Details

analyze42.0ms (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)

sample783.0ms (24%)

Results

749.0ms	8256×	body	128	valid
2.0ms	30×	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

0.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.5b	(/.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))
✓	0.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series34.0ms (1%)

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:

6.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
3.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

simplify83.0ms (2.5%)

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

prune92.0ms (2.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	4	109

Error

Counts

109 → 4

Alt Table

Status	Error	Program
	11.3b	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (/.f64 a (+.f64 1 (exp.f64 b)))) (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)))
▶	0.5b	(log.f64 (exp.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
	0.9b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3))
	0.5b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 2319 to 883 computations (61.9% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))
	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	0.0b	(log.f64 (exp.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
	0.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series82.0ms (2.5%)

Counts

2 → 48

Calls

2 calls:

50.0ms	(exp.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))
31.0ms	(log.f64 (exp.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`exp-prod_binary64`
31×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
19×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`

Counts

2 → 60

Calls

2 calls:

7.0ms	(log.f64 (exp.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
5.0ms	(exp.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))

simplify85.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

402×	`associate-/l/_binary64`
252×	`cancel-sign-sub-inv_binary64`
210×	`distribute-rgt-in_binary64`
205×	`associate-/l*_binary64`
178×	`distribute-lft-in_binary64`

Counts

108 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	276	3424
1	742	3268
2	2784	3138
3	4982	3138

prune201.0ms (6.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	234	0	234
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	234	4	238

Error

Counts

238 → 4

Alt Table

Status	Error	Program
	11.3b	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (/.f64 a (+.f64 1 (exp.f64 b)))) (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)))
✓	0.5b	(log.f64 (exp.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
	0.9b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3))
▶	0.5b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 6842 to 2909 computations (57.5% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	0.0b	(log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
	0.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series711.0ms (21.8%)

Counts

2 → 48

Calls

2 calls:

680.0ms	(log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))
31.0ms	(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	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
0.0ms	(log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))

simplify81.0ms (2.5%)

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	3192
1	773	3027
2	3674	2850
3	5038	2850

prune169.0ms (5.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	175	4	179

Error

Counts

179 → 4

Alt Table

Status	Error	Program
	11.3b	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (/.f64 a (+.f64 1 (exp.f64 b)))) (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)))
✓	0.5b	(log.f64 (exp.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
▶	0.9b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3))
✓	0.5b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 6040 to 3112 computations (48.5% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 b) (exp.f64 a))
✓	0.0b	(pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3)
✓	0.4b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3))
✓	0.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a)))

series149.0ms (4.6%)

Counts

4 → 64

Calls

4 calls:

81.0ms	(pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3)
32.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a)))
31.0ms	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3))
6.0ms	(+.f64 (exp.f64 b) (exp.f64 a))

rewrite36.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`*-un-lft-identity_binary64`
60×	`times-frac_binary64`
48×	`add-sqr-sqrt_binary64`
48×	`add-cube-cbrt_binary64`
42×	`cbrt-prod_binary64`

Counts

4 → 164

Calls

4 calls:

9.0ms	(pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3)
7.0ms	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3))
5.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a)))
3.0ms	(+.f64 (exp.f64 b) (exp.f64 a))

simplify141.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

434×	`unswap-sqr_binary64`
198×	`sub-neg_binary64`
177×	`associate-/l*_binary64`
172×	`associate-+r+_binary64`
163×	`fma-def_binary64`

Counts

228 → 183

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	356	6521
1	1013	6054
2	3735	5934
3	5189	5934

prune152.0ms (4.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	183	4	187

Error

Counts

187 → 4

Alt Table

Status	Error	Program
	11.3b	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (/.f64 a (+.f64 1 (exp.f64 b)))) (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)))
✓	0.5b	(log.f64 (exp.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
✓	0.9b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3))
✓	0.5b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 5307 to 2512 computations (52.7% saved)

regimes294.0ms (9%)

Accuracy

Total 0.5b remaining (77.6%)

Threshold costs 0.5b (77.6%)

Counts

75 → 1

Compiler

Compiled 6221 to 4437 computations (28.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	14	20
2	13	20

end65.0ms (2%)

Compiler: Compiled 89 to 62 computations (30.3% saved)

Details

analyze42.0ms (1.3%)

sample783.0ms (24%)

simplify6.0ms (0.2%)

prune1.0ms (0%)

localize5.0ms (0.2%)

series34.0ms (1%)

rewrite11.0ms (0.4%)

simplify83.0ms (2.5%)

prune92.0ms (2.8%)

localize7.0ms (0.2%)

series82.0ms (2.5%)

rewrite18.0ms (0.5%)

simplify85.0ms (2.6%)

prune201.0ms (6.1%)

localize7.0ms (0.2%)

series711.0ms (21.8%)

rewrite2.0ms (0%)

simplify81.0ms (2.5%)

prune169.0ms (5.2%)

localize8.0ms (0.3%)

series149.0ms (4.6%)

rewrite36.0ms (1.1%)

simplify141.0ms (4.3%)

prune152.0ms (4.6%)

regimes294.0ms (9%)

simplify4.0ms (0.1%)

end65.0ms (2%)

Profiling