Details

analyze43.0ms (1.5%)

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)

sample828.0ms (28.5%)

Results

793.0ms	8256×	body	128	valid
4.0ms	31×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify6.0ms (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

1.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	1.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	1.7b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series34.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

30.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite11.0ms (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:

5.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
3.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

simplify91.0ms (3.1%)

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

prune105.0ms (3.6%)

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

0.6b

Counts

109 → 3

Alt Table

Status	Error	Program
▶	1.8b	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))
	13.7b	(/.f64 1 (+.f64 1 (exp.f64 b)))
	21.6b	(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))

Compiler

Compiled 2285 to 855 computations (62.6% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 b) (exp.f64 a))
✓	1.5b	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))
✓	1.7b	(/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a)))

series69.0ms (2.4%)

Counts

3 → 56

Calls

3 calls:

36.0ms	(/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a)))
28.0ms	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))
4.0ms	(+.f64 (exp.f64 b) (exp.f64 a))

rewrite37.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`*-un-lft-identity_binary64`
54×	`add-sqr-sqrt_binary64`
52×	`times-frac_binary64`
38×	`add-cube-cbrt_binary64`
35×	`sqrt-prod_binary64`

Counts

3 → 125

Calls

3 calls:

14.0ms	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))
7.0ms	(/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a)))
5.0ms	(+.f64 (exp.f64 b) (exp.f64 a))

simplify142.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

480×	`fma-neg_binary64`
329×	`associate-/l/_binary64`
271×	`cancel-sign-sub-inv_binary64`
183×	`sub-neg_binary64`
166×	`distribute-rgt-in_binary64`

Counts

181 → 178

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	275	4490
1	749	4258
2	2783	4168
3	4718	4168
4	4962	4168

prune115.0ms (3.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	178	3	181

Error

0.6b

Counts

181 → 3

Alt Table

Status	Error	Program
✓	1.8b	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))
▶	13.7b	(/.f64 1 (+.f64 1 (exp.f64 b)))
	21.6b	(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))

Compiler

Compiled 4904 to 1576 computations (67.9% 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 (0.3%)

Counts

2 → 8

Calls

2 calls:

7.0ms	(/.f64 1 (+.f64 1 (exp.f64 b)))
1.0ms	(+.f64 1 (exp.f64 b))

rewrite9.0ms (0.3%)

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:

4.0ms	(/.f64 1 (+.f64 1 (exp.f64 b)))
3.0ms	(+.f64 1 (exp.f64 b))

simplify70.0ms (2.4%)

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

prune64.0ms (2.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

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

Error

0.6b

Counts

78 → 3

Alt Table

Status	Error	Program
✓	1.8b	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))
▶	14.0b	(/.f64 1 (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 b)))))
	21.6b	(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))

Compiler

Compiled 947 to 687 computations (27.5% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (exp.f64 b))
✓	0.0b	(/.f64 1 (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 b)))))
✓	0.0b	(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 b))))
✓	0.8b	(log1p.f64 (+.f64 1 (exp.f64 b)))

series172.0ms (5.9%)

Counts

3 → 36

Calls

3 calls:

160.0ms	(log1p.f64 (+.f64 1 (exp.f64 b)))
9.0ms	(/.f64 1 (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 b)))))
2.0ms	(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 b))))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-exp-log_binary64`

Counts

3 → 55

Calls

3 calls:

2.0ms	(/.f64 1 (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 b)))))
0.0ms	(log1p.f64 (+.f64 1 (exp.f64 b)))
0.0ms	(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 b))))

simplify90.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1280×	`fma-neg_binary64`
597×	`fma-def_binary64`
454×	`unswap-sqr_binary64`
379×	`*-commutative_binary64`
332×	`cancel-sign-sub-inv_binary64`

Counts

91 → 108

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	1000
1	176	907
2	395	898
3	884	884
4	2051	884
5	3311	884
6	4761	884
7	4896	884

prune98.0ms (3.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	133	5	138

Error

0.6b

Counts

138 → 5

Alt Table

Status	Error	Program
✓	1.8b	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))
	14.2b	(/.f64 1 (expm1.f64 (*.f64 (sqrt.f64 (log1p.f64 (+.f64 1 (exp.f64 b)))) (sqrt.f64 (log1p.f64 (+.f64 1 (exp.f64 b)))))))
	14.8b	(/.f64 1 (expm1.f64 (.f64 (.f64 (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 b)))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 b))))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 b)))))))
✓	14.0b	(/.f64 1 (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 b)))))
	21.6b	(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))

Compiler

Compiled 1791 to 1386 computations (22.6% saved)

regimes799.0ms (27.5%)

Accuracy

Total 0.4b remaining (71%)

Threshold costs 0.4b (71%)

Counts

172 → 1

Compiler

Compiled 14714 to 10897 computations (25.9% 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

end84.0ms (2.9%)

Compiler: Compiled 111 to 81 computations (27% saved)

Details

analyze43.0ms (1.5%)

sample828.0ms (28.5%)

simplify6.0ms (0.2%)

prune1.0ms (0%)

localize5.0ms (0.2%)

series34.0ms (1.2%)

rewrite11.0ms (0.4%)

simplify91.0ms (3.1%)

prune105.0ms (3.6%)

localize10.0ms (0.3%)

series69.0ms (2.4%)

rewrite37.0ms (1.3%)

simplify142.0ms (4.9%)

prune115.0ms (3.9%)

localize4.0ms (0.1%)

series9.0ms (0.3%)

rewrite9.0ms (0.3%)

simplify70.0ms (2.4%)

prune64.0ms (2.2%)

localize7.0ms (0.2%)

series172.0ms (5.9%)

rewrite5.0ms (0.2%)

simplify90.0ms (3.1%)

prune98.0ms (3.4%)

regimes799.0ms (27.5%)

simplify2.0ms (0.1%)

end84.0ms (2.9%)

Profiling