Details

analyze212.0ms (3.4%)

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
25%	74.9%	0.1%	4
50%	50%	0.1%	5
50%	37.5%	12.6%	6
50%	25%	25.1%	7
50%	18.7%	31.3%	8
50%	12.5%	37.6%	9
50%	9.4%	40.7%	10
50%	6.2%	43.8%	11
50%	4.7%	45.4%	12
50%	3.1%	46.9%	13
50%	2.3%	47.7%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample202.0ms (3.2%)

Algorithm

1×

intervals

Results

149.0ms	65×	body	1024	valid
15.0ms	17×	body	256	valid
9.0ms	31×	body	512	valid
8.0ms	139×	body	128	valid
3.0ms	4×	body	2048	valid
0.0ms	8×	body	128	overflowed

Compiler

Compiled 19 to 15 computations (21.1% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	8	10
2	8	10

prune2.0ms (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

30.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.5b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	4.3b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`log-prod_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 34

Calls

2 calls:

7.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
3.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

series795.0ms (12.8%)

Counts

2 → 48

Calls

2 calls:

775.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
20.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

simplify95.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

618×	`fma-neg_binary64`
418×	`associate-+l+_binary64`
392×	`fma-def_binary64`
238×	`times-frac_binary64`
229×	`associate-+r+_binary64`

Counts

82 → 120

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	123	1238
1	334	1183
2	1034	1155
3	4062	1151
4	4828	1151
5	4973	1151

prune44.0ms (0.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	119	2	121

Error

0.6b

Counts

121 → 2

Alt Table

Status	Error	Program
▶	1.2b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
✓	30.5b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 1305 to 592 computations (54.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite9.0ms (0.1%)

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:

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

series38.0ms (0.6%)

Counts

2 → 8

Calls

2 calls:

37.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
1.0ms	(+.f64 1 (exp.f64 a))

simplify68.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

795×	`fma-def_binary64`
766×	`times-frac_binary64`
380×	`associate-l_binary64`
309×	`associate-r_binary64`
305×	`associate-/l*_binary64`

Counts

60 → 85

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	101	816
1	240	750
2	571	740
3	1389	730
4	4215	730
5	5275	730

prune50.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	83	4	87

Error

0.6b

Counts

87 → 4

Alt Table

Status	Error	Program
▶	1.2b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))))
	2.0b	(+.f64 (log1p.f64 (exp.f64 a)) (.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (/.f64 (cbrt.f64 b) (+.f64 1 (exp.f64 a)))))
	27.4b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))
✓	30.5b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 1266 to 659 computations (47.9% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 b (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))))
	0.0b	(+.f64 1 (exp.f64 a))
✓	0.5b	(log1p.f64 (+.f64 1 (exp.f64 a)))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 40

Calls

2 calls:

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

series1.1s (17.1%)

Counts

2 → 36

Calls

2 calls:

807.0ms	(/.f64 b (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))))
259.0ms	(log1p.f64 (+.f64 1 (exp.f64 a)))

simplify82.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

738×	`fma-neg_binary64`
665×	`cancel-sign-sub-inv_binary64`
433×	`times-frac_binary64`
257×	`associate-r_binary64`
245×	`associate-/l*_binary64`

Counts

76 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	128	1141
1	305	989
2	849	986
3	2833	976
4	4834	976
5	5163	976

prune85.0ms (1.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	166	4	170

Error

0.6b

Counts

170 → 4

Alt Table

Status	Error	Program
✓	1.2b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))))
▶	2.5b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (expm1.f64 (.f64 (.f64 (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))))))
	27.4b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))
✓	30.5b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 2300 to 1386 computations (39.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (.f64 (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))))
	0.8b	(cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))
	0.8b	(cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))
✓	0.8b	(cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`pow1_binary64`
10×	`pow1/3_binary64`
9×	`pow-prod-up_binary64`
7×	`add-sqr-sqrt_binary64`
7×	`cbrt-prod_binary64`

Counts

2 → 51

Calls

2 calls:

9.0ms	(.f64 (.f64 (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))))
1.0ms	(cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))

series784.0ms (12.6%)

Counts

2 → 24

Calls

2 calls:

527.0ms	(cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))
257.0ms	(.f64 (.f64 (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))))

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

571×	`fma-neg_binary64`
348×	`associate-l_binary64`
332×	`unswap-sqr_binary64`
319×	`fma-def_binary64`
310×	`associate-r_binary64`

Counts

75 → 120

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1181
1	255	1096
2	718	1059
3	2369	1049
4	5003	1049

prune129.0ms (2.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	237	4	241

Error

0.6b

Counts

241 → 4

Alt Table

Status	Error	Program
	27.4b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))
	2.7b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (expm1.f64 (.f64 (.f64 (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))) (sqrt.f64 (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))))) (*.f64 (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))) (sqrt.f64 (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))))))))
✓	1.2b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))))
✓	30.5b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 4135 to 2901 computations (29.8% saved)

regimes142.0ms (2.3%)

Accuracy

Total 0.6b remaining (51.1%)

Threshold costs 0.6b (51.1%)

Compiler

Compiled 2957 to 2120 computations (28.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	9	17
2	9	17

end7.0ms (0.1%)

Compiler: Compiled 36 to 21 computations (41.7% saved)

sample2.3s (36.4%)

Algorithm

1×

intervals

Results

995.0ms	1973×	body	1024	valid
259.0ms	985×	body	512	valid
239.0ms	4389×	body	128	valid
116.0ms	173×	body	2048	valid
69.0ms	480×	body	256	valid
7.0ms	143×	body	128	overflowed

Compiler

Compiled 96 to 68 computations (29.2% saved)

Details

analyze212.0ms (3.4%)

sample202.0ms (3.2%)

simplify9.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite12.0ms (0.2%)

series795.0ms (12.8%)

simplify95.0ms (1.5%)

prune44.0ms (0.7%)

localize6.0ms (0.1%)

rewrite9.0ms (0.1%)

series38.0ms (0.6%)

simplify68.0ms (1.1%)

prune50.0ms (0.8%)

localize9.0ms (0.2%)

rewrite4.0ms (0.1%)

series1.1s (17.1%)

simplify82.0ms (1.3%)

prune85.0ms (1.4%)

localize13.0ms (0.2%)

rewrite13.0ms (0.2%)

series784.0ms (12.6%)

simplify71.0ms (1.1%)

prune129.0ms (2.1%)

regimes142.0ms (2.3%)

simplify3.0ms (0%)

end7.0ms (0.1%)

sample2.3s (36.4%)

Profiling