Details

analyze178.0ms (3.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
43.7%	43.7%	12.6%	6
53.1%	31.2%	15.7%	7
59.3%	18.7%	22%	8
62.4%	14%	23.5%	9
64.8%	8.6%	26.6%	10
66%	6.6%	27.4%	11
66.9%	4.1%	29%	12
67.4%	3.2%	29.4%	13
67.9%	2%	30.1%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample31.0ms (0.7%)

Algorithm

1×

intervals

Results

15.0ms	236×	body	128	valid
3.0ms	6×	body	1024	valid
2.0ms	7×	body	512	valid
1.0ms	1×	body	2048	valid
1.0ms	6×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 25 to 19 computations (24% saved)

simplify98.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

837×	`fma-def_binary64`
741×	`fabs-mul_binary64`
531×	`fabs-div_binary64`
469×	`swap-sqr_binary64`
420×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	19	11
2	28	11
3	45	11
4	59	11
5	89	11
6	120	11
7	148	11
8	188	11
9	201	11
10	231	11
11	257	11
12	336	11
13	544	11
14	967	11
15	2930	11
16	3463	11
17	3600	11
18	3896	11
19	4820	11
20	4969	11

prune3.0ms (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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

Compiler

Compiled 36 to 22 computations (38.9% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 x)
✓	0.0b	(log1p.f64 (exp.f64 x))
✓	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

series287.0ms (6.4%)

Counts

3 → 40

Calls

3 calls:

198.0ms	(log1p.f64 (exp.f64 x))
88.0ms	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
2.0ms	(exp.f64 x)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-log-exp_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
4×	`expm1-log1p-u_binary64`

Counts

3 → 45

Calls

3 calls:

2.0ms	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
1.0ms	(exp.f64 x)
0.0ms	(log1p.f64 (exp.f64 x))

simplify90.0ms (2%)

Algorithm

1×	egg-herbie

Rules

398×	`unswap-sqr_binary64`
335×	`*-commutative_binary64`
298×	`cancel-sign-sub-inv_binary64`
285×	`unsub-neg_binary64`
258×	`fma-def_binary64`

Counts

85 → 78

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	97	896
1	214	842
2	525	810
3	1745	807
4	3547	807
5	4797	801
6	5090	801

prune92.0ms (2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	3	79

Error

Counts

79 → 3

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (log1p.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 3))) (*.f64 x y))
	16.3b	(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3)) (fma.f64 x (.f64 y (fma.f64 x y (log1p.f64 (exp.f64 x)))) (pow.f64 (sqrt.f64 (log1p.f64 (exp.f64 x))) 4)))
	25.7b	(log.f64 (/.f64 (+.f64 1 (exp.f64 x)) (exp.f64 (*.f64 x y))))

Compiler

Compiled 1084 to 435 computations (59.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 3)))
✓	0.0b	(cbrt.f64 (pow.f64 (exp.f64 x) 3))
✓	0.0b	(-.f64 (log1p.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 3))) (*.f64 x y))
✓	0.0b	(pow.f64 (exp.f64 x) 3)

series359.0ms (7.9%)

Counts

4 → 52

Calls

4 calls:

267.0ms	(log1p.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 3)))
84.0ms	(-.f64 (log1p.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 3))) (*.f64 x y))
6.0ms	(pow.f64 (exp.f64 x) 3)
2.0ms	(cbrt.f64 (pow.f64 (exp.f64 x) 3))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`cbrt-prod_binary64`
7×	`add-log-exp_binary64`

Counts

4 → 83

Calls

4 calls:

2.0ms	(-.f64 (log1p.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 3))) (*.f64 x y))
2.0ms	(pow.f64 (exp.f64 x) 3)
2.0ms	(cbrt.f64 (pow.f64 (exp.f64 x) 3))
0.0ms	(log1p.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 3)))

simplify94.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

559×	`associate-l_binary64`
458×	`associate-r_binary64`
349×	`fma-def_binary64`
290×	`fma-neg_binary64`
268×	`exp-prod_binary64`

