Details

analyze1.1s (25.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.6%	98.2%	0.2%	10
3.1%	90.4%	6.5%	11
9.2%	84.4%	6.5%	12
13%	80.6%	6.5%	13
24.8%	68.7%	6.5%	14

sample35.0ms (0.8%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	80	valid
3.0ms	73×	body	80	nan
1.0ms	23×	body	80	invalid

simplify40.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	805	14
1	805	14

prune8.0ms (0.2%)

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: 24.6b

Counts

2 → 1

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 z z) (.f64 t a))
6.0b	(.f64 (.f64 x y) z)
8.1b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
23.5b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite27.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
9×	`sqrt-prod_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `times-frac_binary64`
4×	`sqrt-div_binary64`
3×	`pow-prod-down_binary64` `flip3--_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64`
2×	`associate-/r/_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 75

Calls

4 calls:

11.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
5.0ms	(.f64 (.f64 x y) z)
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

series74.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
16.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
11.0ms	(.f64 (.f64 x y) z)
9.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify43.0ms (1%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5307	972

prune151.0ms (3.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	76	11	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	76	12	88

Merged error: 4.3b

Counts

88 → 12

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
1.0b	(-.f64 (.f64 z z) (.f64 t a))
4.2b	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
23.5b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
34×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
24×	`associate-r_binary64` `sqrt-prod_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `sqrt-div_binary64`
4×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
3×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `div-exp_binary64`
2×	`div-inv_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-r/_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 111

Calls

4 calls:

13.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
7.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

series78.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
16.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
13.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
9.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify57.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5256	1640

prune158.0ms (3.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	1	9	10
Picked	1	0	1
Done	1	0	1
Total	123	12	135

Merged error: 4.0b

Counts

135 → 12

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 z z) (.f64 t a))
1.7b	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
1.8b	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
23.5b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite36.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
25×	`associate-r_binary64`
20×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`sqrt-prod_binary64`
12×	`pow1_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64`
4×	`pow-prod-down_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `flip--_binary64`
2×	`cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`

Counts

4 → 91

Calls

4 calls:

13.0ms	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
11.0ms	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

series86.0ms (2%)

Counts

4 → 12

Calls

4 calls:

37.0ms	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
24.0ms	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
16.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
9.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify48.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4973	1238
1	4973	1238

prune136.0ms (3.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	104	11	115

Merged error: 4.0b

Counts

115 → 11

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 z z) (.f64 t a))
1.7b	(.f64 x (.f64 (.f64 y (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
6.6b	(.f64 (.f64 y (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 z) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
23.5b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite53.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-exp-log_binary64`
43×	`associate-r_binary64`
40×	`add-cbrt-cube_binary64`
36×	`times-frac_binary64`
32×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64` `cbrt-unprod_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64`
28×	`pow1_binary64`
21×	`sqrt-prod_binary64`
18×	`cbrt-prod_binary64`
16×	`pow-prod-down_binary64`
6×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
4×	`associate-l_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `associate-*r/_binary64` `flip--_binary64`
2×	`associate-/r/_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`

Counts

4 → 124

Calls

4 calls:

20.0ms	(.f64 (.f64 y (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 z) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
19.0ms	(.f64 x (.f64 (.f64 y (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series96.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(.f64 x (.f64 (.f64 y (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
28.0ms	(.f64 (.f64 y (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 z) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
18.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
9.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify74.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4903	1919
1	4903	1919

prune122.0ms (2.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	135	12	147

Merged error: 4.0b

Counts

147 → 12

regimes854.0ms (19.8%)

Accuracy

Total 3.9b remaining (53.3%)

Threshold costs 0b (0%)

bsearch35.0ms (0.8%)

Steps

Iters	Range		Point
7	9.412867195948032e+140	6.560810260066545e+142	9.594770076281723e+140
4	-1.3318014264147303e+60	-8.937591876171522e+59	-1.3181126064523061e+60

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	75	36
1	75	36

end0.0ms (0%)

sample908.0ms (21%)

Algorithm

1×

intervals

Results

420.0ms	8000×	body	80	valid
100.0ms	2171×	body	80	nan
48.0ms	907×	body	80	invalid

Details

analyze1.1s (25.8%)

sample35.0ms (0.8%)

simplify40.0ms (0.9%)

prune8.0ms (0.2%)

localize15.0ms (0.3%)

rewrite27.0ms (0.6%)

series74.0ms (1.7%)

simplify43.0ms (1%)

prune151.0ms (3.5%)

localize12.0ms (0.3%)

rewrite33.0ms (0.8%)

series78.0ms (1.8%)

simplify57.0ms (1.3%)

prune158.0ms (3.7%)

localize10.0ms (0.2%)

rewrite36.0ms (0.8%)

series86.0ms (2%)

simplify48.0ms (1.1%)

prune136.0ms (3.1%)

localize15.0ms (0.3%)

rewrite53.0ms (1.2%)

series96.0ms (2.2%)

simplify74.0ms (1.7%)

prune122.0ms (2.8%)

regimes854.0ms (19.8%)

bsearch35.0ms (0.8%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample908.0ms (21%)

Profiling