Details

analyze665.0ms (15.2%)

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
12.5%	87.3%	0.2%	7
18.7%	81.1%	0.2%	8
46.8%	53%	0.2%	9
47.6%	52.2%	0.2%	10
48.3%	51.5%	0.2%	11
54.2%	45.6%	0.2%	12
67.6%	32.2%	0.2%	13
68.2%	31.6%	0.2%	14

sample22.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	80	valid
1.0ms	38×	body	80	invalid

simplify40.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	640	13
1	640	13

prune7.0ms (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: 0.0b

Counts

2 → 1

localize12.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (-.f64 (.f64 (/.f64 1.0 8.0) x) (/.f64 (.f64 y z) 2.0)) t)
0.0b	(-.f64 (.f64 (/.f64 1.0 8.0) x) (/.f64 (.f64 y z) 2.0))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64`
2×	`sub-neg_binary64` `pow1_binary64` `diff-log_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `associate-+l+_binary64` `associate-+l-_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `frac-sub_binary64` `associate-*l/_binary64`

Counts

2 → 27

Calls

2 calls:

10.0ms	(+.f64 (-.f64 (.f64 (/.f64 1.0 8.0) x) (/.f64 (.f64 y z) 2.0)) t)
7.0ms	(-.f64 (.f64 (/.f64 1.0 8.0) x) (/.f64 (.f64 y z) 2.0))

series26.0ms (0.6%)

Counts

2 → 6

Calls

2 calls:

14.0ms	(+.f64 (-.f64 (.f64 (/.f64 1.0 8.0) x) (/.f64 (.f64 y z) 2.0)) t)
12.0ms	(-.f64 (.f64 (/.f64 1.0 8.0) x) (/.f64 (.f64 y z) 2.0))

simplify54.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4978	517
1	4978	517

prune91.0ms (2.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	31	2	33
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	31	3	34

Merged error: 0.0b

Counts

34 → 3

localize34.0ms (0.8%)

Local error

Found 4 expressions with local error:

1.2b	(+.f64 (.f64 (.f64 (/.f64 1.0 8.0) x) (.f64 (/.f64 1.0 8.0) x)) (.f64 (/.f64 (.f64 y z) 2.0) (+.f64 (.f64 (/.f64 1.0 8.0) x) (/.f64 (*.f64 y z) 2.0))))
3.3b	(-.f64 (pow.f64 (.f64 (/.f64 1.0 8.0) x) 3) (pow.f64 (/.f64 (.f64 y z) 2.0) 3))
4.6b	(.f64 (/.f64 (.f64 y z) 2.0) (+.f64 (.f64 (/.f64 1.0 8.0) x) (/.f64 (.f64 y z) 2.0)))
36.8b	(/.f64 (-.f64 (pow.f64 (.f64 (/.f64 1.0 8.0) x) 3) (pow.f64 (/.f64 (.f64 y z) 2.0) 3)) (+.f64 (.f64 (.f64 (/.f64 1.0 8.0) x) (.f64 (/.f64 1.0 8.0) x)) (.f64 (/.f64 (.f64 y z) 2.0) (+.f64 (.f64 (/.f64 1.0 8.0) x) (/.f64 (*.f64 y z) 2.0)))))

rewrite106.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`associate-*l/_binary64`
77×	`add-sqr-sqrt_binary64`
56×	`frac-add_binary64`
42×	`times-frac_binary64`
40×	`difference-of-squares_binary64`
35×	`-un-lft-identity_binary64` `associate-r/_binary64` `frac-times_binary64`
30×	`sqr-pow_binary64`
25×	`add-cube-cbrt_binary64`
23×	`associate-/r/_binary64`
16×	`flip3-+_binary64` `flip-+_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`associate-/l*_binary64`
10×	`unpow-prod-down_binary64` `cube-prod_binary64`
8×	`add-log-exp_binary64`
7×	`associate-l_binary64`
6×	`pow1_binary64`
5×	`difference-cubes_binary64` `distribute-lft-out--_binary64`
4×	`cbrt-unprod_binary64` `cube-div_binary64` `prod-exp_binary64`
3×	`associate-/l/_binary64` `associate-/r_binary64` `associate-r*_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
2×	`flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-inv_binary64` `flip--_binary64` `associate-+r+_binary64` `frac-sub_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 185

Calls

4 calls:

