Details

analyze239.0ms (4.2%)

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
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
43.7%	56.2%	0.1%	8
62.4%	37.4%	0.1%	9
65.5%	34.3%	0.1%	10
71.8%	27.7%	0.5%	11
79.2%	19.7%	1.1%	12
80.2%	18.7%	1.1%	13
82.8%	15%	2.2%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample18.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
0.0ms	9×	body	128	invalid

Compiler

Compiled 23 to 24 computations (-4.3% saved)

simplify100.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	111	16
1	111	16

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

5.3b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.7b	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
2.9b	(.f64 y (+.f64 1 (.f64 z z)))
2.9b	(.f64 y (+.f64 1 (.f64 z z)))
3.7b	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`times-frac_binary64_11678`
26×	`add-exp-log_binary64_11710`
20×	`add-sqr-sqrt_binary64_11694`
18×	`add-cube-cbrt_binary64_11707` `*-un-lft-identity_binary64_11672`
16×	`add-cbrt-cube_binary64_11708`
13×	`associate-/l*_binary64_11617`
12×	`div-exp_binary64_11723`
6×	`cbrt-undiv_binary64_11706`
5×	`prod-exp_binary64_11721`
4×	`pow1_binary64_11733` `associate-*r/_binary64_11614`
3×	`cbrt-unprod_binary64_11705` `associate-r_binary64_11612` `div-inv_binary64_11669` `associate-l_binary64_11613`
2×	`associate-/r/_binary64_11618` `1-exp_binary64_11716` `add-log-exp_binary64_11711` `flip-+_binary64_11646` `flip3-+_binary64_11675` `rec-exp_binary64_11722`
1×	`clear-num_binary64_11671` `associate-/r_binary64_11616` `distribute-lft-in_binary64_11621` `unswap-sqr_binary64_11640` `frac-2neg_binary64_11683` `associate-/l/_binary64_11619` `distribute-rgt-in_binary64_11622` `-commutative_binary64_11603` `pow-prod-down_binary64_11743`

Counts

2 → 74

Calls

4 calls:

9.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
6.0ms	(.f64 y (+.f64 1 (.f64 z z)))
0.0ms	(.f64 y (+.f64 1 (.f64 z z)))
0.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))

series249.0ms (4.3%)

Counts

2 → 19

Calls

2 calls:

169.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
80.0ms	(.f64 y (+.f64 1 (.f64 z z)))

Compiler

Compiled 382 to 358 computations (6.3% saved)

simplify72.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5200	1474

prune118.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	86	7	93
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	86	8	94

Error

4.2b

Counts

94 → 8

Compiler

Compiled 1492 to 889 computations (40.4% saved)

localize10.0ms (0.2%)

Local error

Found 8 expressions with local error:

15.6b	(sqrt.f64 (+.f64 1 (*.f64 z z)))
3.7b	(/.f64 (/.f64 1 x) (.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z)))))
0.1b	(.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z))))
0.0b	(.f64 y (sqrt.f64 (+.f64 1 (.f64 z z))))
0.1b	(.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z))))
3.7b	(/.f64 (/.f64 1 x) (.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z)))))
15.6b	(sqrt.f64 (+.f64 1 (*.f64 z z)))
15.6b	(sqrt.f64 (+.f64 1 (*.f64 z z)))

rewrite49.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-exp-log_binary64_11710`
31×	`times-frac_binary64_11678`
30×	`add-cbrt-cube_binary64_11708`
28×	`sqrt-div_binary64_11689`
24×	`add-sqr-sqrt_binary64_11694`
22×	`add-cube-cbrt_binary64_11707` `*-un-lft-identity_binary64_11672`
18×	`div-exp_binary64_11723`
16×	`associate-*r/_binary64_11614`
15×	`prod-exp_binary64_11721`
14×	`flip-+_binary64_11646` `flip3-+_binary64_11675`
13×	`associate-/l*_binary64_11617`
11×	`pow1_binary64_11733`
9×	`cbrt-undiv_binary64_11706` `cbrt-unprod_binary64_11705` `sqrt-prod_binary64_11688`
8×	`associate-/r/_binary64_11618` `frac-times_binary64_11682`
6×	`associate-r_binary64_11612`
4×	`add-log-exp_binary64_11711` `associate-*l/_binary64_11615`
3×	`1-exp_binary64_11716` `div-inv_binary64_11669` `pow-prod-down_binary64_11743` `rec-exp_binary64_11722`
2×	`rem-sqrt-square_binary64_11685` `pow1/2_binary64_11752` `sqrt-pow1_binary64_11690`
1×	`clear-num_binary64_11671` `associate-/r_binary64_11616` `frac-2neg_binary64_11683` `associate-/l/_binary64_11619` `-commutative_binary64_11603` `associate-l_binary64_11613`

Counts

4 → 123

Calls

8 calls:

15.0ms	(/.f64 (/.f64 1 x) (.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z)))))
11.0ms	(.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
0.0ms	(.f64 y (sqrt.f64 (+.f64 1 (.f64 z z))))

series338.0ms (5.9%)

