Details

analyze3.1s (20.5%)

Algorithm

2×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5017	231
0	5	5
1	5	5

Search

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

Symmetry

(sort x y)

(sort t a)

Compiler

Compiled 30 to 26 computations (13.3% saved)

sample1.5s (10.1%)

Algorithm

2×

intervals

Results

30.0ms	512×	body	128	valid
11.0ms	197×	body	128	nan
3.0ms	47×	body	128	invalid

Compiler

Compiled 5564 to 6672 computations (-19.9% saved)

simplify54.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	806	21
1	806	21

prune3.0ms (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

28.1b

Counts

2 → 1

Compiler

Compiled 28 to 24 computations (14.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 z z) (.f64 t a))
4.2b	(.f64 (.f64 x y) z)
7.8b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
26.8b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite135.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

24.1b

Rules

18×	`add-exp-log_binary64_8641` `add-cbrt-cube_binary64_8639`
11×	`add-sqr-sqrt_binary64_8625`
10×	`pow1_binary64_8664` `add-cube-cbrt_binary64_8638` `*-un-lft-identity_binary64_8603`
9×	`sqrt-prod_binary64_8619`
6×	`add-log-exp_binary64_8642` `prod-exp_binary64_8652` `cbrt-unprod_binary64_8636` `times-frac_binary64_8609` `associate-/r*_binary64_8547`
4×	`sqrt-div_binary64_8620`
3×	`flip3--_binary64_8607` `flip--_binary64_8578` `div-exp_binary64_8654` `cbrt-undiv_binary64_8637` `pow-prod-down_binary64_8674` `associate-r_binary64_8543`
2×	`associate-/r/_binary64_8549`
1×	`pow1/2_binary64_8683` `sqrt-pow1_binary64_8621` `rem-sqrt-square_binary64_8616` `frac-2neg_binary64_8614` `clear-num_binary64_8602` `div-inv_binary64_8600` `associate-/l_binary64_8548` `associate-l_binary64_8544` `-commutative_binary64_8534` `diff-log_binary64_8695` `sub-neg_binary64_8596` `cancel-sign-sub-inv_binary64_8569`

Counts

4 → 76

Calls

4 calls:

9.0ms	(/.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))

Compiler

Compiled 1787 to 278 computations (84.4% saved)

series1.1s (7.6%)

Error

4.7b

Counts

4 → 63

Calls

4 calls:

614.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
176.0ms	(-.f64 (.f64 z z) (.f64 t a))
157.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
136.0ms	(.f64 (.f64 x y) z)

Compiler

Compiled 2693 to 1894 computations (29.7% saved)

simplify61.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5451	2139

prune132.0ms (0.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	129	10	139
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	130	10	140

Error

4.4b

Counts

140 → 10

Compiler

Compiled 2503 to 479 computations (80.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
0.6b	(-.f64 (.f64 z z) (.f64 t a))
2.5b	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
26.8b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite151.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

4.4b

Rules

36×	`times-frac_binary64_8609`
34×	`add-sqr-sqrt_binary64_8625`
33×	`add-cube-cbrt_binary64_8638` `*-un-lft-identity_binary64_8603`
24×	`sqrt-prod_binary64_8619` `associate-r_binary64_8543`
18×	`add-exp-log_binary64_8641` `add-cbrt-cube_binary64_8639`
10×	`pow1_binary64_8664`
6×	`add-log-exp_binary64_8642` `sqrt-div_binary64_8620` `prod-exp_binary64_8652` `cbrt-unprod_binary64_8636` `associate-/r*_binary64_8547`
4×	`flip3--_binary64_8607` `flip--_binary64_8578` `associate-/r/_binary64_8549`
3×	`pow-prod-down_binary64_8674` `div-exp_binary64_8654` `cbrt-undiv_binary64_8637` `associate-/l*_binary64_8548`
2×	`div-inv_binary64_8600`
1×	`pow1/2_binary64_8683` `sqrt-pow1_binary64_8621` `rem-sqrt-square_binary64_8616` `associate-r/_binary64_8545` `associate-l_binary64_8544` `-commutative_binary64_8534` `diff-log_binary64_8695` `sub-neg_binary64_8596` `cancel-sign-sub-inv_binary64_8569` `frac-2neg_binary64_8614` `clear-num_binary64_8602`

