Details

analyze95.0ms (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%	18.7%	12.6%	7
68.7%	12.5%	18.8%	8
68.7%	12.5%	18.8%	9
68.7%	9.4%	22%	10
68.7%	9.4%	22%	11
68.7%	7.8%	23.5%	12
68.7%	7.8%	23.5%	13
68.7%	7%	24.3%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample31.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
1.0ms	26×	body	128	overflowed

Compiler

Compiled 23 to 15 computations (34.8% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

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

0.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.8b	(/.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))
✓	0.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series34.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
5.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite11.0ms (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:

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

simplify85.0ms (1.2%)

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

prune249.0ms (3.4%)

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

0.4b

Counts

109 → 4

Alt Table

Status	Error	Program
	1.3b	(cbrt.f64 (.f64 (.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))) (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))) (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
▶	0.8b	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	12.2b	(/.f64 1 (+.f64 1 (exp.f64 b)))
	1.3b	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (/.f64 (exp.f64 a) (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 2333 to 867 computations (62.8% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	0.0b	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
✓	1.2b	(-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
✓	2.4b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series1.1s (15.2%)

Counts

3 → 72

Calls

3 calls:

481.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
336.0ms	(-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
281.0ms	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
24×	`prod-diff_binary64`
23×	`add-cube-cbrt_binary64`
19×	`exp-sum_binary64`

Counts

3 → 95

Calls

3 calls:

6.0ms	(-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
6.0ms	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
3.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

simplify129.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-neg_binary64`
540×	`times-frac_binary64`
303×	`cancel-sign-sub-inv_binary64`
290×	`sub-neg_binary64`
134×	`+-commutative_binary64`

Counts

167 → 179

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	259	3797
1	648	3524
2	2381	3260
3	4522	3255
4	4920	3255

prune226.0ms (3.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	216	2	218
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	219	3	222

Error

0.4b

Counts

222 → 3

Alt Table

Status	Error	Program
▶	1.2b	(exp.f64 (-.f64 a (log.f64 (log.f64 (*.f64 (exp.f64 (exp.f64 a)) (exp.f64 (exp.f64 b)))))))
	1.3b	(cbrt.f64 (.f64 (.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))) (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))) (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
	12.1b	(exp.f64 (neg.f64 (log1p.f64 (exp.f64 b))))

Compiler

Compiled 5467 to 2015 computations (63.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(log.f64 (*.f64 (exp.f64 (exp.f64 a)) (exp.f64 (exp.f64 b))))
✓	0.3b	(*.f64 (exp.f64 (exp.f64 a)) (exp.f64 (exp.f64 b)))
✓	1.2b	(log.f64 (log.f64 (*.f64 (exp.f64 (exp.f64 a)) (exp.f64 (exp.f64 b)))))
✓	1.2b	(-.f64 a (log.f64 (log.f64 (*.f64 (exp.f64 (exp.f64 a)) (exp.f64 (exp.f64 b))))))

series2.3s (31.8%)

Counts

4 → 96

Calls

4 calls:

1.0s	(log.f64 (log.f64 (*.f64 (exp.f64 (exp.f64 a)) (exp.f64 (exp.f64 b)))))
723.0ms	(-.f64 a (log.f64 (log.f64 (*.f64 (exp.f64 (exp.f64 a)) (exp.f64 (exp.f64 b))))))
521.0ms	(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)))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
21×	`pow1_binary64`
17×	`add-cube-cbrt_binary64`
15×	`log-pow_binary64`

Counts

4 → 94

Calls

4 calls:

9.0ms	(-.f64 a (log.f64 (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))))
4.0ms	(log.f64 (log.f64 (*.f64 (exp.f64 (exp.f64 a)) (exp.f64 (exp.f64 b)))))

simplify124.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

610×	`fma-neg_binary64`
270×	`times-frac_binary64`
248×	`distribute-rgt-in_binary64`
246×	`cancel-sign-sub-inv_binary64`
210×	`distribute-lft-in_binary64`

Counts

190 → 203

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	3437
1	569	3065
2	2122	2795
3	4566	2795
4	5099	2795

prune156.0ms (2.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	203	0	203
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	203	3	206

Error

0.4b

Counts

206 → 3

Alt Table

Status	Error	Program
✓	1.2b	(exp.f64 (-.f64 a (log.f64 (log.f64 (*.f64 (exp.f64 (exp.f64 a)) (exp.f64 (exp.f64 b)))))))
▶	1.3b	(cbrt.f64 (.f64 (.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))) (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))) (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
	12.1b	(exp.f64 (neg.f64 (log1p.f64 (exp.f64 b))))

Compiler

Compiled 4696 to 1490 computations (68.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))) (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))) (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))
✓	0.0b	(*.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))) (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))
✓	0.6b	(cbrt.f64 (.f64 (.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))) (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))) (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
	0.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series359.0ms (5%)

Counts

3 → 72

Calls

3 calls:

200.0ms

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

126.0ms

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

32.0ms

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

rewrite86.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`*-un-lft-identity_binary64`
77×	`times-frac_binary64`
65×	`add-cbrt-cube_binary64`
62×	`add-sqr-sqrt_binary64`
47×	`add-cube-cbrt_binary64`

Counts

3 → 180

Calls

3 calls:

22.0ms

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

19.0ms

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

16.0ms

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

simplify192.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

703×	`associate-/l*_binary64`
584×	`times-frac_binary64`
545×	`fma-def_binary64`
201×	`*-commutative_binary64`
176×	`associate-*r/_binary64`

Counts

252 → 283

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	719	12182
1	2283	9717
2	5197	9717

prune437.0ms (6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	490	0	490
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	490	3	493

Error

0.4b

Counts

493 → 3

Alt Table

Status	Error	Program
✓	1.2b	(exp.f64 (-.f64 a (log.f64 (log.f64 (*.f64 (exp.f64 (exp.f64 a)) (exp.f64 (exp.f64 b)))))))
✓	1.3b	(cbrt.f64 (.f64 (.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))) (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))) (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
	12.1b	(exp.f64 (neg.f64 (log1p.f64 (exp.f64 b))))

Compiler

Compiled 24176 to 7536 computations (68.8% saved)

regimes923.0ms (12.8%)

Accuracy

Total 0.3b remaining (52.7%)

Threshold costs 0.3b (52.7%)

Counts

226 → 1

Compiler

Compiled 20942 to 13688 computations (34.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`unsub-neg_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	17	15
2	19	15
3	20	15
4	20	15

end0.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

sample589.0ms (8.2%)

Algorithm

1×

intervals

Results

291.0ms	8000×	body	128	valid
22.0ms	689×	body	128	overflowed

Compiler

Compiled 74 to 43 computations (41.9% saved)

Details

analyze95.0ms (1.3%)

sample31.0ms (0.4%)

simplify7.0ms (0.1%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series34.0ms (0.5%)

rewrite11.0ms (0.1%)

simplify85.0ms (1.2%)

prune249.0ms (3.4%)

localize7.0ms (0.1%)

series1.1s (15.2%)

rewrite21.0ms (0.3%)

simplify129.0ms (1.8%)

prune226.0ms (3.1%)

localize12.0ms (0.2%)

series2.3s (31.8%)

rewrite33.0ms (0.5%)

simplify124.0ms (1.7%)

prune156.0ms (2.2%)

localize8.0ms (0.1%)

series359.0ms (5%)

rewrite86.0ms (1.2%)

simplify192.0ms (2.7%)

prune437.0ms (6%)

regimes923.0ms (12.8%)

simplify2.0ms (0%)

end0.0ms (0%)

sample589.0ms (8.2%)

Profiling