Details

analyze553.0ms (16.6%)

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
3.1%	96.7%	0.2%	8
19.9%	79.9%	0.2%	9
22.8%	77%	0.2%	10
35.1%	64.7%	0.2%	11
45%	54.8%	0.2%	12
53.8%	45.1%	1.2%	13
56.2%	42.4%	1.5%	14

sample24.0ms (0.7%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	80	valid
1.0ms	17×	body	80	invalid

simplify212.0ms (6.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (209.0ms)

Iter	Nodes	Cost
0	5403	9

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: 2.2b

Counts

2 → 1

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 x y) (-.f64 z y))
2.1b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

rewrite28.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
70×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-l_binary64`
26×	`add-cube-cbrt_binary64`
22×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r_binary64` `associate-/l_binary64`
4×	`pow1_binary64` `associate-/r/_binary64`
3×	`flip3--_binary64` `associate-r_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

2 → 102

Calls

2 calls:

14.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
9.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

series45.0ms (1.3%)

Counts

2 → 6

Calls

2 calls:

30.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
14.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

simplify52.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5649	1183

prune142.0ms (4.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	101	7	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	7	109

Merged error: 0.0b

Counts

109 → 7

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 x (-.f64 z y)) (/.f64 y (-.f64 z y)))
0.0b	(/.f64 x (-.f64 z y))
0.0b	(/.f64 y (-.f64 z y))
2.1b	(*.f64 (-.f64 (/.f64 x (-.f64 z y)) (/.f64 y (-.f64 z y))) t)

rewrite84.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`*-un-lft-identity_binary64`
80×	`add-sqr-sqrt_binary64`
66×	`times-frac_binary64`
32×	`distribute-lft-out--_binary64`
30×	`add-cube-cbrt_binary64`
20×	`difference-of-squares_binary64`
18×	`associate-l_binary64`
12×	`associate-/r/_binary64`
10×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`flip3--_binary64` `flip--_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `distribute-rgt-out--_binary64` `associate-/l*_binary64` `div-inv_binary64`
4×	`associate-*l/_binary64`
3×	`associate-r_binary64`
2×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `sub-div_binary64` `frac-sub_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 139

Calls

4 calls:

37.0ms	(*.f64 (-.f64 (/.f64 x (-.f64 z y)) (/.f64 y (-.f64 z y))) t)
29.0ms	(-.f64 (/.f64 x (-.f64 z y)) (/.f64 y (-.f64 z y)))
6.0ms	(/.f64 y (-.f64 z y))
6.0ms	(/.f64 x (-.f64 z y))

series80.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(*.f64 (-.f64 (/.f64 x (-.f64 z y)) (/.f64 y (-.f64 z y))) t)
18.0ms	(-.f64 (/.f64 x (-.f64 z y)) (/.f64 y (-.f64 z y)))
9.0ms	(/.f64 x (-.f64 z y))
7.0ms	(/.f64 y (-.f64 z y))

simplify58.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5231	1706

prune165.0ms (5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	151	7	158

Merged error: 0.0b

Counts

158 → 7

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.2b	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 z y)))
2.1b	(.f64 (.f64 (-.f64 x y) (/.f64 1 (-.f64 z y))) t)

rewrite35.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
26×	`add-exp-log_binary64`
24×	`associate-r_binary64`
22×	`*-un-lft-identity_binary64`
17×	`times-frac_binary64`
16×	`add-cbrt-cube_binary64`
13×	`add-cube-cbrt_binary64` `prod-exp_binary64`
10×	`associate-*l/_binary64`
9×	`pow1_binary64`
7×	`cbrt-unprod_binary64`
6×	`associate-l_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`pow-prod-down_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `frac-times_binary64`
3×	`unswap-sqr_binary64`
2×	`add-log-exp_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `associate-/r/_binary64` `rec-exp_binary64` `un-div-inv_binary64` `-commutative_binary64`
1×	`div-inv_binary64`

Counts

2 → 78

Calls

2 calls:

16.0ms	(.f64 (.f64 (-.f64 x y) (/.f64 1 (-.f64 z y))) t)
15.0ms	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 z y)))

series42.0ms (1.3%)

Counts

2 → 6

Calls

2 calls:

30.0ms	(.f64 (.f64 (-.f64 x y) (/.f64 1 (-.f64 z y))) t)
12.0ms	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 z y)))

simplify75.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4999	750
1	4999	750

prune106.0ms (3.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	83	8	91

Merged error: 0b

Counts

91 → 8

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.1b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
4.4b	(cbrt.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t))
4.4b	(cbrt.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t))
4.4b	(cbrt.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t))

rewrite47.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
36×	`*-un-lft-identity_binary64`
31×	`associate-l_binary64`
26×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `associate-*l/_binary64`
3×	`cbrt-div_binary64` `associate-r_binary64` `pow1/3_binary64` `cbrt-prod_binary64`
2×	`cbrt-unprod_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

4 → 80

Calls

4 calls:

15.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
10.0ms	(cbrt.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t))
9.0ms	(cbrt.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t))
9.0ms	(cbrt.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t))

series346.0ms (10.4%)

Counts

4 → 12

Calls

4 calls:

106.0ms	(cbrt.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t))
106.0ms	(cbrt.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t))
105.0ms	(cbrt.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t))
29.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

simplify40.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5251	1048

prune95.0ms (2.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	92	8	100

Merged error: 0b

Counts

100 → 8

regimes531.0ms (16%)

Accuracy

Total 2.4b remaining (99.3%)

Threshold costs 0b (0%)

bsearch32.0ms (1%)

Steps

Iters	Range		Point
8	9.947408340566814e-179	2.6397479240591788e-176	1.9469965754910335e-177
7	-3.291563849668862e-41	-1.685723416176602e-42	-2.0915467853000205e-42

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	31
1	44	31

end0.0ms (0%)

sample491.0ms (14.8%)

Algorithm

1×

intervals

Results

256.0ms	8000×	body	80	valid
17.0ms	582×	body	80	invalid

Details

analyze553.0ms (16.6%)

sample24.0ms (0.7%)

simplify212.0ms (6.4%)

prune7.0ms (0.2%)

localize7.0ms (0.2%)

rewrite28.0ms (0.8%)

series45.0ms (1.3%)

simplify52.0ms (1.5%)

prune142.0ms (4.3%)

localize8.0ms (0.2%)

rewrite84.0ms (2.5%)

series80.0ms (2.4%)

simplify58.0ms (1.7%)

prune165.0ms (5%)

localize8.0ms (0.2%)

rewrite35.0ms (1%)

series42.0ms (1.3%)

simplify75.0ms (2.3%)

prune106.0ms (3.2%)

localize11.0ms (0.3%)

rewrite47.0ms (1.4%)

series346.0ms (10.4%)

simplify40.0ms (1.2%)

prune95.0ms (2.9%)

regimes531.0ms (16%)

bsearch32.0ms (1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample491.0ms (14.8%)

Profiling