alt Table

Status	Error	Program
	2.4b	(.f32 (fma.f32 -64 (pow.f32 u 4) (fma.f32 (pow.f32 u 3) -64/3 (fma.f32 u -4 (.f32 (*.f32 u u) -8)))) (neg.f32 s))
	12.1b	(.f32 (-.f32 (log1p.f32 (pow.f32 (.f32 u -4) 3)) (log.f32 (+.f32 1 (-.f32 (.f32 (.f32 u u) 16) (*.f32 u -4))))) (neg.f32 s))
	2.3b	(+.f32 (.f32 s (fma.f32 4 u (.f32 64 (pow.f32 u 4)))) (.f32 s (.f32 (.f32 u u) (+.f32 8 (.f32 u 64/3)))))
	2.4b	(.f32 (fma.f32 u (-.f32 -4 (.f32 u 8)) (fma.f32 (pow.f32 u 4) -64 (*.f32 (pow.f32 u 3) -64/3))) (neg.f32 s))
	1.5b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (pow.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 2) 1/3)) (neg.f32 s))
✓	0.2b	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 3)) (neg.f32 s))
	2.4b	(+.f32 (.f32 8 (.f32 s (pow.f32 u 2))) (+.f32 (.f32 64/3 (.f32 s (pow.f32 u 3))) (+.f32 (.f32 64 (.f32 s (pow.f32 u 4))) (.f32 4 (.f32 s u)))))
	11.4b	(*.f32 (log.f32 (fma.f32 u -4 1)) (neg.f32 s))
▶	0.7b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))

Compiler

Compiled 4494 to 3369 computations (25% saved)

localize26.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log1p.f32 (*.f32 u -4))
✓	0.1b	(cbrt.f32 (log1p.f32 (*.f32 u -4)))
✓	0.2b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))
✓	0.7b	(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 3)

series275.0ms (4.9%)

Counts

3 → 40

Calls

12 calls:

96.0ms	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))	s	0
70.0ms	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))	s	inf
69.0ms	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))	s	-inf
10.0ms	(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 3)	u	-inf
8.0ms	(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 3)	u	inf

rewrite44.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

760×	`expm1-log1p-u_binary32`
759×	`log1p-expm1-u_binary32`
143×	`prod-diff_binary32`
99×	`add-sqr-sqrt_binary32`
93×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	224	23
2	2461	23

Stop Event

1×	node limit

Counts

3 → 59

simplify48.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

310×	`times-frac_binary32`
242×	`cancel-sign-sub-inv_binary32`
217×	`associate-*l/_binary32`
198×	`fma-def_binary32`
194×	`associate-*r/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	1869
1	601	1682
2	2015	1645

Stop Event

1×	node limit

Counts

99 → 116

prune125.0ms (2.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	157	3	160
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	157	12	169

Error

0.0b

Counts

169 → 12

Alt Table

Status	Error	Program
	1.5b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (pow.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 2) 1/3)) (neg.f32 s))
▶	1.0b	(.f32 (.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) 2) (.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2))) (neg.f32 s))
	2.4b	(.f32 (fma.f32 -64 (pow.f32 u 4) (fma.f32 (pow.f32 u 3) -64/3 (fma.f32 u -4 (.f32 (*.f32 u u) -8)))) (neg.f32 s))
	12.1b	(.f32 (-.f32 (log1p.f32 (pow.f32 (.f32 u -4) 3)) (log.f32 (+.f32 1 (-.f32 (.f32 (.f32 u u) 16) (*.f32 u -4))))) (neg.f32 s))
	3.0b	(fma.f32 8 (.f32 u (.f32 u s)) (.f32 s (+.f32 (.f32 u 4) (*.f32 64/3 (pow.f32 u 3)))))
	1.2b	(.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) 2) 3) (cbrt.f32 (log1p.f32 (.f32 u -4)))) (neg.f32 s))
	2.3b	(+.f32 (.f32 s (fma.f32 4 u (.f32 64 (pow.f32 u 4)))) (.f32 s (.f32 (.f32 u u) (+.f32 8 (.f32 u 64/3)))))
	2.4b	(.f32 (fma.f32 u (-.f32 -4 (.f32 u 8)) (fma.f32 (pow.f32 u 4) -64 (*.f32 (pow.f32 u 3) -64/3))) (neg.f32 s))
✓	0.2b	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 3)) (neg.f32 s))
	2.4b	(+.f32 (.f32 8 (.f32 s (pow.f32 u 2))) (+.f32 (.f32 64/3 (.f32 s (pow.f32 u 3))) (+.f32 (.f32 64 (.f32 s (pow.f32 u 4))) (.f32 4 (.f32 s u)))))
	11.4b	(*.f32 (log.f32 (fma.f32 u -4 1)) (neg.f32 s))
✓	0.7b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))

Compiler

Compiled 4094 to 3192 computations (22% saved)

localize47.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) 2) (.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2)))
✓	0.3b	(.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2))
✓	0.5b	(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2)
✓	0.5b	(pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) 2)

series705.0ms (12.6%)

