Details

analyze818.0ms (4.4%)

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%	50%	0.1%	6
50%	50%	0.1%	7
50%	50%	0.1%	8
50%	50%	0.1%	9
50%	50%	0.1%	10
50%	50%	0.1%	11
50%	50%	0.1%	12
50%	50%	0.1%	13
50%	50%	0.1%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample13.0s (70.8%)

Symmetry

(sort a b)

Results

10.0s	7835×	body	8192	exit
1.5s	1971×	body	1024	valid
620.0ms	4590×	body	128	valid
435.0ms	946×	body	512	valid
238.0ms	529×	body	256	valid
212.0ms	220×	body	2048	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify9.0ms (0%)

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

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

30.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.8b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	3.2b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series522.0ms (2.8%)

Counts

2 → 48

Calls

2 calls:

517.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite8.0ms (0%)

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:

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

simplify88.0ms (0.5%)

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 → 83

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

prune53.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	81	3	84

Error

0.9b

Counts

84 → 3

Alt Table

Status	Error	Program
✓	30.8b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
	31.7b	(.f64 (.f64 (cbrt.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (cbrt.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))))) (cbrt.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
▶	1.0b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))

Compiler

Compiled 1379 to 616 computations (55.3% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 a))
✓	0.0b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
✓	0.0b	(/.f64 b (+.f64 1 (exp.f64 a)))
✓	0.2b	(log1p.f64 (exp.f64 a))

series475.0ms (2.6%)

Counts

4 → 44

Calls

4 calls:

262.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
192.0ms	(log1p.f64 (exp.f64 a))
19.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
2.0ms	(+.f64 1 (exp.f64 a))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
9×	`add-log-exp_binary64`

Counts

4 → 81

Calls

4 calls:

7.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
5.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
3.0ms	(+.f64 1 (exp.f64 a))
0.0ms	(log1p.f64 (exp.f64 a))

simplify106.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

571×	`fma-neg_binary64`
461×	`cancel-sign-sub-inv_binary64`
403×	`fma-def_binary64`
224×	`distribute-rgt-in_binary64`
201×	`associate-+l+_binary64`

Counts

125 → 120

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	152	1715
1	382	1640
2	927	1622
3	2571	1611
4	4779	1610
5	4994	1610
6	4923	1610

prune94.0ms (0.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	116	4	120
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	116	7	123

Error

0.8b

Counts

123 → 7

Alt Table

Status	Error	Program
▶	1.5b	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
	31.7b	(.f64 (.f64 (cbrt.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (cbrt.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))))) (cbrt.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
✓	30.8b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
	32.7b	(fma.f64 1/2 b (log.f64 2))
✓	1.0b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	1.7b	(+.f64 (log1p.f64 (exp.f64 a)) (.f64 (.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
	26.5b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))

Compiler

Compiled 2197 to 1154 computations (47.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	0.0b	(/.f64 b (+.f64 1 (exp.f64 a)))
✓	0.0b	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
	0.2b	(log1p.f64 (exp.f64 a))

series256.0ms (1.4%)

Counts

1 → 24

Calls

1 calls:

256.0ms

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

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 11

Calls

1 calls:

0.0ms

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

simplify77.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

661×	`fma-neg_binary64`
538×	`cancel-sign-sub-inv_binary64`
445×	`associate-+l+_binary64`
413×	`sub-neg_binary64`
374×	`associate--r+_binary64`

Counts

35 → 30

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	49	630
1	108	590
2	288	580
3	890	576
4	2075	575
5	4421	575
6	4998	575
7	4959	575

prune98.0ms (0.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	124	7	131

Error

0.8b

Counts

131 → 7

Alt Table

Status	Error	Program
✓	30.8b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
	32.7b	(fma.f64 1/2 b (log.f64 2))
	16.8b	(*.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))) (sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))))
	31.2b	(-.f64 (exp.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) 1)
✓	1.0b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
▶	1.7b	(+.f64 (log1p.f64 (exp.f64 a)) (.f64 (.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
	26.5b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))

Compiler

Compiled 2498 to 1455 computations (41.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))
	0.2b	(log1p.f64 (exp.f64 a))
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))
✓	0.7b	(cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))

series1.6s (8.6%)

Counts

3 → 72

Calls

3 calls:

970.0ms

(*.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

590.0ms

(cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))

30.0ms

(*.f64 (*.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

rewrite66.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

134×	`cbrt-prod_binary64`
114×	`*-un-lft-identity_binary64`
91×	`times-frac_binary64`
88×	`add-sqr-sqrt_binary64`
60×	`add-cube-cbrt_binary64`

Counts

3 → 191

Calls

3 calls:

20.0ms

(*.f64 (*.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

18.0ms

(*.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

3.0ms

(cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))

simplify174.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

608×	`fma-def_binary64`
345×	`times-frac_binary64`
321×	`fma-neg_binary64`
296×	`associate-l_binary64`
279×	`associate-r_binary64`

Counts

263 → 278

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	282	6834
1	584	5969
2	1970	5544
3	3998	5367
4	5083	5367

prune364.0ms (2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	395	2	397
Fresh	2	2	4
Picked	1	0	1
Done	0	2	2
Total	398	6	404

Error

0.8b

Counts

404 → 6

Alt Table

Status	Error	Program
✓	30.8b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
	32.7b	(fma.f64 1/2 b (log.f64 2))
	31.2b	(-.f64 (exp.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) 1)
✓	1.0b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	2.2b	(+.f64 (log1p.f64 (exp.f64 a)) (.f64 (.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) 5)) (cbrt.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))))
	2.2b	(+.f64 (log1p.f64 (exp.f64 a)) (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) 4) (*.f64 (cbrt.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))

Compiler

Compiled 13959 to 8286 computations (40.6% saved)

regimes254.0ms (1.4%)

Accuracy

Total 0.5b remaining (53.6%)

Threshold costs 0.5b (53.6%)

Counts

50 → 1

Compiler

Compiled 6294 to 4331 computations (31.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	13	16
2	12	16

end261.0ms (1.4%)

Compiler: Compiled 166 to 116 computations (30.1% saved)

Details

analyze818.0ms (4.4%)

sample13.0s (70.8%)

simplify9.0ms (0%)

prune1.0ms (0%)

localize5.0ms (0%)

series522.0ms (2.8%)

rewrite8.0ms (0%)

simplify88.0ms (0.5%)

prune53.0ms (0.3%)

localize7.0ms (0%)

series475.0ms (2.6%)

rewrite18.0ms (0.1%)

simplify106.0ms (0.6%)

prune94.0ms (0.5%)

localize9.0ms (0.1%)

series256.0ms (1.4%)

rewrite1.0ms (0%)

simplify77.0ms (0.4%)

prune98.0ms (0.5%)

localize10.0ms (0.1%)

series1.6s (8.6%)

rewrite66.0ms (0.4%)

simplify174.0ms (0.9%)

prune364.0ms (2%)

regimes254.0ms (1.4%)

simplify2.0ms (0%)

end261.0ms (1.4%)

Profiling