Counts

4 → 35

Calls

4 calls:

172.0ms	(/.f64 (/.f64 1 x) (.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z)))))
83.0ms	(.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z))))
42.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
41.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

Compiler

Compiled 900 to 808 computations (10.2% saved)

simplify87.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4982	2707
1	4982	2707

prune174.0ms (3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	158	8	166

Error

4.2b

Counts

166 → 8

Compiler

Compiled 3242 to 1988 computations (38.7% saved)

localize8.0ms (0.1%)

Local error

Found 6 expressions with local error:

3.5b	(.f64 x (.f64 y (+.f64 1 (*.f64 z z))))
2.9b	(.f64 y (+.f64 1 (.f64 z z)))
0.6b	(/.f64 1 (.f64 x (.f64 y (+.f64 1 (*.f64 z z)))))
0.6b	(/.f64 1 (.f64 x (.f64 y (+.f64 1 (*.f64 z z)))))
2.9b	(.f64 y (+.f64 1 (.f64 z z)))
3.5b	(.f64 x (.f64 y (+.f64 1 (*.f64 z z))))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-exp-log_binary64_11710`
19×	`add-cbrt-cube_binary64_11708`
16×	`pow1_binary64_11733`
13×	`prod-exp_binary64_11721`
10×	`add-sqr-sqrt_binary64_11694` `associate-*r/_binary64_11614`
8×	`add-cube-cbrt_binary64_11707` `*-un-lft-identity_binary64_11672`
7×	`cbrt-unprod_binary64_11705` `pow-prod-down_binary64_11743`
6×	`div-exp_binary64_11723` `associate-l_binary64_11613`
5×	`distribute-lft-in_binary64_11621` `distribute-rgt-in_binary64_11622`
4×	`associate-r_binary64_11612`
3×	`cbrt-undiv_binary64_11706` `1-exp_binary64_11716` `add-log-exp_binary64_11711` `pow-flip_binary64_11746` `flip-+_binary64_11646` `flip3-+_binary64_11675` `times-frac_binary64_11678` `rec-exp_binary64_11722` `associate-/l*_binary64_11617`
2×	`associate-/r/_binary64_11618` `*-commutative_binary64_11603`
1×	`inv-pow_binary64_11757` `clear-num_binary64_11671` `associate-/r*_binary64_11616` `unswap-sqr_binary64_11640` `frac-2neg_binary64_11683` `div-inv_binary64_11669`

Counts

3 → 81

Calls

6 calls:

8.0ms	(.f64 y (+.f64 1 (.f64 z z)))
8.0ms	(/.f64 1 (.f64 x (.f64 y (+.f64 1 (*.f64 z z)))))
7.0ms	(.f64 x (.f64 y (+.f64 1 (*.f64 z z))))
0.0ms	(/.f64 1 (.f64 x (.f64 y (+.f64 1 (*.f64 z z)))))
0.0ms	(.f64 y (+.f64 1 (.f64 z z)))

series403.0ms (7%)

Counts

3 → 31

Calls

3 calls:

170.0ms	(/.f64 1 (.f64 x (.f64 y (+.f64 1 (*.f64 z z)))))
154.0ms	(.f64 x (.f64 y (+.f64 1 (*.f64 z z))))
79.0ms	(.f64 y (+.f64 1 (.f64 z z)))

Compiler

Compiled 615 to 576 computations (6.3% saved)

simplify73.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5106	1514

prune83.0ms (1.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	112	8	120

Error

4.2b

Counts

120 → 8

Compiler

Compiled 1635 to 932 computations (43% saved)

localize10.0ms (0.2%)

Local error

Found 8 expressions with local error:

15.6b	(sqrt.f64 (+.f64 1 (*.f64 z z)))
1.8b	(/.f64 (/.f64 1 x) (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y))
1.2b	(/.f64 (/.f64 (/.f64 1 x) (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y)) (sqrt.f64 (+.f64 1 (*.f64 z z))))
0.0b	(.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y)
1.2b	(/.f64 (/.f64 (/.f64 1 x) (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y)) (sqrt.f64 (+.f64 1 (*.f64 z z))))
1.8b	(/.f64 (/.f64 1 x) (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y))
15.6b	(sqrt.f64 (+.f64 1 (*.f64 z z)))
15.6b	(sqrt.f64 (+.f64 1 (*.f64 z z)))

rewrite69.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

299×	`times-frac_binary64_11678`
118×	`add-sqr-sqrt_binary64_11694`
116×	`add-cube-cbrt_binary64_11707` `*-un-lft-identity_binary64_11672`
66×	`sqrt-prod_binary64_11688`
58×	`add-exp-log_binary64_11710`
34×	`add-cbrt-cube_binary64_11708`
33×	`div-exp_binary64_11723`
32×	`associate-/l*_binary64_11617`
22×	`sqrt-div_binary64_11689`
18×	`associate-/r/_binary64_11618` `div-inv_binary64_11669`
17×	`cbrt-undiv_binary64_11706`
16×	`associate-*l/_binary64_11615`
11×	`flip-+_binary64_11646` `flip3-+_binary64_11675`
8×	`prod-exp_binary64_11721`
7×	`associate-/r*_binary64_11616`
6×	`pow1_binary64_11733`
4×	`cbrt-unprod_binary64_11705` `1-exp_binary64_11716` `add-log-exp_binary64_11711` `rec-exp_binary64_11722`
2×	`rem-sqrt-square_binary64_11685` `clear-num_binary64_11671` `pow1/2_binary64_11752` `sqrt-pow1_binary64_11690` `frac-2neg_binary64_11683` `associate-/l/_binary64_11619`