Counts

4 → 44

Calls

12 calls:

336.0ms	(.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2))	u	-inf
325.0ms	(.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2))	u	inf
8.0ms	(pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) 2)	u	-inf
8.0ms	(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2)	u	-inf
7.0ms	(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 2)	u	inf

rewrite50.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

787×	`expm1-log1p-u_binary32`
786×	`log1p-expm1-u_binary32`
143×	`prod-diff_binary32`
99×	`add-sqr-sqrt_binary32`
98×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	68
1	238	51
2	2499	51

Stop Event

1×	node limit

Counts

4 → 68

simplify235.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

551×	`*-commutative_binary32`
313×	`+-commutative_binary32`
303×	`fma-def_binary32`
284×	`associate-+r+_binary32`
218×	`associate-r_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1338	20805
1	4511	20031

Stop Event

1×	node limit

Counts

112 → 155

prune608.0ms (10.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	153	2	155
Fresh	4	5	9
Picked	1	0	1
Done	0	2	2
Total	158	9	167

Error

0.0b

Counts

167 → 9

Alt Table

Status	Error	Program
	0.6b	(.f32 (.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) 2) (cbrt.f32 (.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (pow.f32 (log1p.f32 (.f32 u -4)) 2)))) (neg.f32 s))
	2.3b	(+.f32 (.f32 s (fma.f32 4 u (.f32 64 (pow.f32 u 4)))) (.f32 s (.f32 (.f32 u u) (+.f32 8 (.f32 u 64/3)))))
	2.4b	(.f32 (fma.f32 u (-.f32 -4 (.f32 u 8)) (fma.f32 (pow.f32 u 4) -64 (*.f32 (pow.f32 u 3) -64/3))) (neg.f32 s))
	1.5b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) (pow.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 2) 1/3)) (neg.f32 s))
	2.0b	(.f32 (.f32 (log.f32 (exp.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) 2))) (.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (.f32 u -4)))) (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 2))) (neg.f32 s))
✓	0.2b	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 (.f32 u -4)) 3)) (neg.f32 s))
	2.4b	(+.f32 (.f32 8 (.f32 s (pow.f32 u 2))) (+.f32 (.f32 64/3 (.f32 s (pow.f32 u 3))) (+.f32 (.f32 64 (.f32 s (pow.f32 u 4))) (.f32 4 (.f32 s u)))))
✓	0.7b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 u -4))) 3) (neg.f32 s))
	3.0b	(fma.f32 8 (.f32 u (.f32 u s)) (.f32 s (+.f32 (.f32 u 4) (*.f32 64/3 (pow.f32 u 3)))))

Compiler

Compiled 25512 to 21750 computations (14.7% saved)

regimes517.0ms (9.3%)

Accuracy

Total 0.1b remaining (71.8%)

Threshold costs 0.1b (71.8%)

Counts

74 → 1

Compiler

Compiled 9025 to 7212 computations (20.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary32`
3×	`+-commutative_binary32`
3×	`sub-neg_binary32`
3×	`neg-sub0_binary32`
3×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	19	16
2	27	16
3	33	16
4	36	16
5	37	16

Stop Event

1×

saturated

end150.0ms (2.7%)

Stop Event

1×

fuel

Compiler

Compiled 221 to 176 computations (20.4% saved)

Iter	Nodes	Cost
0	10	14
1	24	11
2	41	11
3	70	11
4	97	11
5	127	11
6	167	11
7	241	11
8	359	11
9	435	11
10	511	11
11	603	11
12	741	11
13	853	11
14	866	11

Iter	Nodes	Cost
0	10	14
1	24	11
2	41	11
3	70	11
4	97	11
5	127	11
6	167	11
7	241	11
8	359	11
9	435	11
10	511	11
11	603	11
12	741	11
13	853	11
14	866	11

Details

analyze101.0ms (1.8%)

sample1.5s (27.5%)

preprocess116.0ms (2.1%)

simplify18.0ms (0.3%)

prune8.0ms (0.1%)

localize17.0ms (0.3%)

series244.0ms (4.4%)

rewrite38.0ms (0.7%)

simplify37.0ms (0.7%)

prune60.0ms (1.1%)

localize25.0ms (0.4%)

series298.0ms (5.3%)

rewrite50.0ms (0.9%)

simplify57.0ms (1%)

prune147.0ms (2.6%)

localize26.0ms (0.5%)

series275.0ms (4.9%)

rewrite44.0ms (0.8%)

simplify48.0ms (0.9%)

prune125.0ms (2.2%)

localize47.0ms (0.8%)

series705.0ms (12.6%)

rewrite50.0ms (0.9%)

simplify235.0ms (4.2%)

prune608.0ms (10.9%)

regimes517.0ms (9.3%)

simplify2.0ms (0%)

end150.0ms (2.7%)

Profiling

Iter	Nodes	Cost
0	10	14
1	24	11
2	41	11
3	70	11
4	97	11
5	127	11
6	167	11
7	241	11
8	359	11
9	435	11
10	511	11
11	603	11
12	741	11
13	853	11
14	866	11