Details

analyze1.1s (10.1%)

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

Compiler

Compiled 15 to 13 computations (13.3% saved)

sample32.0ms (0.3%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
3.0ms	77×	body	128	nan
1.0ms	21×	body	128	invalid

Compiler

Compiled 29 to 30 computations (-3.4% saved)

simplify150.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	806	21
1	806	21

prune2.0ms (0%)

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

Error

20.0b

Counts

2 → 1

Compiler

Compiled 28 to 24 computations (14.3% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

22.2b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
6.3b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
4.2b	(.f64 (.f64 x y) z)
0.4b	(-.f64 (.f64 z z) (.f64 t a))
0.4b	(-.f64 (.f64 z z) (.f64 t a))
4.2b	(.f64 (.f64 x y) z)
6.3b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
22.2b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-cbrt-cube_binary64_6593` `add-exp-log_binary64_6595`
11×	`add-sqr-sqrt_binary64_6579`
10×	`add-cube-cbrt_binary64_6592` `pow1_binary64_6618` `*-un-lft-identity_binary64_6557`
9×	`sqrt-prod_binary64_6573`
6×	`associate-/r*_binary64_6501` `prod-exp_binary64_6606` `add-log-exp_binary64_6596` `cbrt-unprod_binary64_6590` `times-frac_binary64_6563`
4×	`sqrt-div_binary64_6574`
3×	`associate-r_binary64_6497` `pow-prod-down_binary64_6628` `flip--_binary64_6532` `div-exp_binary64_6608` `cbrt-undiv_binary64_6591` `flip3--_binary64_6561`
2×	`associate-/r/_binary64_6503`
1×	`-commutative_binary64_6488` `sqrt-pow1_binary64_6575` `sub-neg_binary64_6550` `div-inv_binary64_6554` `associate-l_binary64_6498` `diff-log_binary64_6649` `clear-num_binary64_6556` `frac-2neg_binary64_6568` `pow1/2_binary64_6637` `rem-sqrt-square_binary64_6570` `cancel-sign-sub-inv_binary64_6523` `associate-/l_binary64_6502`

Counts

4 → 76

Calls

8 calls:

11.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
6.0ms	(.f64 (.f64 x y) z)
5.0ms	(-.f64 (.f64 z z) (.f64 t a))
5.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
0.0ms	(-.f64 (.f64 z z) (.f64 t a))

series755.0ms (7%)

Counts

4 → 64

Calls

4 calls:

419.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
127.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
116.0ms	(-.f64 (.f64 z z) (.f64 t a))
93.0ms	(.f64 (.f64 x y) z)

Compiler

Compiled 1898 to 1662 computations (12.4% saved)

simplify63.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5467	2173

prune159.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	131	9	140
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	9	141

Error

3.6b

Counts

141 → 9

Compiler

Compiled 2529 to 474 computations (81.3% saved)

localize12.0ms (0.1%)

Local error

Found 8 expressions with local error:

22.2b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
2.8b	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
0.4b	(-.f64 (.f64 z z) (.f64 t a))
0.1b	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
0.1b	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
0.4b	(-.f64 (.f64 z z) (.f64 t a))
2.8b	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
22.2b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64_6563`
34×	`add-sqr-sqrt_binary64_6579`
33×	`add-cube-cbrt_binary64_6592` `*-un-lft-identity_binary64_6557`
24×	`sqrt-prod_binary64_6573` `associate-r_binary64_6497`
18×	`add-cbrt-cube_binary64_6593` `add-exp-log_binary64_6595`
10×	`pow1_binary64_6618`
6×	`associate-/r*_binary64_6501` `sqrt-div_binary64_6574` `prod-exp_binary64_6606` `add-log-exp_binary64_6596` `cbrt-unprod_binary64_6590`
4×	`flip--_binary64_6532` `associate-/r/_binary64_6503` `flip3--_binary64_6561`
3×	`pow-prod-down_binary64_6628` `div-exp_binary64_6608` `cbrt-undiv_binary64_6591` `associate-/l*_binary64_6502`
2×	`div-inv_binary64_6554`
1×	`-commutative_binary64_6488` `sqrt-pow1_binary64_6575` `associate-r/_binary64_6499` `sub-neg_binary64_6550` `associate-l_binary64_6498` `diff-log_binary64_6649` `clear-num_binary64_6556` `frac-2neg_binary64_6568` `pow1/2_binary64_6637` `rem-sqrt-square_binary64_6570` `cancel-sign-sub-inv_binary64_6523`

