Details

analyze20.0ms (0.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
50%	50%	0.1%	2
50%	50%	0.1%	3
50%	25%	25.1%	4
50%	25%	25.1%	5
50%	12.5%	37.6%	6
50%	12.5%	37.6%	7
50%	6.2%	43.8%	8
50%	6.2%	43.8%	9
50%	3.1%	46.9%	10
50%	3.1%	46.9%	11
50%	1.6%	48.5%	12
50%	1.6%	48.5%	13
50%	0.8%	49.3%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample653.0ms (28.6%)

Infinites

6.9% of outputs are infinite.

Results

579.0ms	8256×	body	128	valid
10.0ms	124×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify17.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

151×	`fma-def_binary64`
131×	`fma-neg_binary64`
45×	`cancel-sign-sub-inv_binary64`
38×	`sub-neg_binary64`
31×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	63	10
4	127	10
5	233	10
6	324	10
7	361	10
8	400	10
9	414	10
10	383	10

prune3.0ms (0.1%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
▶	0.1b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

Compiler

Compiled 55 to 36 computations (34.5% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
✓	0.2b	(*.f64 y (sqrt.f64 x))

series19.0ms (0.8%)

Counts

2 → 15

Calls

2 calls:

10.0ms	(*.f64 y (sqrt.f64 x))
8.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

rewrite14.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
13×	`associate-+l+_binary64`
13×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`

Counts

2 → 58

Calls

2 calls:

6.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
5.0ms	(*.f64 y (sqrt.f64 x))

simplify74.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

433×	`fma-neg_binary64`
391×	`times-frac_binary64`
347×	`fma-def_binary64`
321×	`associate-l_binary64`
256×	`distribute-rgt-in_binary64`

Counts

73 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	92	672
1	214	646
2	643	637
3	2361	637
4	4129	637
5	4926	637

prune79.0ms (3.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	79	5	84
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	80	6	86

Error

0.0b

Counts

86 → 6

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))
	35.1b	(+.f64 (-.f64 1 x) (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (sqrt.f64 x))))
	0.4b	(+.f64 (-.f64 1 x) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (sqrt.f64 x))))
	33.6b	(+.f64 (-.f64 1 x) (.f64 (sqrt.f64 (.f64 y (sqrt.f64 x))) (sqrt.f64 (*.f64 y (sqrt.f64 x)))))
	0.4b	(+.f64 (-.f64 1 x) (.f64 (.f64 (cbrt.f64 (.f64 y (sqrt.f64 x))) (cbrt.f64 (.f64 y (sqrt.f64 x)))) (cbrt.f64 (*.f64 y (sqrt.f64 x)))))
✓	0.1b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

Compiler

Compiled 1451 to 654 computations (54.9% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))
✓	0.1b	(sqrt.f64 (sqrt.f64 x))
✓	0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
✓	0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))

series257.0ms (11.3%)

Counts

4 → 55

Calls

4 calls:

220.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
18.0ms	(sqrt.f64 (sqrt.f64 x))
11.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
9.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))

rewrite27.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
31×	`sqrt-prod_binary64`
24×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`

Counts

4 → 109

Calls

4 calls:

7.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
7.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))
7.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
1.0ms	(sqrt.f64 (sqrt.f64 x))

simplify103.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

500×	`times-frac_binary64`
485×	`fma-neg_binary64`
437×	`fma-def_binary64`
287×	`distribute-rgt-in_binary64`
268×	`distribute-lft-in_binary64`

Counts

164 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	1445
1	297	1396
2	938	1387
3	2579	1387
4	4265	1387
5	5337	1387

prune142.0ms (6.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	164	4	168
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	168	6	174

Error

0.0b

Counts

174 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
	0.2b	(+.f64 (-.f64 1 x) (.f64 (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x)))))
▶	0.2b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4)))
	35.1b	(+.f64 (-.f64 1 x) (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (sqrt.f64 x))))
	27.7b	(/.f64 (-.f64 (.f64 (-.f64 1 x) (-.f64 1 x)) (.f64 y (*.f64 y x))) (-.f64 1 (fma.f64 y (sqrt.f64 x) x)))
	0.2b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 x)) 3))))

Compiler

Compiled 3277 to 1205 computations (63.2% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4)))
	0.1b	(sqrt.f64 (sqrt.f64 x))
	0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
✓	0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4))

series27.0ms (1.2%)

Counts

2 → 27

Calls

2 calls:

16.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4))
11.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4)))

rewrite18.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`add-exp-log_binary64`
13×	`associate-+l+_binary64`
12×	`add-cube-cbrt_binary64`

Counts

2 → 60

Calls

2 calls:

8.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4)))
6.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4))

simplify84.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

930×	`fma-neg_binary64`
453×	`fma-def_binary64`
445×	`cancel-sign-sub-inv_binary64`
371×	`times-frac_binary64`
323×	`exp-prod_binary64`