Counts

4 → 248

Calls

8 calls:

21.0ms	(/.f64 (/.f64 (/.f64 1 x) (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y)) (sqrt.f64 (+.f64 1 (*.f64 z z))))
10.0ms	(/.f64 (/.f64 1 x) (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
0.0ms	(.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y)

series500.0ms (8.7%)

Counts

4 → 38

Calls

4 calls:

232.0ms	(/.f64 (/.f64 1 x) (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y))
179.0ms	(/.f64 (/.f64 (/.f64 1 x) (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y)) (sqrt.f64 (+.f64 1 (*.f64 z z))))
47.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
42.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

Compiler

Compiled 1219 to 1063 computations (12.8% saved)

simplify126.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

286 → 286

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4950	8909
1	4950	8909

prune447.0ms (7.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	286	0	286
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	286	8	294

Error

4.2b

Counts

294 → 8

Compiler

Compiled 7596 to 4630 computations (39% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	163	709
1	163	709

regimes426.0ms (7.4%)

Compiler: Compiled 4274 to 3684 computations (13.8% saved)

bsearch0.0ms (0%)

regimes116.0ms (2%)

Compiler: Compiled 472 to 546 computations (-15.7% saved)

bsearch0.0ms (0%)

regimes277.0ms (4.8%)

Compiler: Compiled 241 to 312 computations (-29.5% saved)

bsearch37.0ms (0.7%)

Steps

Iters	Range		Point
11	1.492049511592043e-09	470262124096873.25	1.0112305529574455
7	-377398696.80991304	-1592175.3884116453	-1624482.6004077473

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes190.0ms (3.3%)

Compiler: Compiled 142 to 224 computations (-57.7% saved)

bsearch14.0ms (0.2%)

Steps

Iters	Range		Point
7	3.22762692803721e-12	3.6553067065191543e-10	3.5935016702128946e-10

Compiler

Compiled 3 to 4 computations (-33.3% saved)

regimes128.0ms (2.2%)

Compiler: Compiled 78 to 152 computations (-94.9% saved)

bsearch37.0ms (0.6%)

Steps

Iters	Range		Point
11	1.492049511592043e-09	470262124096873.25	82604658314878.4
8	-9.565949087709471e+37	-3.368461110191749e+34	-2.0940098344860414e+36

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes64.0ms (1.1%)

Compiler: Compiled 30 to 72 computations (-140% saved)

bsearch39.0ms (0.7%)

Steps

Iters	Range		Point
11	1.492049511592043e-09	470262124096873.25	128205759659906.72
8	-9.565949087709471e+37	-3.368461110191749e+34	-2.8703967636759144e+37

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes24.0ms (0.4%)

Accuracy

Total 1.6b remaining (25.1%)

Threshold costs 0b (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch8.0ms (0.1%)

Compiler: Compiled 105 to 89 computations (15.2% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	139
1	57	139

end0.0ms (0%)

sample1.2s (20%)

Algorithm

1×

intervals

Results

310.0ms	8000×	body	128	valid
16.0ms	445×	body	128	invalid

Compiler

Compiled 615 to 521 computations (15.3% saved)

Pareto

0.30802238967695134

Details

analyze239.0ms (4.2%)

sample18.0ms (0.3%)

simplify100.0ms (1.7%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite21.0ms (0.4%)

series249.0ms (4.3%)

simplify72.0ms (1.3%)

prune118.0ms (2.1%)

localize10.0ms (0.2%)

rewrite49.0ms (0.9%)

series338.0ms (5.9%)

simplify87.0ms (1.5%)

prune174.0ms (3%)

localize8.0ms (0.1%)

rewrite29.0ms (0.5%)

series403.0ms (7%)

simplify73.0ms (1.3%)

prune83.0ms (1.4%)

localize10.0ms (0.2%)

rewrite69.0ms (1.2%)

series500.0ms (8.7%)

simplify126.0ms (2.2%)

prune447.0ms (7.8%)

simplify11.0ms (0.2%)

regimes426.0ms (7.4%)

bsearch0.0ms (0%)

regimes116.0ms (2%)

bsearch0.0ms (0%)

regimes277.0ms (4.8%)

bsearch37.0ms (0.7%)

regimes190.0ms (3.3%)

bsearch14.0ms (0.2%)

regimes128.0ms (2.2%)

bsearch37.0ms (0.6%)

regimes64.0ms (1.1%)

bsearch39.0ms (0.7%)

regimes24.0ms (0.4%)

bsearch8.0ms (0.1%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.2s (20%)

Profiling