Counts

135 → 139

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	144	1262
1	300	1206
2	802	1155
3	3605	1153
4	4935	1153
5	4902	1153

prune93.0ms (2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	139	3	142

Error

Counts

142 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (log1p.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 3))) (*.f64 x y))
▶	16.3b	(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3)) (fma.f64 x (.f64 y (fma.f64 x y (log1p.f64 (exp.f64 x)))) (pow.f64 (sqrt.f64 (log1p.f64 (exp.f64 x))) 4)))
	25.7b	(log.f64 (/.f64 (+.f64 1 (exp.f64 x)) (exp.f64 (*.f64 x y))))

Compiler

Compiled 2156 to 1158 computations (46.3% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(pow.f64 (log1p.f64 (exp.f64 x)) 3)
✓	0.8b	(pow.f64 (sqrt.f64 (log1p.f64 (exp.f64 x))) 4)
✓	3.2b	(fma.f64 x (*.f64 y (fma.f64 x y (log1p.f64 (exp.f64 x)))) (pow.f64 (sqrt.f64 (log1p.f64 (exp.f64 x))) 4))
✓	13.5b	(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3)) (fma.f64 x (.f64 y (fma.f64 x y (log1p.f64 (exp.f64 x)))) (pow.f64 (sqrt.f64 (log1p.f64 (exp.f64 x))) 4)))

series746.0ms (16.5%)

Counts

4 → 72

Calls

4 calls:

277.0ms	(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3)) (fma.f64 x (.f64 y (fma.f64 x y (log1p.f64 (exp.f64 x)))) (pow.f64 (sqrt.f64 (log1p.f64 (exp.f64 x))) 4)))
216.0ms	(pow.f64 (sqrt.f64 (log1p.f64 (exp.f64 x))) 4)
207.0ms	(pow.f64 (log1p.f64 (exp.f64 x)) 3)
46.0ms	(fma.f64 x (*.f64 y (fma.f64 x y (log1p.f64 (exp.f64 x)))) (pow.f64 (sqrt.f64 (log1p.f64 (exp.f64 x))) 4))

rewrite34.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`add-sqr-sqrt_binary64`
39×	`times-frac_binary64`
36×	`*-un-lft-identity_binary64`
32×	`difference-of-squares_binary64`
28×	`add-cube-cbrt_binary64`

Counts

4 → 132

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3)) (fma.f64 x (.f64 y (fma.f64 x y (log1p.f64 (exp.f64 x)))) (pow.f64 (sqrt.f64 (log1p.f64 (exp.f64 x))) 4)))
2.0ms	(pow.f64 (sqrt.f64 (log1p.f64 (exp.f64 x))) 4)
1.0ms	(pow.f64 (log1p.f64 (exp.f64 x)) 3)
0.0ms	(fma.f64 x (*.f64 y (fma.f64 x y (log1p.f64 (exp.f64 x)))) (pow.f64 (sqrt.f64 (log1p.f64 (exp.f64 x))) 4))

simplify229.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

353×	`unswap-sqr_binary64`
270×	`fma-neg_binary64`
245×	`distribute-rgt-in_binary64`
234×	`fma-def_binary64`
179×	`exp-prod_binary64`

Counts

204 → 220

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	295	7554
1	709	6976
2	2210	6701
3	4193	6698
4	4970	6698
5	4966	6698

prune152.0ms (3.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	220	3	223

Error

Counts

223 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (log1p.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 3))) (*.f64 x y))
✓	16.3b	(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3)) (fma.f64 x (.f64 y (fma.f64 x y (log1p.f64 (exp.f64 x)))) (pow.f64 (sqrt.f64 (log1p.f64 (exp.f64 x))) 4)))
▶	25.7b	(log.f64 (/.f64 (+.f64 1 (exp.f64 x)) (exp.f64 (*.f64 x y))))

