Details

analyze1.1s (7.8%)

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)

sample121.0ms (0.8%)

Algorithm

1×

intervals

Results

28.0ms	270×	body	128	nan
25.0ms	231×	body	128	valid
17.0ms	164×	body	128	invalid
3.0ms	5×	body	1024	valid
3.0ms	8×	body	512	valid
3.0ms	12×	body	256	valid
2.0ms	6×	body	512	invalid
2.0ms	3×	body	1024	invalid
0.0ms	1×	body	256	invalid

Compiler

Compiled 55 to 41 computations (25.5% saved)

simplify59.0ms (0.4%)

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 (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))
✓	0.0b	(-.f64 (log.f64 z) t)
✓	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)))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
36×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
30×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

4 → 112

Calls

4 calls:

10.0ms	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))
4.0ms	(-.f64 (log.f64 z) t)
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)))

series1.2s (8.3%)

Counts

4 → 135

Calls

4 calls:

446.0ms	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))
392.0ms	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))
308.0ms	(-.f64 (log.f64 z) t)
46.0ms	(exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))

simplify144.0ms (1%)

Algorithm

1×	egg-herbie

Rules

593×	`associate-r_binary64`
545×	`fma-def_binary64`
474×	`associate-l_binary64`
170×	`*-commutative_binary64`
137×	`sub-neg_binary64`

Counts

247 → 447

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	550	7305
1	1551	6531
2	4986	6531

prune264.0ms (1.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	444	3	447
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	445	3	448

Error

0.0b

Counts

448 → 3

Alt Table

Status	Error	Program
	12.9b	(.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 a b (.f64 y t)))))
	0.1b	(.f64 x (.f64 (.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)))))))
▶	0.0b	(.f64 x (expm1.f64 (log1p.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))))

Compiler

Compiled 9498 to 3520 computations (62.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (log.f64 z) t)
✓	0.0b	(expm1.f64 (log1p.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)))

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

series2.0s (14.1%)

Counts

1 → 60

Calls

1 calls:

2.0s	(expm1.f64 (log1p.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))

simplify136.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

518×	`associate-r_binary64`
352×	`associate-l_binary64`
254×	`associate-/l*_binary64`
190×	`associate-/r*_binary64`
175×	`fma-def_binary64`

Counts

71 → 139

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	392	8300
1	1293	6880
2	4985	6880

prune327.0ms (2.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	426	0	426
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	426	3	429

Error

0.0b

Counts

429 → 3

Alt Table

Status	Error	Program
	12.9b	(.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 a b (.f64 y t)))))
▶	0.1b	(.f64 x (.f64 (.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)))))))
✓	0.0b	(.f64 x (expm1.f64 (log1p.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))))

Compiler

Compiled 17281 to 7253 computations (58% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`cbrt-prod_binary64`
17×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`
8×	`pow1_binary64`

Counts

1 → 45

Calls

1 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))))))

series1.8s (12.7%)

Counts

1 → 60

Calls

1 calls:

1.8s

(*.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))))))

simplify169.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

511×	`associate-r_binary64`
414×	`fma-neg_binary64`
406×	`associate-l_binary64`
350×	`times-frac_binary64`
335×	`fma-def_binary64`

Counts

105 → 202

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	327	6963
1	1073	5768
2	4232	5368
3	5318	5368

prune468.0ms (3.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	2033	3	2036
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	2035	4	2039

Error

Counts

2039 → 4

Alt Table

Status	Error	Program
	0.1b	(.f64 x (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) 4) (.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) (cbrt.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)))))))
▶	0.1b	(.f64 x (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) (cbrt.f64 (sqrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))) (.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) (cbrt.f64 (sqrt.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	(.f64 x (expm1.f64 (log1p.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))))
	11.5b	(.f64 x (.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 a b (.f64 y t)))) 2)) (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))))

Compiler

Compiled 19065 to 4942 computations (74.1% saved)

localize22.0ms (0.2%)

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)))
	0.1b	(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)))
	0.1b	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify350.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune830.0ms (5.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	31440	0	31440
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	31440	4	31444

Error

Counts

31444 → 4

Alt Table

Status	Error	Program
	0.1b	(.f64 x (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) 4) (.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) (cbrt.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)))))))
✓	0.1b	(.f64 x (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) (cbrt.f64 (sqrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))) (.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) (cbrt.f64 (sqrt.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	(.f64 x (expm1.f64 (log1p.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))))
	11.5b	(.f64 x (.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 a b (.f64 y t)))) 2)) (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))))

Compiler

Compiled 20431 to 2861 computations (86% saved)

regimes1.1s (7.7%)

Accuracy

Total 0.0b remaining (2.5%)

Threshold costs 0.0b (2.5%)

Compiler

Compiled 46739 to 20265 computations (56.6% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
5×	`*-commutative_binary64`
5×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	29
1	28	29
2	36	29
3	41	29
4	43	29
5	43	29

end1.0ms (0%)

Compiler: Compiled 24 to 17 computations (29.2% saved)

sample4.1s (28.7%)

Algorithm

1×

intervals

Results

1.1s	10604×	body	128	nan
780.0ms	7344×	body	128	valid
585.0ms	5492×	body	128	invalid
110.0ms	294×	body	512	valid
91.0ms	127×	body	1024	valid
55.0ms	126×	body	512	invalid
51.0ms	234×	body	256	valid
40.0ms	63×	body	1024	invalid
33.0ms	132×	body	256	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 284 to 126 computations (55.6% saved)

Details

analyze1.1s (7.8%)

sample121.0ms (0.8%)

simplify59.0ms (0.4%)

prune4.0ms (0%)

localize13.0ms (0.1%)

rewrite21.0ms (0.1%)

series1.2s (8.3%)

simplify144.0ms (1%)

prune264.0ms (1.8%)

localize15.0ms (0.1%)

rewrite1.0ms (0%)

series2.0s (14.1%)

simplify136.0ms (0.9%)

prune327.0ms (2.3%)

localize17.0ms (0.1%)

rewrite10.0ms (0.1%)

series1.8s (12.7%)

simplify169.0ms (1.2%)

prune468.0ms (3.3%)

localize22.0ms (0.2%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify350.0ms (2.4%)

prune830.0ms (5.8%)

regimes1.1s (7.7%)

simplify4.0ms (0%)

end1.0ms (0%)

sample4.1s (28.7%)

Profiling