Details

analyze1.1s (3.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	90.4%	9.6%	9
0%	45.2%	54.8%	10
0%	45.2%	54.8%	11
0%	45.2%	54.8%	12
0%	45.2%	54.8%	13
0%	44.4%	55.6%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample5.2s (18.6%)

Results

3.1s	16240×	body	128	invalid
1.4s	7560×	body	128	valid
171.0ms	307×	body	512	valid
108.0ms	126×	body	512	invalid
98.0ms	272×	body	256	valid
97.0ms	117×	body	1024	valid
37.0ms	107×	body	256	invalid
32.0ms	39×	body	1024	invalid

Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify51.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-def_binary64`
557×	`associate-/l*_binary64`
456×	`unswap-sqr_binary64`
365×	`*-commutative_binary64`
332×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	26
1	34	25
2	73	25
3	158	25
4	405	25
5	1252	25
6	2771	25
7	4527	25
8	5117	25

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

Compiler

Compiled 84 to 54 computations (35.7% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
✓	0.0b	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))
✓	0.0b	(exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))
✓	0.1b	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))

series1.2s (4.4%)

Counts

4 → 164

Calls

4 calls:

502.0ms	(.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
360.0ms	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))
322.0ms	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))
40.0ms	(exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

4 → 95

Calls

4 calls:

5.0ms	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))
4.0ms	(.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
1.0ms	(exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))
0.0ms	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))

simplify204.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

789×	`fma-def_binary64`
292×	`*-commutative_binary64`
185×	`sub-neg_binary64`
182×	`times-frac_binary64`
175×	`associate-r_binary64`

Counts

259 → 297

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	713	11258
1	2189	10188
2	4843	10188
3	4989	10188

prune252.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	295	2	297
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	295	3	298

Error

0.0b

Counts

298 → 3

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (.f64 x (.f64 (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))) (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))
	15.0b	(.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 a b (.f64 y t)))))
✓	0.0b	(.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

Compiler

Compiled 13815 to 5194 computations (62.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
✓	0.0b	(.f64 (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))
	0.0b	(exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))
	0.1b	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))

series2.8s (10.2%)

Counts

2 → 120

Calls

2 calls:

1.6s

(*.f64 (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))

1.3s

(cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`cbrt-prod_binary64`
19×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 59

Calls

2 calls:

6.0ms

(*.f64 (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))

1.0ms

(cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

simplify164.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

667×	`associate-l_binary64`
582×	`fma-def_binary64`
244×	`*-commutative_binary64`
187×	`cancel-sign-sub-inv_binary64`
180×	`associate--l+_binary64`

Counts

179 → 182

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	542	11928
1	1784	10472
2	5053	10472

prune1.0s (3.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	713	1	714
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	714	3	717

Error

0.0b

Counts

717 → 3

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (.f64 x (.f64 (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))) (cbrt.f64 (exp.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))))
	15.0b	(.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 a b (.f64 y t)))))
✓	0.0b	(.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

Compiler

Compiled 63083 to 18238 computations (71.1% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
✓	13.8b	(cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))

series7.5s (26.8%)

Counts

3 → 180

Calls

3 calls:

6.7s

(*.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

413.0ms

(cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))

370.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

6.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

4.0ms

(*.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

1.0ms

(cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))

simplify574.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

273 → 225

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5292	85412

prune1.9s (6.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	646	0	646
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	646	3	649

Error

0.0b

Counts

649 → 3

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (.f64 x (.f64 (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))) (cbrt.f64 (exp.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))))
▶	15.0b	(.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 a b (.f64 y t)))))
✓	0.0b	(.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

Compiler

Compiled 118720 to 52176 computations (56.1% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (fma.f64 a b (*.f64 y t)))
✓	0.0b	(.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 a b (.f64 y t)))))
✓	0.5b	(/.f64 (pow.f64 z y) (exp.f64 (fma.f64 a b (*.f64 y t))))
✓	0.8b	(fma.f64 a b (*.f64 y t))

series1.1s (3.9%)

Counts

4 → 196

Calls

4 calls:

648.0ms	(.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 a b (.f64 y t)))))
427.0ms	(/.f64 (pow.f64 z y) (exp.f64 (fma.f64 a b (*.f64 y t))))
11.0ms	(exp.f64 (fma.f64 a b (*.f64 y t)))
9.0ms	(fma.f64 a b (*.f64 y t))

rewrite28.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`times-frac_binary64`
50×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
40×	`add-cube-cbrt_binary64`
32×	`associate-r_binary64`

Counts

4 → 136

Calls

4 calls:

9.0ms	(.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 a b (.f64 y t)))))
5.0ms	(/.f64 (pow.f64 z y) (exp.f64 (fma.f64 a b (*.f64 y t))))
1.0ms	(exp.f64 (fma.f64 a b (*.f64 y t)))
0.0ms	(fma.f64 a b (*.f64 y t))

simplify196.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

697×	`fma-def_binary64`
457×	`associate-r_binary64`
358×	`associate-l_binary64`
259×	`associate-/l*_binary64`
217×	`*-commutative_binary64`

Counts

332 → 299

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	403	8024
1	1042	7709
2	3999	7664
3	4875	7664
4	5016	7664

prune336.0ms (1.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	297	2	299
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	298	4	302

Error

Counts

302 → 4

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (.f64 x (.f64 (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))) (cbrt.f64 (exp.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))))
	15.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 a b (.f64 y t))))))
	15.0b	(/.f64 (.f64 x (pow.f64 z y)) (exp.f64 (fma.f64 a b (.f64 y t))))
✓	0.0b	(.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

Compiler

Compiled 8303 to 1708 computations (79.4% saved)

regimes4.1s (14.6%)

Accuracy

Total 0.1b remaining (46.4%)

Threshold costs 0.1b (46.4%)

Counts

337 → 1

Compiler

Compiled 170264 to 69513 computations (59.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
8×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	23
1	29	23
2	45	23
3	58	23
4	64	23
5	65	23
6	65	23

end82.0ms (0.3%)

Compiler: Compiled 195 to 93 computations (52.3% saved)

Details

analyze1.1s (3.9%)

sample5.2s (18.6%)

simplify51.0ms (0.2%)

prune4.0ms (0%)

localize13.0ms (0%)

series1.2s (4.4%)

rewrite18.0ms (0.1%)

simplify204.0ms (0.7%)

prune252.0ms (0.9%)

localize16.0ms (0.1%)

series2.8s (10.2%)

rewrite16.0ms (0.1%)

simplify164.0ms (0.6%)

prune1.0s (3.7%)

localize23.0ms (0.1%)

series7.5s (26.8%)

rewrite24.0ms (0.1%)

simplify574.0ms (2.1%)

prune1.9s (6.6%)

localize11.0ms (0%)

series1.1s (3.9%)

rewrite28.0ms (0.1%)

simplify196.0ms (0.7%)

prune336.0ms (1.2%)

regimes4.1s (14.6%)

simplify3.0ms (0%)

end82.0ms (0.3%)

Profiling