Compiler

Compiled 9147 to 3665 computations (59.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 x))
✓	0.0b	(exp.f64 (*.f64 x y))
✓	0.0b	(/.f64 (+.f64 1 (exp.f64 x)) (exp.f64 (*.f64 x y)))
✓	1.3b	(log.f64 (/.f64 (+.f64 1 (exp.f64 x)) (exp.f64 (*.f64 x y))))

series621.0ms (13.7%)

Counts

4 → 76

Calls

4 calls:

592.0ms	(log.f64 (/.f64 (+.f64 1 (exp.f64 x)) (exp.f64 (*.f64 x y))))
23.0ms	(/.f64 (+.f64 1 (exp.f64 x)) (exp.f64 (*.f64 x y)))
4.0ms	(exp.f64 (*.f64 x y))
2.0ms	(+.f64 1 (exp.f64 x))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
22×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
16×	`log-prod_binary64`

Counts

4 → 93

Calls

4 calls:

5.0ms	(/.f64 (+.f64 1 (exp.f64 x)) (exp.f64 (*.f64 x y)))
4.0ms	(log.f64 (/.f64 (+.f64 1 (exp.f64 x)) (exp.f64 (*.f64 x y))))
3.0ms	(exp.f64 (*.f64 x y))
2.0ms	(+.f64 1 (exp.f64 x))

simplify115.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

373×	`cancel-sign-sub-inv_binary64`
355×	`fma-neg_binary64`
203×	`sub-neg_binary64`
195×	`fma-def_binary64`
181×	`unswap-sqr_binary64`

Counts

169 → 183

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	259	3365
1	760	3210
2	2824	3073
3	4559	3041
4	5013	3041

prune96.0ms (2.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	183	3	186

Error

Counts

186 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (log1p.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 3))) (*.f64 x y))
✓	16.3b	(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3)) (fma.f64 x (.f64 y (fma.f64 x y (log1p.f64 (exp.f64 x)))) (pow.f64 (sqrt.f64 (log1p.f64 (exp.f64 x))) 4)))
✓	25.7b	(log.f64 (/.f64 (+.f64 1 (exp.f64 x)) (exp.f64 (*.f64 x y))))

Compiler

Compiled 4033 to 1998 computations (50.5% saved)

regimes160.0ms (3.5%)

Accuracy

Total -0.0b remaining (-0.9%)

Threshold costs -0.0b (-0.9%)

Counts

56 → 1

Compiler

Compiled 2363 to 1714 computations (27.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
5×	`*-commutative_binary64`
5×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	22	23
2	34	23
3	41	23
4	45	23
5	46	23
6	46	23

end1.0ms (0%)

Compiler: Compiled 17 to 12 computations (29.4% saved)

sample965.0ms (21.3%)

Algorithm

1×

intervals

Results

457.0ms	7408×	body	128	valid
90.0ms	188×	body	1024	valid
62.0ms	239×	body	512	valid
25.0ms	164×	body	256	valid
3.0ms	50×	body	128	invalid
1.0ms	1×	body	2048	valid
1.0ms	9×	body	128	overflowed

Compiler

Compiled 85 to 58 computations (31.8% saved)

Details

analyze178.0ms (3.9%)

sample31.0ms (0.7%)

simplify98.0ms (2.2%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series287.0ms (6.4%)

rewrite5.0ms (0.1%)

simplify90.0ms (2%)

prune92.0ms (2%)

localize8.0ms (0.2%)

series359.0ms (7.9%)

rewrite10.0ms (0.2%)

simplify94.0ms (2.1%)

prune93.0ms (2%)

localize18.0ms (0.4%)

series746.0ms (16.5%)

rewrite34.0ms (0.7%)

simplify229.0ms (5.1%)

prune152.0ms (3.4%)

localize9.0ms (0.2%)

series621.0ms (13.7%)

rewrite19.0ms (0.4%)

simplify115.0ms (2.5%)

prune96.0ms (2.1%)

regimes160.0ms (3.5%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample965.0ms (21.3%)

Profiling