Counts

4 → 112

Calls

8 calls:

15.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
8.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
5.0ms	(-.f64 (.f64 z z) (.f64 t a))
5.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
0.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

series802.0ms (7.4%)

Counts

4 → 68

Calls

4 calls:

419.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
132.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
131.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
121.0ms	(-.f64 (.f64 z z) (.f64 t a))

Compiler

Compiled 2093 to 1855 computations (11.4% saved)

simplify58.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4974	3299
1	4974	3299

prune129.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	181	8	189

Error

3.6b

Counts

189 → 8

Compiler

Compiled 3526 to 618 computations (82.5% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

2.4b	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
1.7b	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
0.4b	(-.f64 (.f64 z z) (.f64 t a))
0.1b	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
0.4b	(-.f64 (.f64 z z) (.f64 t a))
1.7b	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
2.4b	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
22.2b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite46.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_6579`
25×	`associate-r_binary64_6497`
20×	`add-cube-cbrt_binary64_6592` `times-frac_binary64_6563` `*-un-lft-identity_binary64_6557`
18×	`add-cbrt-cube_binary64_6593` `add-exp-log_binary64_6595`
13×	`sqrt-prod_binary64_6573`
12×	`pow1_binary64_6618`
7×	`prod-exp_binary64_6606` `cbrt-unprod_binary64_6590`
6×	`associate-l_binary64_6498` `add-log-exp_binary64_6596`
4×	`pow-prod-down_binary64_6628` `sqrt-div_binary64_6574`
3×	`flip--_binary64_6532` `associate-*r/_binary64_6499` `unswap-sqr_binary64_6525` `flip3--_binary64_6561`
2×	`*-commutative_binary64_6488` `div-exp_binary64_6608` `cbrt-undiv_binary64_6591` `associate-/r/_binary64_6503`
1×	`sqrt-pow1_binary64_6575` `sub-neg_binary64_6550` `div-inv_binary64_6554` `diff-log_binary64_6649` `pow1/2_binary64_6637` `rem-sqrt-square_binary64_6570` `cancel-sign-sub-inv_binary64_6523`

Counts

4 → 92

Calls

8 calls:

15.0ms	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
14.0ms	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
5.0ms	(-.f64 (.f64 z z) (.f64 t a))
0.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

series901.0ms (8.3%)

Counts

4 → 71

Calls

4 calls:

415.0ms	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
247.0ms	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
124.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
114.0ms	(-.f64 (.f64 z z) (.f64 t a))

Compiler

Compiled 2209 to 1940 computations (12.2% saved)

simplify55.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4991	2765
1	4991	2765

prune122.0ms (1.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	163	8	171

Error

3.6b

Counts

171 → 8

Compiler

Compiled 3034 to 640 computations (78.9% saved)

localize16.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.4b	(-.f64 (.f64 z z) (.f64 t a))
0.3b	(.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
0.1b	(sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
0.1b	(/.f64 z (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))
1.7b	(.f64 y (/.f64 z (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))))
2.4b	(.f64 x (.f64 y (/.f64 z (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))))
22.9b	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
22.9b	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite49.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-cbrt-cube_binary64_6593` `add-exp-log_binary64_6595`
12×	`prod-exp_binary64_6606` `add-sqr-sqrt_binary64_6579` `cbrt-unprod_binary64_6590`
11×	`pow1_binary64_6618`
10×	`associate-r_binary64_6497` `add-cube-cbrt_binary64_6592` `*-un-lft-identity_binary64_6557`
6×	`associate-l_binary64_6498` `cbrt-prod_binary64_6588` `cbrt-div_binary64_6589`
5×	`associate-*r/_binary64_6499`
4×	`pow-prod-down_binary64_6628` `div-exp_binary64_6608` `cbrt-undiv_binary64_6591` `add-log-exp_binary64_6596`
3×	`flip--_binary64_6532` `times-frac_binary64_6563` `flip3--_binary64_6561`
2×	`*-commutative_binary64_6488` `pow1/3_binary64_6639` `sqrt-div_binary64_6574` `associate-/r/_binary64_6503`
1×	`unswap-sqr_binary64_6525` `div-inv_binary64_6554`

Counts

4 → 78

Calls

8 calls:

15.0ms	(.f64 y (/.f64 z (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))))
15.0ms	(.f64 x (.f64 y (/.f64 z (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))))
5.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
5.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
0.0ms	(/.f64 z (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))

series2.0s (18.8%)

Counts

4 → 68

Calls

4 calls:

958.0ms	(.f64 x (.f64 y (/.f64 z (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))))
618.0ms	(.f64 y (/.f64 z (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))))
244.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
217.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

Compiler

Compiled 4752 to 3849 computations (19% saved)

simplify72.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5506	4561

prune137.0ms (1.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	146	8	154

Error

3.6b

Counts

154 → 8

Compiler

Compiled 4545 to 921 computations (79.7% saved)

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	239	968
1	239	968

regimes792.0ms (7.3%)

Compiler: Compiled 4460 to 3406 computations (23.6% saved)

bsearch49.0ms (0.5%)

Steps

Iters	Range		Point
10	6.093844524704292e+85	1.1290235454833277e+101	3.422582606751965e+100
6	-2.886151319062817e+121	-4.7589209837107184e+120	-1.7958128377052614e+121

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes555.0ms (5.1%)

Compiler: Compiled 886 to 1098 computations (-23.9% saved)

bsearch50.0ms (0.5%)

Steps

Iters	Range		Point
9	3.0134734339706607e-55	6.539048241745994e-47	1.2568411837978658e-54
5	-9.329049814959603e-92	-4.4798690628841974e-92	-6.787769142766883e-92

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes383.0ms (3.5%)

Compiler: Compiled 453 to 665 computations (-46.8% saved)

bsearch32.0ms (0.3%)

Steps

Iters	Range		Point
8	-6.603726457882336e-147	-2.54848420166536e-150	-2.602311216522087e-150

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes272.0ms (2.5%)

Compiler: Compiled 166 to 350 computations (-110.8% saved)

bsearch67.0ms (0.6%)

Steps

Iters	Range		Point
11	8.10613364828278e-178	5.945718616138218e-154	9.163533629704878e-172
8	-6.603726457882336e-147	-2.54848420166536e-150	-4.369096939137676e-149

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes96.0ms (0.9%)

Compiler: Compiled 52 to 206 computations (-296.2% saved)

bsearch42.0ms (0.4%)

Steps

Iters	Range		Point
11	8.10613364828278e-178	5.945718616138218e-154	1.4585272085326925e-170

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes44.0ms (0.4%)

Accuracy

Total 3.2b remaining (50%)

Threshold costs 0b (0%)

Compiler

Compiled 25 to 140 computations (-460% saved)

bsearch8.0ms (0.1%)

Compiler: Compiled 104 to 91 computations (12.5% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	124	152
1	124	152

end0.0ms (0%)

sample1.6s (15%)

Algorithm

1×

intervals

Results

398.0ms	8000×	body	128	valid
99.0ms	2117×	body	128	nan
39.0ms	824×	body	128	invalid

Compiler

Compiled 782 to 605 computations (22.6% saved)

Pareto

0.6186582110521707

Details

analyze1.1s (10.1%)

sample32.0ms (0.3%)

simplify150.0ms (1.4%)

prune2.0ms (0%)

localize11.0ms (0.1%)

rewrite33.0ms (0.3%)

series755.0ms (7%)

simplify63.0ms (0.6%)

prune159.0ms (1.5%)

localize12.0ms (0.1%)

rewrite42.0ms (0.4%)

series802.0ms (7.4%)

simplify58.0ms (0.5%)

prune129.0ms (1.2%)

localize11.0ms (0.1%)

rewrite46.0ms (0.4%)

series901.0ms (8.3%)

simplify55.0ms (0.5%)

prune122.0ms (1.1%)

localize16.0ms (0.1%)

rewrite49.0ms (0.5%)

series2.0s (18.8%)

simplify72.0ms (0.7%)

prune137.0ms (1.3%)

simplify15.0ms (0.1%)

regimes792.0ms (7.3%)

bsearch49.0ms (0.5%)

regimes555.0ms (5.1%)

bsearch50.0ms (0.5%)

regimes383.0ms (3.5%)

bsearch32.0ms (0.3%)

regimes272.0ms (2.5%)

bsearch67.0ms (0.6%)

regimes96.0ms (0.9%)

bsearch42.0ms (0.4%)

regimes44.0ms (0.4%)

bsearch8.0ms (0.1%)

simplify5.0ms (0%)

end0.0ms (0%)

sample1.6s (15%)

Profiling