Details

analyze49.0ms (1.3%)

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
25%	74.9%	0.1%	3
62.4%	37.5%	0.1%	4
68.7%	31.2%	0.1%	5
68.7%	18.7%	12.6%	6
68.7%	17.2%	14.1%	7
68.7%	10.1%	21.2%	8
68.7%	9%	22.3%	9
68.7%	5.3%	26%	10
68.7%	4.6%	26.7%	11
68.7%	2.7%	28.6%	12
68.7%	2.3%	29%	13
68.7%	1.4%	30%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample823.0ms (21.4%)

Results

793.0ms	8256×	body	128	valid
3.0ms	29×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	8	13
2	8	13

prune1.0ms (0%)

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

0.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	0.3b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series35.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

31.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
5×	`distribute-lft-out_binary64`

Counts

2 → 52

Calls

2 calls:

10.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
3.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

simplify85.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

806×	`fma-neg_binary64`
536×	`times-frac_binary64`
493×	`fma-def_binary64`
389×	`associate-/l*_binary64`
245×	`associate-/r*_binary64`

Counts

100 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	168	1981
1	449	1869
2	1403	1853
3	4915	1853
4	5640	1853

prune73.0ms (1.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	3	109

Error

0.2b

Counts

109 → 3

Alt Table

Status	Error	Program
	0.5b	(/.f64 (exp.f64 a) (log.f64 (*.f64 (exp.f64 (exp.f64 a)) (exp.f64 (exp.f64 b)))))
▶	0.3b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
	12.1b	(/.f64 1 (+.f64 1 (exp.f64 b)))

Compiler

Compiled 2263 to 847 computations (62.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	0.0b	(log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))
	0.3b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series737.0ms (19.2%)

Counts

2 → 48

Calls

2 calls:

705.0ms	(log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))
32.0ms	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))
0.0ms	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))

simplify80.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

357×	`times-frac_binary64`
337×	`cancel-sign-sub-inv_binary64`
229×	`associate-/r*_binary64`
225×	`unswap-sqr_binary64`
211×	`associate-/l*_binary64`

Counts

70 → 67

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	251	3189
1	773	3027
2	3674	2850
3	5038	2850

prune146.0ms (3.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	175	3	178

Error

0.2b

Counts

178 → 3

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 (exp.f64 a) (log.f64 (*.f64 (exp.f64 (exp.f64 a)) (exp.f64 (exp.f64 b)))))
✓	0.3b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
	12.1b	(/.f64 1 (+.f64 1 (exp.f64 b)))

Compiler

Compiled 5996 to 3082 computations (48.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (*.f64 (exp.f64 (exp.f64 a)) (exp.f64 (exp.f64 b))))
✓	0.0b	(exp.f64 (exp.f64 a))
✓	0.3b	(/.f64 (exp.f64 a) (log.f64 (*.f64 (exp.f64 (exp.f64 a)) (exp.f64 (exp.f64 b)))))
✓	0.4b	(*.f64 (exp.f64 (exp.f64 a)) (exp.f64 (exp.f64 b)))

series1.1s (28.9%)

Counts

4 → 76

Calls

4 calls:

574.0ms	(/.f64 (exp.f64 a) (log.f64 (*.f64 (exp.f64 (exp.f64 a)) (exp.f64 (exp.f64 b)))))
522.0ms	(log.f64 (*.f64 (exp.f64 (exp.f64 a)) (exp.f64 (exp.f64 b))))
11.0ms	(*.f64 (exp.f64 (exp.f64 a)) (exp.f64 (exp.f64 b)))
2.0ms	(exp.f64 (exp.f64 a))

rewrite23.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
21×	`pow1_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`times-frac_binary64`
18×	`add-cube-cbrt_binary64`

Counts

4 → 90

Calls

4 calls:

7.0ms	(/.f64 (exp.f64 a) (log.f64 (*.f64 (exp.f64 (exp.f64 a)) (exp.f64 (exp.f64 b)))))
5.0ms	(*.f64 (exp.f64 (exp.f64 a)) (exp.f64 (exp.f64 b)))
4.0ms	(log.f64 (*.f64 (exp.f64 (exp.f64 a)) (exp.f64 (exp.f64 b))))
1.0ms	(exp.f64 (exp.f64 a))

simplify109.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

935×	`fma-def_binary64`
370×	`times-frac_binary64`
320×	`fma-neg_binary64`
173×	`distribute-rgt-in_binary64`
161×	`distribute-lft-in_binary64`

Counts

166 → 189

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	240	2911
1	581	2668
2	1926	2612
3	4747	2610
4	4986	2610

prune118.0ms (3.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	189	3	192

Error

0.2b

Counts

192 → 3

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 (exp.f64 a) (log.f64 (*.f64 (exp.f64 (exp.f64 a)) (exp.f64 (exp.f64 b)))))
✓	0.3b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
▶	12.1b	(/.f64 1 (+.f64 1 (exp.f64 b)))

Compiler

Compiled 3849 to 1241 computations (67.8% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 b))
✓	0.0b	(/.f64 1 (+.f64 1 (exp.f64 b)))

series9.0ms (0.2%)

Counts

2 → 8

Calls

2 calls:

7.0ms	(/.f64 1 (+.f64 1 (exp.f64 b)))
2.0ms	(+.f64 1 (exp.f64 b))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
6×	`add-exp-log_binary64`

Counts

2 → 56

Calls

2 calls:

5.0ms	(/.f64 1 (+.f64 1 (exp.f64 b)))
2.0ms	(+.f64 1 (exp.f64 b))

simplify71.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

561×	`fma-neg_binary64`
525×	`fma-def_binary64`
498×	`unswap-sqr_binary64`
428×	`associate-+l+_binary64`
349×	`cancel-sign-sub-inv_binary64`

Counts

64 → 75

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	81	733
1	185	669
2	382	663
3	887	653
4	2169	653
5	3922	653
6	5318	653

prune57.0ms (1.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	75	3	78

Error

0.2b

Counts

78 → 3

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 (exp.f64 a) (log.f64 (*.f64 (exp.f64 (exp.f64 a)) (exp.f64 (exp.f64 b)))))
	12.4b	(/.f64 1 (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 b)))))
✓	0.3b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 905 to 661 computations (27% saved)

regimes204.0ms (5.3%)

Accuracy

Total 0.2b remaining (43.2%)

Threshold costs 0.2b (43.2%)

Counts

54 → 1

Compiler

Compiled 3608 to 2697 computations (25.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	12	15
2	17	15
3	19	15
4	20	15
5	20	15

end54.0ms (1.4%)

Compiler: Compiled 57 to 42 computations (26.3% saved)

Details

analyze49.0ms (1.3%)

sample823.0ms (21.4%)

simplify7.0ms (0.2%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series35.0ms (0.9%)

rewrite16.0ms (0.4%)

simplify85.0ms (2.2%)

prune73.0ms (1.9%)

localize9.0ms (0.2%)

series737.0ms (19.2%)

rewrite2.0ms (0%)

simplify80.0ms (2.1%)

prune146.0ms (3.8%)

localize9.0ms (0.2%)

series1.1s (28.9%)

rewrite23.0ms (0.6%)

simplify109.0ms (2.8%)

prune118.0ms (3.1%)

localize4.0ms (0.1%)

series9.0ms (0.2%)

rewrite10.0ms (0.2%)

simplify71.0ms (1.8%)

prune57.0ms (1.5%)

regimes204.0ms (5.3%)

simplify2.0ms (0.1%)

end54.0ms (1.4%)

Profiling