Details

analyze472.0ms (21.2%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
12.5%	71.8%	15.7%	8
25%	56.2%	18.9%	9
31.2%	43.7%	25.1%	10
39%	34.7%	26.3%	11
44.9%	27.9%	27.3%	12
47.8%	22%	30.2%	13
52.6%	16.8%	30.7%	14

sample17.0ms (0.8%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	80	valid
0.0ms	16×	body	80	invalid

simplify16.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	247	9
1	247	9

prune6.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0.0b

Counts

2 → 1

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

0.0b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64`
1×	`*-un-lft-identity_binary64` `sub-neg_binary64` `pow1_binary64` `flip3--_binary64` `diff-log_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `flip--_binary64`

Counts

1 → 11

Calls

1 calls:

4.0ms

(-.f64 (*.f64 x x) (*.f64 (*.f64 y 4.0) z))

series11.0ms (0.5%)

Counts

1 → 3

Calls

1 calls:

11.0ms

(-.f64 (*.f64 x x) (*.f64 (*.f64 y 4.0) z))

simplify49.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

14 → 14

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4905	179
1	4905	179

prune20.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	13	1	14
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	13	2	15

Merged error: 0.0b

Counts

15 → 2

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z))
0.1b	(.f64 (sqrt.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4.0) z))) (sqrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z))))
2.7b	(sqrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z)))
2.7b	(sqrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z)))

rewrite31.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
24×	`sqrt-prod_binary64`
21×	`pow1_binary64`
16×	`sqrt-div_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`pow1/2_binary64` `sqrt-pow1_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`swap-sqr_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
5×	`pow-prod-up_binary64`
4×	`unswap-sqr_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `pow-sqr_binary64`
2×	`associate-r/_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 98

Calls

4 calls:

13.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4.0) z))) (sqrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z))))
6.0ms	(sqrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z)))
4.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z))
4.0ms	(sqrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z)))

series57.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

18.0ms	(sqrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z)))
17.0ms	(sqrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z)))
11.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4.0) z))) (sqrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z))))
11.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z))

simplify68.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4930	1456
1	4930	1456

prune140.0ms (6.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	109	3	112

Merged error: 0.0b

Counts

112 → 3

localize16.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (sqrt.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4.0) z))) (fabs.f64 (cbrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z)))))
2.7b	(sqrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z)))
3.1b	(cbrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z)))
3.1b	(cbrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z)))

rewrite23.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`pow1_binary64` `sqrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64` `cbrt-prod_binary64`
4×	`cbrt-div_binary64` `add-log-exp_binary64` `flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
3×	`associate-r_binary64`
2×	`pow1/3_binary64` `unswap-sqr_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 65

Calls

4 calls:

8.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4.0) z))) (fabs.f64 (cbrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z)))
4.0ms	(cbrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z)))
4.0ms	(cbrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z)))

series117.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4.0) z))) (fabs.f64 (cbrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z)))))
28.0ms	(cbrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z)))
28.0ms	(cbrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z)))
21.0ms	(sqrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z)))

simplify51.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4938	1390
1	4938	1390

prune131.0ms (5.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	77	3	80

Merged error: 0.0b

Counts

80 → 3

localize10.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z))
0.1b	(pow.f64 (sqrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z))) 4)
2.7b	(sqrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z)))
17.9b	(sqrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z))) 4))

rewrite23.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`sqrt-prod_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`unpow-prod-down_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64`
5×	`add-exp-log_binary64` `rem-sqrt-square_binary64`
4×	`add-cbrt-cube_binary64`
3×	`pow-unpow_binary64` `pow1/2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64`
2×	`flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-pow2_binary64` `pow-exp_binary64`

Counts

4 → 72

Calls

4 calls:

6.0ms	(sqrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z))) 4))
6.0ms	(pow.f64 (sqrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z))) 4)
4.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z))
4.0ms	(sqrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z)))

series56.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

20.0ms	(sqrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z)))
14.0ms	(pow.f64 (sqrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z))) 4)
11.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z))
11.0ms	(sqrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 x x) (.f64 (*.f64 y 4.0) z))) 4))

simplify49.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4946	1006
1	4946	1006

prune97.0ms (4.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	84	3	87

Merged error: 0.0b

Counts

87 → 3

regimes343.0ms (15.4%)

Accuracy

Total 0.0b remaining (3.1%)

Threshold costs 0.0b (3.1%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	9
1	52	9

end0.0ms (0%)

sample406.0ms (18.2%)

Algorithm

1×

intervals

Results

232.0ms	8000×	body	80	valid
13.0ms	475×	body	80	invalid

Details

analyze472.0ms (21.2%)

sample17.0ms (0.8%)

simplify16.0ms (0.7%)

prune6.0ms (0.3%)

localize6.0ms (0.3%)

rewrite5.0ms (0.2%)

series11.0ms (0.5%)

simplify49.0ms (2.2%)

prune20.0ms (0.9%)

localize9.0ms (0.4%)

rewrite31.0ms (1.4%)

series57.0ms (2.6%)

simplify68.0ms (3.1%)

prune140.0ms (6.3%)

localize16.0ms (0.7%)

rewrite23.0ms (1%)

series117.0ms (5.3%)

simplify51.0ms (2.3%)

prune131.0ms (5.9%)

localize10.0ms (0.5%)

rewrite23.0ms (1%)

series56.0ms (2.5%)

simplify49.0ms (2.2%)

prune97.0ms (4.3%)

regimes343.0ms (15.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample406.0ms (18.2%)

Profiling