Details

analyze266.0ms (9.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample22.0ms (0.8%)

Algorithm

1×

intervals

Results

16.0ms

256×

body

128

valid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify253.0ms (8.6%)

Algorithm

1×	egg-herbie

Rules

1534×	`div-sub_binary64`
888×	`distribute-rgt-in_binary64`
690×	`times-frac_binary64`
535×	`sub-neg_binary64`
432×	`distribute-rgt-neg-in_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	25	21
2	43	21
3	57	21
4	66	21
5	76	21
6	113	21
7	151	21
8	240	21
9	385	21
10	484	21
11	552	21
12	650	21
13	1275	21
14	2898	21
15	3244	21
16	3247	21
17	3326	21
18	3358	21
19	3426	21
20	3437	21
21	3725	21
22	3759	21
23	3775	21
24	3775	21
25	3775	21
26	4954	21
27	5830	21

prune1.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))

Compiler

Compiled 30 to 24 computations (20% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))
0.0b	(*.f64 6 (-.f64 x 1))
0.1b	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))

rewrite93.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

15×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
9×	`add-cube-cbrt_binary64`

Counts

3 → 70

Calls

3 calls:

10.0ms	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))
5.0ms	(*.f64 6 (-.f64 x 1))
4.0ms	(+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))

Compiler

Compiled 1533 to 1141 computations (25.6% saved)

series19.0ms (0.7%)

Error

0.1b

Counts

3 → 12

Calls

3 calls:

6.0ms	(*.f64 6 (-.f64 x 1))
4.0ms	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))
3.0ms	(+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))

Compiler

Compiled 294 to 237 computations (19.4% saved)

simplify71.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

429×	`distribute-rgt-in_binary64`
383×	`distribute-lft-in_binary64`
372×	`times-frac_binary64`
330×	`div-sub_binary64`
328×	`associate-l_binary64`

Counts

82 → 53

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	119	1349
1	313	1153
2	1003	1147
3	3991	1147
4	4907	1147

prune37.0ms (1.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	48	5	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	5	54

Error

Counts

54 → 5

Alt Table

Status	Error	Program
	0.3b	(/.f64 (.f64 (-.f64 x 1) (/.f64 6 (sqrt.f64 (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x)))))) (sqrt.f64 (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))))
	27.2b	(.f64 (/.f64 (+.f64 -6 (.f64 6 x)) (+.f64 (pow.f64 (+.f64 x 1) 3) (pow.f64 (.f64 4 (sqrt.f64 x)) 3))) (+.f64 (.f64 (+.f64 x 1) (+.f64 x 1)) (-.f64 (.f64 (.f64 4 (sqrt.f64 x)) (.f64 4 (sqrt.f64 x))) (.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x))))))
▶	0.1b	(.f64 6 (/.f64 (-.f64 x 1) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x)))))
	0.1b	(/.f64 (-.f64 6 (.f64 6 x)) (-.f64 -1 (+.f64 x (.f64 4 (sqrt.f64 x)))))
	0.4b	(/.f64 (.f64 (.f64 6 (+.f64 1 (sqrt.f64 x))) (-.f64 (sqrt.f64 x) 1)) (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x))))

Compiler

Compiled 993 to 735 computations (26% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))
0.0b	(.f64 6 (/.f64 (-.f64 x 1) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x)))))
0.0b	(/.f64 (-.f64 x 1) (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x))))

rewrite145.0ms (4.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

60×	`add-sqr-sqrt_binary64`
48×	`*-un-lft-identity_binary64`
43×	`times-frac_binary64`
27×	`associate-r_binary64`
27×	`add-cube-cbrt_binary64`

Counts

3 → 107

Calls

3 calls:

11.0ms	(.f64 6 (/.f64 (-.f64 x 1) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x)))))
7.0ms	(/.f64 (-.f64 x 1) (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x))))
4.0ms	(+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))

Compiler

Compiled 2482 to 1808 computations (27.2% saved)

series16.0ms (0.5%)

Error

Counts

3 → 9

Calls

3 calls:

5.0ms	(.f64 6 (/.f64 (-.f64 x 1) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x)))))
4.0ms	(/.f64 (-.f64 x 1) (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x))))
4.0ms	(+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))

Compiler

Compiled 195 to 168 computations (13.8% saved)

simplify145.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

596×	`div-sub_binary64`
387×	`distribute-rgt-in_binary64`
346×	`distribute-lft-in_binary64`
321×	`distribute-rgt-out_binary64`
295×	`associate-l_binary64`