52.0ms	(/.f64 (-.f64 (pow.f64 (.f64 (/.f64 1.0 8.0) x) 3) (pow.f64 (/.f64 (.f64 y z) 2.0) 3)) (+.f64 (.f64 (.f64 (/.f64 1.0 8.0) x) (.f64 (/.f64 1.0 8.0) x)) (.f64 (/.f64 (.f64 y z) 2.0) (+.f64 (.f64 (/.f64 1.0 8.0) x) (/.f64 (*.f64 y z) 2.0)))))
15.0ms	(+.f64 (.f64 (.f64 (/.f64 1.0 8.0) x) (.f64 (/.f64 1.0 8.0) x)) (.f64 (/.f64 (.f64 y z) 2.0) (+.f64 (.f64 (/.f64 1.0 8.0) x) (/.f64 (*.f64 y z) 2.0))))
15.0ms	(-.f64 (pow.f64 (.f64 (/.f64 1.0 8.0) x) 3) (pow.f64 (/.f64 (.f64 y z) 2.0) 3))
13.0ms	(.f64 (/.f64 (.f64 y z) 2.0) (+.f64 (.f64 (/.f64 1.0 8.0) x) (/.f64 (.f64 y z) 2.0)))

series147.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(/.f64 (-.f64 (pow.f64 (.f64 (/.f64 1.0 8.0) x) 3) (pow.f64 (/.f64 (.f64 y z) 2.0) 3)) (+.f64 (.f64 (.f64 (/.f64 1.0 8.0) x) (.f64 (/.f64 1.0 8.0) x)) (.f64 (/.f64 (.f64 y z) 2.0) (+.f64 (.f64 (/.f64 1.0 8.0) x) (/.f64 (*.f64 y z) 2.0)))))
48.0ms	(-.f64 (pow.f64 (.f64 (/.f64 1.0 8.0) x) 3) (pow.f64 (/.f64 (.f64 y z) 2.0) 3))
29.0ms	(+.f64 (.f64 (.f64 (/.f64 1.0 8.0) x) (.f64 (/.f64 1.0 8.0) x)) (.f64 (/.f64 (.f64 y z) 2.0) (+.f64 (.f64 (/.f64 1.0 8.0) x) (/.f64 (*.f64 y z) 2.0))))
16.0ms	(.f64 (/.f64 (.f64 y z) 2.0) (+.f64 (.f64 (/.f64 1.0 8.0) x) (/.f64 (.f64 y z) 2.0)))

simplify103.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4985	9743
1	4985	9743

prune945.0ms (21.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	195	2	197
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	197	3	200

Merged error: 0b

Counts

200 → 3

localize23.0ms (0.5%)

Local error

Found 4 expressions with local error:

1.2b	(+.f64 (+.f64 (.f64 0.0625 (.f64 x (.f64 y z))) (.f64 (.f64 (.f64 y z) (.f64 y z)) 0.25)) (.f64 0.015625 (*.f64 x x)))
3.3b	(-.f64 (pow.f64 (.f64 (/.f64 1.0 8.0) x) 3) (pow.f64 (/.f64 (.f64 y z) 2.0) 3))
4.5b	(.f64 x (.f64 y z))
36.8b	(/.f64 (-.f64 (pow.f64 (.f64 (/.f64 1.0 8.0) x) 3) (pow.f64 (/.f64 (.f64 y z) 2.0) 3)) (+.f64 (+.f64 (.f64 0.0625 (.f64 x (.f64 y z))) (.f64 (.f64 (.f64 y z) (.f64 y z)) 0.25)) (.f64 0.015625 (*.f64 x x))))

rewrite67.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-sqr-sqrt_binary64`
40×	`difference-of-squares_binary64`
39×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
30×	`sqr-pow_binary64`
23×	`add-cube-cbrt_binary64`
13×	`associate-/l*_binary64`
11×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`unpow-prod-down_binary64` `cube-prod_binary64`
9×	`pow1_binary64`
5×	`difference-cubes_binary64` `distribute-lft-out--_binary64`
4×	`cube-div_binary64`
3×	`pow-prod-down_binary64` `associate-/l/_binary64` `associate-/r_binary64` `cbrt-unprod_binary64` `associate-l*_binary64` `prod-exp_binary64` `sum-log_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `frac-sub_binary64` `associate-*l/_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `associate-+l+_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `*-commutative_binary64`

Counts

4 → 126

Calls

4 calls:

28.0ms	(/.f64 (-.f64 (pow.f64 (.f64 (/.f64 1.0 8.0) x) 3) (pow.f64 (/.f64 (.f64 y z) 2.0) 3)) (+.f64 (+.f64 (.f64 0.0625 (.f64 x (.f64 y z))) (.f64 (.f64 (.f64 y z) (.f64 y z)) 0.25)) (.f64 0.015625 (*.f64 x x))))
16.0ms	(-.f64 (pow.f64 (.f64 (/.f64 1.0 8.0) x) 3) (pow.f64 (/.f64 (.f64 y z) 2.0) 3))
12.0ms	(+.f64 (+.f64 (.f64 0.0625 (.f64 x (.f64 y z))) (.f64 (.f64 (.f64 y z) (.f64 y z)) 0.25)) (.f64 0.015625 (*.f64 x x)))
5.0ms	(.f64 x (.f64 y z))

series137.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

51.0ms	(-.f64 (pow.f64 (.f64 (/.f64 1.0 8.0) x) 3) (pow.f64 (/.f64 (.f64 y z) 2.0) 3))
49.0ms	(/.f64 (-.f64 (pow.f64 (.f64 (/.f64 1.0 8.0) x) 3) (pow.f64 (/.f64 (.f64 y z) 2.0) 3)) (+.f64 (+.f64 (.f64 0.0625 (.f64 x (.f64 y z))) (.f64 (.f64 (.f64 y z) (.f64 y z)) 0.25)) (.f64 0.015625 (*.f64 x x))))
29.0ms	(+.f64 (+.f64 (.f64 0.0625 (.f64 x (.f64 y z))) (.f64 (.f64 (.f64 y z) (.f64 y z)) 0.25)) (.f64 0.015625 (*.f64 x x)))
8.0ms	(.f64 x (.f64 y z))

simplify57.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5203	5817

prune344.0ms (7.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	138	3	141

Merged error: 0b

Counts

141 → 3

localize29.0ms (0.7%)

Local error

Found 4 expressions with local error:

9.2b	(sqrt.f64 (/.f64 (*.f64 y z) 2.0))
9.2b	(sqrt.f64 (/.f64 (*.f64 y z) 2.0))
23.5b	(sqrt.f64 (pow.f64 (*.f64 (/.f64 1.0 8.0) x) 3))
23.5b	(sqrt.f64 (pow.f64 (*.f64 (/.f64 1.0 8.0) x) 3))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`sqrt-prod_binary64`
14×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow1_binary64` `rem-sqrt-square_binary64` `times-frac_binary64`
4×	`add-log-exp_binary64` `pow1/2_binary64` `sqr-pow_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64`
2×	`cube-div_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `div-inv_binary64` `unpow3_binary64` `associate-*l/_binary64` `cube-mult_binary64`

Counts

4 → 76

Calls

4 calls:

3.0ms	(sqrt.f64 (/.f64 (*.f64 y z) 2.0))
3.0ms	(sqrt.f64 (/.f64 (*.f64 y z) 2.0))
3.0ms	(sqrt.f64 (pow.f64 (*.f64 (/.f64 1.0 8.0) x) 3))
3.0ms	(sqrt.f64 (pow.f64 (*.f64 (/.f64 1.0 8.0) x) 3))

series63.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(sqrt.f64 (/.f64 (*.f64 y z) 2.0))
26.0ms	(sqrt.f64 (/.f64 (*.f64 y z) 2.0))
6.0ms	(sqrt.f64 (pow.f64 (*.f64 (/.f64 1.0 8.0) x) 3))
5.0ms	(sqrt.f64 (pow.f64 (*.f64 (/.f64 1.0 8.0) x) 3))

simplify37.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5095	814

prune231.0ms (5.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	88	3	91

Merged error: 0b

Counts

91 → 3

regimes487.0ms (11.1%)

Accuracy

Total 0.0b remaining (1.9%)

Threshold costs 0.0b (1.9%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	13
1	49	13

end0.0ms (0%)

sample609.0ms (13.9%)

Algorithm

1×

intervals

Results

330.0ms	7999×	body	80	valid
45.0ms	1144×	body	80	invalid
0.0ms	1×	body	640	valid

Details

analyze665.0ms (15.2%)

sample22.0ms (0.5%)

simplify40.0ms (0.9%)

prune7.0ms (0.2%)

localize12.0ms (0.3%)

rewrite17.0ms (0.4%)

series26.0ms (0.6%)

simplify54.0ms (1.2%)

prune91.0ms (2.1%)

localize34.0ms (0.8%)

rewrite106.0ms (2.4%)

series147.0ms (3.4%)

simplify103.0ms (2.4%)

prune945.0ms (21.6%)

localize23.0ms (0.5%)

rewrite67.0ms (1.5%)

series137.0ms (3.1%)

simplify57.0ms (1.3%)

prune344.0ms (7.9%)

localize29.0ms (0.7%)

rewrite13.0ms (0.3%)

series63.0ms (1.4%)

simplify37.0ms (0.8%)

prune231.0ms (5.3%)

regimes487.0ms (11.1%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample609.0ms (13.9%)

Profiling