Counts

4 → 112

Calls

4 calls:

13.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
6.0ms	(/.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)))

Compiler

Compiled 2928 to 440 computations (85% saved)

series1.2s (8.1%)

Error

4.4b

Counts

4 → 67

Calls

4 calls:

628.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
185.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
174.0ms	(-.f64 (.f64 z z) (.f64 t a))
173.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

Compiler

Compiled 2903 to 2170 computations (25.2% saved)

simplify60.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4965	3265
1	4965	3265

prune159.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	180	9	189

Error

4.4b

Counts

189 → 9

Compiler

Compiled 3502 to 627 computations (82.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b	(/.f64 1 (-.f64 (.f64 z z) (.f64 t a)))
5.2b	(.f64 x (.f64 z y))
7.8b	(.f64 (.f64 x (.f64 z y)) (sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (*.f64 t a)))))
26.0b	(sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (.f64 t a))))

rewrite176.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

4.4b

Rules

32×	`add-sqr-sqrt_binary64_8625`
30×	`sqrt-prod_binary64_8619`
29×	`times-frac_binary64_8609` `*-un-lft-identity_binary64_8603`
28×	`add-cube-cbrt_binary64_8638`
22×	`add-exp-log_binary64_8641`
21×	`pow1_binary64_8664`
20×	`add-cbrt-cube_binary64_8639`
19×	`associate-r_binary64_8543`
9×	`pow-prod-down_binary64_8674` `prod-exp_binary64_8652` `cbrt-unprod_binary64_8636`
6×	`associate-/r/_binary64_8549`
4×	`add-log-exp_binary64_8642` `associate-l_binary64_8544`
3×	`sqrt-pow1_binary64_8621` `div-inv_binary64_8600` `flip3--_binary64_8607` `flip--_binary64_8578` `rem-sqrt-square_binary64_8616` `associate-/l_binary64_8548` `associate-/r_binary64_8547`
2×	`inv-pow_binary64_8688` `pow-flip_binary64_8677` `sqrt-div_binary64_8620` `*-commutative_binary64_8534` `div-exp_binary64_8654`
1×	`pow1/2_binary64_8683` `associate-*r/_binary64_8545` `1-exp_binary64_8647` `rec-exp_binary64_8653` `cbrt-undiv_binary64_8637` `frac-2neg_binary64_8614` `clear-num_binary64_8602`

Counts

4 → 118

Calls

4 calls:

14.0ms	(.f64 (.f64 x (.f64 z y)) (sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (*.f64 t a)))))
6.0ms	(sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (.f64 t a))))
6.0ms	(/.f64 1 (-.f64 (.f64 z z) (.f64 t a)))
5.0ms	(.f64 x (.f64 z y))

Compiler

Compiled 3104 to 988 computations (68.2% saved)

series991.0ms (6.6%)

Error

4.4b

Counts

4 → 50

Calls

4 calls:

575.0ms	(.f64 (.f64 x (.f64 z y)) (sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (*.f64 t a)))))
151.0ms	(sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (.f64 t a))))
148.0ms	(.f64 x (.f64 z y))
78.0ms	(/.f64 1 (-.f64 (.f64 z z) (.f64 t a)))

Compiler

Compiled 2453 to 1825 computations (25.6% saved)

simplify83.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5999	2913

prune175.0ms (1.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	166	11	177

Error

4.4b

Counts

177 → 11

Compiler

Compiled 3522 to 1130 computations (67.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.2b	(.f64 x (.f64 z y))
7.8b	(.f64 (.f64 x (.f64 z y)) (.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (.f64 t a))))) (sqrt.f64 (sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (.f64 t a)))))))
26.0b	(sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (.f64 t a))))
26.0b	(sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (.f64 t a))))