Counts

116 → 98

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	138	3051
1	355	2807
2	1075	2799
3	3505	2799
4	4679	2799
5	5664	2799

prune87.0ms (3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	98	5	103

Error

Counts

103 → 5

Alt Table

Status	Error	Program
	0.3b	(/.f64 (.f64 (-.f64 x 1) (/.f64 6 (sqrt.f64 (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x)))))) (sqrt.f64 (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))))
	27.2b	(.f64 (/.f64 (+.f64 -6 (.f64 6 x)) (+.f64 (pow.f64 (+.f64 x 1) 3) (pow.f64 (.f64 4 (sqrt.f64 x)) 3))) (+.f64 (.f64 (+.f64 x 1) (+.f64 x 1)) (-.f64 (.f64 (.f64 4 (sqrt.f64 x)) (.f64 4 (sqrt.f64 x))) (.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x))))))
✓	0.1b	(.f64 6 (/.f64 (-.f64 x 1) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x)))))
▶	0.1b	(/.f64 (-.f64 6 (.f64 6 x)) (-.f64 -1 (+.f64 x (.f64 4 (sqrt.f64 x)))))
	0.4b	(.f64 6 (.f64 (+.f64 1 (sqrt.f64 x)) (/.f64 (+.f64 -1 (sqrt.f64 x)) (+.f64 (+.f64 1 x) (*.f64 4 (sqrt.f64 x))))))

Compiler

Compiled 2141 to 1563 computations (27% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 -1 (+.f64 x (*.f64 4 (sqrt.f64 x))))
0.0b	(+.f64 x (*.f64 4 (sqrt.f64 x)))
0.0b	(-.f64 6 (*.f64 6 x))
0.1b	(/.f64 (-.f64 6 (.f64 6 x)) (-.f64 -1 (+.f64 x (.f64 4 (sqrt.f64 x)))))

rewrite94.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

27×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
13×	`add-log-exp_binary64`

Counts

4 → 83

Calls

4 calls:

6.0ms	(/.f64 (-.f64 6 (.f64 6 x)) (-.f64 -1 (+.f64 x (.f64 4 (sqrt.f64 x)))))
4.0ms	(-.f64 -1 (+.f64 x (*.f64 4 (sqrt.f64 x))))
3.0ms	(-.f64 6 (*.f64 6 x))
2.0ms	(+.f64 x (*.f64 4 (sqrt.f64 x)))

Compiler

Compiled 1948 to 1441 computations (26% saved)

series28.0ms (1%)

Error

Counts

4 → 15

Calls

4 calls:

11.0ms	(-.f64 6 (*.f64 6 x))
4.0ms	(/.f64 (-.f64 6 (.f64 6 x)) (-.f64 -1 (+.f64 x (.f64 4 (sqrt.f64 x)))))
4.0ms	(+.f64 x (*.f64 4 (sqrt.f64 x)))
4.0ms	(-.f64 -1 (+.f64 x (*.f64 4 (sqrt.f64 x))))

Compiler

Compiled 402 to 328 computations (18.4% saved)

simplify104.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

502×	`associate-l_binary64`
477×	`associate-r_binary64`
430×	`div-sub_binary64`
234×	`distribute-rgt-in_binary64`
204×	`distribute-lft-in_binary64`

Counts

98 → 40

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	143	2116
1	385	1961
2	1027	1949
3	4166	1949
4	5314	1949

prune34.0ms (1.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	40	5	45

Error

Counts

45 → 5

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (.f64 (-.f64 x 1) (/.f64 6 (sqrt.f64 (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x)))))) (sqrt.f64 (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))))
	27.2b	(.f64 (/.f64 (+.f64 -6 (.f64 6 x)) (+.f64 (pow.f64 (+.f64 x 1) 3) (pow.f64 (.f64 4 (sqrt.f64 x)) 3))) (+.f64 (.f64 (+.f64 x 1) (+.f64 x 1)) (-.f64 (.f64 (.f64 4 (sqrt.f64 x)) (.f64 4 (sqrt.f64 x))) (.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x))))))
✓	0.1b	(.f64 6 (/.f64 (-.f64 x 1) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x)))))
✓	0.1b	(/.f64 (-.f64 6 (.f64 6 x)) (-.f64 -1 (+.f64 x (.f64 4 (sqrt.f64 x)))))
	0.4b	(.f64 6 (.f64 (+.f64 1 (sqrt.f64 x)) (/.f64 (+.f64 -1 (sqrt.f64 x)) (+.f64 (+.f64 1 x) (*.f64 4 (sqrt.f64 x))))))

