Details

analyze415.0ms (3.6%)

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
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
43.7%	56.2%	0.1%	6
53.1%	42.1%	4.8%	7
59.3%	35.9%	4.8%	8
62.4%	30.4%	7.1%	9
64.8%	28.1%	7.1%	10
66%	25.8%	8.3%	11
66.9%	24.8%	8.3%	12
67.4%	23.7%	8.9%	13
67.9%	23.3%	8.9%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample4.3s (37.8%)

Results

2.7s	2502×	body	8192	exit
1.2s	7606×	body	128	valid
154.0ms	230×	body	1024	valid
111.0ms	254×	body	512	valid
49.0ms	166×	body	256	valid
9.0ms	69×	body	128	invalid

Compiler

Compiled 35 to 26 computations (25.7% saved)

simplify103.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

837×	`fma-def_binary64`
741×	`fabs-mul_binary64`
531×	`fabs-div_binary64`
469×	`swap-sqr_binary64`
420×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	19	11
2	28	11
3	45	11
4	59	11
5	89	11
6	120	11
7	148	11
8	188	11
9	201	11
10	231	11
11	257	11
12	336	11
13	544	11
14	967	11
15	2930	11
16	3463	11
17	3600	11
18	3896	11
19	4820	11
20	4969	11

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.8b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
	0.8b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

Compiler

Compiled 58 to 38 computations (34.5% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 x))
✓	0.7b	(log.f64 (+.f64 1 (exp.f64 x)))

series208.0ms (1.8%)

Counts

2 → 8

Calls

2 calls:

206.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
2.0ms	(+.f64 1 (exp.f64 x))

rewrite8.0ms (0.1%)

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 → 35

Calls

2 calls:

3.0ms	(+.f64 1 (exp.f64 x))
3.0ms	(log.f64 (+.f64 1 (exp.f64 x)))

simplify63.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

932×	`fma-neg_binary64`
715×	`cancel-sign-sub-inv_binary64`
595×	`fma-def_binary64`
481×	`associate-+l+_binary64`
382×	`*-commutative_binary64`

Counts

43 → 59

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	424
1	161	375
2	317	369
3	768	356
4	2089	356
5	3795	356
6	5051	356

prune37.0ms (0.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	59	2	61

Error

0.2b

Counts

61 → 2

Alt Table

Status	Error	Program
✓	0.8b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
▶	12.6b	(-.f64 (fma.f64 1/2 x (log.f64 2)) (*.f64 x y))

Compiler

Compiled 858 to 472 computations (45% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 1/2 x (log.f64 2)) (*.f64 x y))
✓	0.0b	(fma.f64 1/2 x (log.f64 2))

series17.0ms (0.1%)

Counts

2 → 36

Calls

2 calls:

12.0ms	(-.f64 (fma.f64 1/2 x (log.f64 2)) (*.f64 x y))
5.0ms	(fma.f64 1/2 x (log.f64 2))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`
3×	`fma-neg_binary64`

Counts

2 → 31

Calls

2 calls:

3.0ms	(-.f64 (fma.f64 1/2 x (log.f64 2)) (*.f64 x y))
0.0ms	(fma.f64 1/2 x (log.f64 2))

simplify77.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

569×	`unsub-neg_binary64`
518×	`associate-+r+_binary64`
473×	`associate-+l+_binary64`
428×	`times-frac_binary64`
362×	`fma-neg_binary64`

Counts

67 → 55

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	61	839
1	135	764
2	386	677
3	1673	675
4	3295	675
5	4810	667
6	5328	667

prune37.0ms (0.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	54	3	57

Error

0.2b

Counts

57 → 3

Alt Table

Status	Error	Program
✓	0.8b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
▶	13.7b	(-.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x (log.f64 2))) 2) (cbrt.f64 (fma.f64 1/2 x (log.f64 2)))) (.f64 x y))
✓	12.6b	(-.f64 (fma.f64 1/2 x (log.f64 2)) (*.f64 x y))

Compiler

Compiled 869 to 570 computations (34.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 1/2 x (log.f64 2))
✓	0.2b	(pow.f64 (cbrt.f64 (fma.f64 1/2 x (log.f64 2))) 2)
✓	0.8b	(*.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x (log.f64 2))) 2) (cbrt.f64 (fma.f64 1/2 x (log.f64 2))))
✓	1.3b	(cbrt.f64 (fma.f64 1/2 x (log.f64 2)))

series40.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

22.0ms	(pow.f64 (cbrt.f64 (fma.f64 1/2 x (log.f64 2))) 2)
12.0ms	(cbrt.f64 (fma.f64 1/2 x (log.f64 2)))
5.0ms	(*.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x (log.f64 2))) 2) (cbrt.f64 (fma.f64 1/2 x (log.f64 2))))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
16×	`unpow-prod-down_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 82

Calls

3 calls:

6.0ms	(*.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x (log.f64 2))) 2) (cbrt.f64 (fma.f64 1/2 x (log.f64 2))))
2.0ms	(pow.f64 (cbrt.f64 (fma.f64 1/2 x (log.f64 2))) 2)
1.0ms	(cbrt.f64 (fma.f64 1/2 x (log.f64 2)))

simplify87.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

855×	`times-frac_binary64`
525×	`associate-/l*_binary64`
418×	`fma-def_binary64`
208×	`unswap-sqr_binary64`
173×	`associate-/r/_binary64`

Counts

118 → 183

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	226	2744
1	543	2617
2	1656	2481
3	5260	2481

prune235.0ms (2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	263	1	264
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	264	3	267

Error

0.2b

Counts

267 → 3

Alt Table

Status	Error	Program
✓	0.8b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
▶	17.6b	(-.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x (log.f64 2))) (.f64 (cbrt.f64 2) (cbrt.f64 2))) (cbrt.f64 2)) (cbrt.f64 (fma.f64 1/2 x (log.f64 2)))) (*.f64 x y))
✓	12.6b	(-.f64 (fma.f64 1/2 x (log.f64 2)) (*.f64 x y))

Compiler

Compiled 8111 to 6457 computations (20.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (cbrt.f64 (fma.f64 1/2 x (log.f64 2))) (*.f64 (cbrt.f64 2) (cbrt.f64 2)))
✓	0.7b	(.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x (log.f64 2))) (.f64 (cbrt.f64 2) (cbrt.f64 2))) (cbrt.f64 2)) (cbrt.f64 (fma.f64 1/2 x (log.f64 2))))
✓	1.0b	(cbrt.f64 2)
	1.3b	(cbrt.f64 (fma.f64 1/2 x (log.f64 2)))

series5.0s (44%)

Counts

3 → 24

Calls

3 calls:

5.0s

(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x (log.f64 2))) (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (cbrt.f64 2)) (cbrt.f64 (fma.f64 1/2 x (log.f64 2))))

50.0ms

(pow.f64 (cbrt.f64 (fma.f64 1/2 x (log.f64 2))) (*.f64 (cbrt.f64 2) (cbrt.f64 2)))

0.0ms

(cbrt.f64 2)

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`unpow-prod-down_binary64`
32×	`add-sqr-sqrt_binary64`
20×	`cbrt-prod_binary64`
14×	`associate-l_binary64`
12×	`unswap-sqr_binary64`

Counts

3 → 82

Calls

3 calls:

10.0ms

(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x (log.f64 2))) (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (cbrt.f64 2)) (cbrt.f64 (fma.f64 1/2 x (log.f64 2))))

2.0ms

(pow.f64 (cbrt.f64 (fma.f64 1/2 x (log.f64 2))) (*.f64 (cbrt.f64 2) (cbrt.f64 2)))

1.0ms

(cbrt.f64 2)

simplify146.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

672×	`fma-def_binary64`
267×	`associate-r_binary64`
213×	`associate-l_binary64`
184×	`times-frac_binary64`
172×	`*-commutative_binary64`

Counts

106 → 164

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	265	4862
1	700	4462
2	2798	4320
3	4738	4320
4	4963	4320

prune363.0ms (3.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	287	1	288
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	288	3	291

Error

0.2b

Counts

291 → 3

Alt Table

Status	Error	Program
✓	0.8b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
	17.6b	(-.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x (log.f64 2))) (.f64 (cbrt.f64 2) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 2) 2)) (cbrt.f64 (cbrt.f64 2))))) (cbrt.f64 2)) (cbrt.f64 (fma.f64 1/2 x (log.f64 2)))) (.f64 x y))
✓	12.6b	(-.f64 (fma.f64 1/2 x (log.f64 2)) (*.f64 x y))

Compiler

Compiled 12554 to 10686 computations (14.9% saved)

regimes98.0ms (0.9%)

Accuracy

Total 0.3b remaining (56.6%)

Threshold costs 0.3b (56.6%)

Counts

25 → 1

Compiler

Compiled 1549 to 1278 computations (17.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	18	14
2	27	14
3	33	14
4	37	14
5	38	14
6	37	14

end77.0ms (0.7%)

Compiler: Compiled 79 to 63 computations (20.3% saved)

Details

analyze415.0ms (3.6%)

sample4.3s (37.8%)

simplify103.0ms (0.9%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series208.0ms (1.8%)

rewrite8.0ms (0.1%)

simplify63.0ms (0.5%)

prune37.0ms (0.3%)

localize7.0ms (0.1%)

series17.0ms (0.1%)

rewrite4.0ms (0%)

simplify77.0ms (0.7%)

prune37.0ms (0.3%)

localize10.0ms (0.1%)

series40.0ms (0.3%)

rewrite13.0ms (0.1%)

simplify87.0ms (0.8%)

prune235.0ms (2%)

localize17.0ms (0.1%)

series5.0s (44%)

rewrite19.0ms (0.2%)

simplify146.0ms (1.3%)

prune363.0ms (3.2%)

regimes98.0ms (0.9%)

simplify3.0ms (0%)

end77.0ms (0.7%)

Profiling