rewrite262.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

4.4b

Rules

34×	`pow1_binary64_8664`
30×	`add-exp-log_binary64_8641` `add-cbrt-cube_binary64_8639` `sqrt-prod_binary64_8619`
27×	`add-sqr-sqrt_binary64_8625`
22×	`times-frac_binary64_8609`
21×	`*-un-lft-identity_binary64_8603`
19×	`add-cube-cbrt_binary64_8638`
18×	`pow-prod-down_binary64_8674` `prod-exp_binary64_8652` `cbrt-unprod_binary64_8636`
10×	`sqrt-div_binary64_8620`
6×	`sqrt-pow1_binary64_8621` `rem-sqrt-square_binary64_8616`
4×	`add-log-exp_binary64_8642` `associate-/r/_binary64_8549` `associate-r/_binary64_8545` `associate-l*_binary64_8544`
2×	`pow1/2_binary64_8683` `inv-pow_binary64_8688` `pow-flip_binary64_8677` `div-inv_binary64_8600` `flip3--_binary64_8607` `flip--_binary64_8578` `associate-r_binary64_8543` `*-commutative_binary64_8534`
1×	`frac-times_binary64_8613` `associate-*l/_binary64_8546`

Counts

4 → 109

Calls

4 calls:

34.0ms	(.f64 (.f64 x (.f64 z y)) (.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (.f64 t a))))) (sqrt.f64 (sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (.f64 t a)))))))
6.0ms	(sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (.f64 t a))))
6.0ms	(sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (.f64 t a))))
5.0ms	(.f64 x (.f64 z y))

Compiler

Compiled 4454 to 1653 computations (62.9% saved)

series1.2s (8.2%)

Error

4.4b

Counts

4 → 54

Calls

4 calls:

659.0ms	(.f64 (.f64 x (.f64 z y)) (.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (.f64 t a))))) (sqrt.f64 (sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (.f64 t a)))))))
179.0ms	(sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (.f64 t a))))
174.0ms	(sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (.f64 t a))))
163.0ms	(.f64 x (.f64 z y))

Compiler

Compiled 3953 to 2665 computations (32.6% saved)

simplify69.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5108	2882

prune230.0ms (1.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	163	11	174

Error

4.4b

Counts

174 → 11

Compiler

Compiled 4639 to 1662 computations (64.2% saved)

regimes2.0s (13.2%)

Accuracy

Total 3.1b remaining (48.6%)

Threshold costs 0b (0%)

Compiler

Compiled 11168 to 7182 computations (35.7% saved)

bsearch82.0ms (0.6%)

Steps

Iters	Range		Point
9	8.082554028808715e+145	2.0793487153877234e+155	1.870284617036561e+146
10	-2.511232902655691e+155	-1.118858647714264e+142	-1.6232727474793533e+146

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify33.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	73	43
1	73	43

Remove

(sort t a)

(sort x y)

Compiler

Compiled 116 to 80 computations (31% saved)

end0.0ms (0%)

sample1.9s (13%)

Algorithm

1×

intervals

Results

412.0ms	8000×	body	128	valid
133.0ms	2851×	body	128	nan
42.0ms	866×	body	128	invalid

Compiler

Compiled 1318 to 858 computations (34.9% saved)

Details

analyze3.1s (20.5%)

sample1.5s (10.1%)

simplify54.0ms (0.4%)

prune3.0ms (0%)

localize11.0ms (0.1%)

rewrite135.0ms (0.9%)

series1.1s (7.6%)

simplify61.0ms (0.4%)

prune132.0ms (0.9%)

localize11.0ms (0.1%)

rewrite151.0ms (1%)

series1.2s (8.1%)

simplify60.0ms (0.4%)

prune159.0ms (1.1%)

localize15.0ms (0.1%)

rewrite176.0ms (1.2%)

series991.0ms (6.6%)

simplify83.0ms (0.6%)

prune175.0ms (1.2%)

localize15.0ms (0.1%)

rewrite262.0ms (1.8%)

series1.2s (8.2%)

simplify69.0ms (0.5%)

prune230.0ms (1.5%)

regimes2.0s (13.2%)

bsearch82.0ms (0.6%)

simplify33.0ms (0.2%)

end0.0ms (0%)

sample1.9s (13%)

Profiling