Counts

87 → 98

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	116	1168
1	283	1084
2	960	1069
3	2618	744
4	3645	743
5	5012	743

prune143.0ms (6.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	151	5	156

Error

Counts

156 → 5

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 (-.f64 1 x) (.f64 (pow.f64 x 1/4) (.f64 y (sqrt.f64 (sqrt.f64 x)))))
	0.2b	(+.f64 (-.f64 1 x) (.f64 (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x (/.f64 1/4 2))) (pow.f64 x (/.f64 1/4 2))))
	0.2b	(+.f64 (-.f64 1 x) (.f64 (.f64 (pow.f64 x 1/4) (.f64 y (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1/4))) (pow.f64 (cbrt.f64 x) 1/4)))
	27.7b	(/.f64 (-.f64 (.f64 (-.f64 1 x) (-.f64 1 x)) (.f64 y (*.f64 y x))) (-.f64 1 (fma.f64 y (sqrt.f64 x) x)))
✓	0.1b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

Compiler

Compiled 2973 to 1510 computations (49.2% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 1 x) (.f64 (pow.f64 x 1/4) (.f64 y (sqrt.f64 (sqrt.f64 x)))))
	0.1b	(sqrt.f64 (sqrt.f64 x))
	0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
✓	0.3b	(.f64 (pow.f64 x 1/4) (.f64 y (sqrt.f64 (sqrt.f64 x))))

series28.0ms (1.2%)

Counts

2 → 27

Calls

2 calls:

16.0ms	(.f64 (pow.f64 x 1/4) (.f64 y (sqrt.f64 (sqrt.f64 x))))
12.0ms	(+.f64 (-.f64 1 x) (.f64 (pow.f64 x 1/4) (.f64 y (sqrt.f64 (sqrt.f64 x)))))

rewrite17.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`add-exp-log_binary64`
13×	`associate-+l+_binary64`
12×	`add-cube-cbrt_binary64`

Counts

2 → 60

Calls

2 calls:

7.0ms	(+.f64 (-.f64 1 x) (.f64 (pow.f64 x 1/4) (.f64 y (sqrt.f64 (sqrt.f64 x)))))
6.0ms	(.f64 (pow.f64 x 1/4) (.f64 y (sqrt.f64 (sqrt.f64 x))))

simplify104.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

1066×	`fma-neg_binary64`
455×	`cancel-sign-sub-inv_binary64`
400×	`fma-def_binary64`
338×	`exp-prod_binary64`
329×	`times-frac_binary64`

Counts

87 → 99

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	112	1147
1	274	1074
2	872	1050
3	2524	733
4	3412	732
5	4951	732
6	4846	732

prune138.0ms (6.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	151	5	156

Error

Counts

156 → 5

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 (-.f64 1 x) (.f64 (pow.f64 x 1/4) (.f64 y (sqrt.f64 (sqrt.f64 x)))))
	0.2b	(+.f64 (-.f64 1 x) (.f64 (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x (/.f64 1/4 2))) (pow.f64 x (/.f64 1/4 2))))
	0.2b	(+.f64 (-.f64 1 x) (.f64 (.f64 (pow.f64 x 1/4) (.f64 y (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1/4))) (pow.f64 (cbrt.f64 x) 1/4)))
	27.7b	(/.f64 (-.f64 (.f64 (-.f64 1 x) (-.f64 1 x)) (.f64 y (*.f64 y x))) (-.f64 1 (fma.f64 y (sqrt.f64 x) x)))
✓	0.1b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

Compiler

Compiled 2895 to 1452 computations (49.8% saved)

regimes191.0ms (8.3%)

Accuracy

Total 0.1b remaining (81.2%)

Threshold costs 0.1b (81.2%)

Counts

62 → 1

Compiler

Compiled 3347 to 2272 computations (32.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	11	10
2	15	10
3	17	10
4	18	10
5	17	10

end89.0ms (3.9%)

Compiler: Compiled 113 to 79 computations (30.1% saved)

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	63	10
4	127	10
5	233	10
6	324	10
7	361	10
8	400	10
9	414	10
10	383	10

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	63	10
4	127	10
5	233	10
6	324	10
7	361	10
8	400	10
9	414	10
10	383	10

Details

analyze20.0ms (0.9%)

sample653.0ms (28.6%)

simplify17.0ms (0.8%)

prune3.0ms (0.1%)

localize7.0ms (0.3%)

series19.0ms (0.8%)

rewrite14.0ms (0.6%)

simplify74.0ms (3.3%)

prune79.0ms (3.5%)

localize7.0ms (0.3%)

series257.0ms (11.3%)

rewrite27.0ms (1.2%)

simplify103.0ms (4.5%)

prune142.0ms (6.2%)

localize10.0ms (0.4%)

series27.0ms (1.2%)

rewrite18.0ms (0.8%)

simplify84.0ms (3.7%)

prune143.0ms (6.3%)

localize10.0ms (0.4%)

series28.0ms (1.2%)

rewrite17.0ms (0.8%)

simplify104.0ms (4.5%)

prune138.0ms (6.1%)

regimes191.0ms (8.3%)

simplify3.0ms (0.1%)

end89.0ms (3.9%)

Profiling

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	63	10
4	127	10
5	233	10
6	324	10
7	361	10
8	400	10
9	414	10
10	383	10