Compiler

Compiled 778 to 574 computations (26.2% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x))))
0.1b	(/.f64 6 (sqrt.f64 (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))))
0.2b	(/.f64 (.f64 (-.f64 x 1) (/.f64 6 (sqrt.f64 (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x)))))) (sqrt.f64 (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))))
0.2b	(.f64 (-.f64 x 1) (/.f64 6 (sqrt.f64 (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))))

rewrite191.0ms (6.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

51×	`add-sqr-sqrt_binary64`
44×	`times-frac_binary64`
41×	`*-un-lft-identity_binary64`
38×	`add-cube-cbrt_binary64`
31×	`sqrt-prod_binary64`

Counts

4 → 144

Calls

4 calls:

16.0ms	(/.f64 (.f64 (-.f64 x 1) (/.f64 6 (sqrt.f64 (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x)))))) (sqrt.f64 (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))))
13.0ms	(.f64 (-.f64 x 1) (/.f64 6 (sqrt.f64 (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))))
6.0ms	(/.f64 6 (sqrt.f64 (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))))
4.0ms	(sqrt.f64 (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x))))

Compiler

Compiled 5008 to 3710 computations (25.9% saved)

series27.0ms (0.9%)

Error

Counts

4 → 12

Calls

4 calls:

8.0ms	(.f64 (-.f64 x 1) (/.f64 6 (sqrt.f64 (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))))
6.0ms	(/.f64 6 (sqrt.f64 (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))))
5.0ms	(sqrt.f64 (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x))))
4.0ms	(/.f64 (.f64 (-.f64 x 1) (/.f64 6 (sqrt.f64 (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x)))))) (sqrt.f64 (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))))

Compiler

Compiled 552 to 444 computations (19.6% saved)

simplify145.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

557×	`associate-/l/_binary64`
422×	`div-sub_binary64`
383×	`distribute-rgt-in_binary64`
354×	`distribute-lft-in_binary64`
352×	`associate-/r*_binary64`

Counts

156 → 82

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	4845
1	455	3951
2	1714	3945
3	4722	3945
4	5751	3945

prune73.0ms (2.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	82	5	87

Error

Counts

87 → 5

Alt Table

Status	Error	Program
	0.3b	(/.f64 (.f64 (-.f64 x 1) (/.f64 6 (sqrt.f64 (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x)))))) (sqrt.f64 (+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))))
	27.2b	(.f64 (/.f64 (+.f64 -6 (.f64 6 x)) (+.f64 (pow.f64 (+.f64 x 1) 3) (pow.f64 (.f64 4 (sqrt.f64 x)) 3))) (+.f64 (.f64 (+.f64 x 1) (+.f64 x 1)) (-.f64 (.f64 (.f64 4 (sqrt.f64 x)) (.f64 4 (sqrt.f64 x))) (.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x))))))
	0.1b	(.f64 6 (/.f64 (-.f64 x 1) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x)))))
	0.1b	(/.f64 (-.f64 6 (.f64 6 x)) (-.f64 -1 (+.f64 x (.f64 4 (sqrt.f64 x)))))
	0.4b	(.f64 6 (.f64 (+.f64 1 (sqrt.f64 x)) (/.f64 (+.f64 -1 (sqrt.f64 x)) (+.f64 (+.f64 1 x) (*.f64 4 (sqrt.f64 x))))))

Compiler

Compiled 1925 to 1417 computations (26.4% saved)

regimes285.0ms (9.7%)

Accuracy

Total 0.0b remaining (86.8%)

Threshold costs 0.0b (86.8%)

Compiler

Compiled 6540 to 5114 computations (21.8% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	20	21
2	21	21
3	19	21

end1.0ms (0%)

Compiler: Compiled 15 to 12 computations (20% saved)

sample750.0ms (25.6%)

Algorithm

1×

intervals

Results

483.0ms	8000×	body	128	valid
0.0ms	3×	body	128	nan

Compiler

Compiled 155 to 119 computations (23.2% saved)

Details

analyze266.0ms (9.1%)

sample22.0ms (0.8%)

simplify253.0ms (8.6%)

prune1.0ms (0.1%)

localize9.0ms (0.3%)

rewrite93.0ms (3.2%)

series19.0ms (0.7%)

simplify71.0ms (2.4%)

prune37.0ms (1.3%)

localize10.0ms (0.3%)

rewrite145.0ms (4.9%)

series16.0ms (0.5%)

simplify145.0ms (4.9%)

prune87.0ms (3%)

localize9.0ms (0.3%)

rewrite94.0ms (3.2%)

series28.0ms (1%)

simplify104.0ms (3.6%)

prune34.0ms (1.2%)

localize16.0ms (0.5%)

rewrite191.0ms (6.5%)

series27.0ms (0.9%)

simplify145.0ms (4.9%)

prune73.0ms (2.5%)

regimes285.0ms (9.7%)

simplify4.0ms (0.2%)

end1.0ms (0%)

sample750.0ms (25.6%)

Profiling