Details

analyze1.1s (7.2%)

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
12.5%	87.4%	0.1%	6
20.3%	73.3%	6.4%	7
27.3%	66.3%	6.4%	8
38.2%	53%	8.7%	9
46%	40.6%	13.4%	10
49.9%	35.1%	15%	11
54.9%	26.9%	18.1%	12
57.4%	22%	20.6%	13
59.7%	18%	22.4%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample69.0ms (0.4%)

Algorithm

1×

intervals

Results

38.0ms	256×	body	128	valid
2.0ms	17×	body	128	nan
0.0ms	3×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify609.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (488.0ms)

Iter	Nodes	Cost
0	2977	54
1	2977	54

prune20.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

18.3b

Counts

2 → 1

Compiler

Compiled 72 to 50 computations (30.6% saved)

localize44.0ms (0.3%)

Local error

Found 8 expressions with local error:

1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a))
0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
0.0b	(.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))))))
1.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite46.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64` `sqrt-prod_binary64`
6×	`pow1_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64`
1×	`distribute-lft-out--_binary64`

Counts

4 → 59

Calls

8 calls:

15.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
11.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
8.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
0.0ms	(.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))))))

series832.0ms (5.2%)

Counts

4 → 62

Calls

4 calls:

233.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
226.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
189.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
183.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 3835 to 2856 computations (25.5% saved)

simplify67.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5126	1949

prune451.0ms (2.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	113	8	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	8	122

Error

6.4b

Counts

122 → 8

Compiler

Compiled 4987 to 2946 computations (40.9% saved)

localize37.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 c (+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))))
0.0b	(sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
0.0b	(sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
0.0b	(.f64 -2 (/.f64 c (+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))))))))
10.4b	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `sqrt-div_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 56

Calls

8 calls:

5.0ms	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
0.0ms	(.f64 -2 (/.f64 c (+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))))))))

series796.0ms (5%)

Counts

4 → 56

Calls

4 calls:

231.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
200.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
187.0ms	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
177.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 4472 to 3201 computations (28.4% saved)

simplify70.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5292	1839

prune345.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	113	7	120

Error

6.4b

Counts

120 → 7

Compiler

Compiled 5710 to 3428 computations (40% saved)

localize25.0ms (0.2%)

Local error

Found 8 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
0.0b	(.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))))))
0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
1.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite39.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/r*_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 72

Calls

8 calls:

14.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
12.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
0.0ms	(.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))))))

series837.0ms (5.3%)

Counts

4 → 64

Calls

4 calls:

249.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
226.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
195.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
166.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))

Compiler

Compiled 3112 to 2399 computations (22.9% saved)

simplify97.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5031	2647

prune381.0ms (2.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	132	4	136
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	135	8	143

Error

6.3b

Counts

143 → 8

Compiler

Compiled 4594 to 2537 computations (44.8% saved)

localize41.0ms (0.3%)

Local error

Found 8 expressions with local error:

1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
0.2b	(.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))))))
0.1b	(/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
0.0b	(.f64 -2 (.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))))
0.2b	(.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))))))
1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
1.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite43.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
18×	`associate-r_binary64`
14×	`add-cube-cbrt_binary64` `times-frac_binary64`
13×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
4×	`distribute-lft-out_binary64` `prod-exp_binary64`
3×	`associate-l_binary64` `unswap-sqr_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 80

Calls

8 calls:

24.0ms	(.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
0.0ms	(.f64 -2 (.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))))

series949.0ms (6%)

Counts

4 → 64

Calls

4 calls:

284.0ms	(.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))))))
233.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
224.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
207.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 3264 to 2551 computations (21.8% saved)

simplify106.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5083	2586

prune243.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	144	8	152

Error

6.3b

Counts

152 → 8

Compiler

Compiled 4806 to 2745 computations (42.9% saved)

simplify47.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	472	2495
1	472	2495

regimes815.0ms (5.1%)

Accuracy

Total 1.2b remaining (19.3%)

Threshold costs 0b (0%)

Compiler

Compiled 4947 to 3552 computations (28.2% saved)

bsearch111.0ms (0.7%)

Steps

Iters	Range		Point
9	1.2871520138642924e+101	1.3720355240833784e+107	1.3576793229541498e+107
9	-9.758885459891598e+92	-2.813444525055501e+85	-9.120756384475955e+92

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	130	208
1	130	208

end0.0ms (0%)

sample7.6s (47.8%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
82.0ms	655×	body	128	nan
46.0ms	368×	body	128	invalid

Compiler

Compiled 5252 to 3732 computations (28.9% saved)

Pareto

0.26714563219775955

Details

analyze1.1s (7.2%)

sample69.0ms (0.4%)

simplify609.0ms (3.8%)

prune20.0ms (0.1%)

localize44.0ms (0.3%)

rewrite46.0ms (0.3%)

series832.0ms (5.2%)

simplify67.0ms (0.4%)

prune451.0ms (2.8%)

localize37.0ms (0.2%)

rewrite22.0ms (0.1%)

series796.0ms (5%)

simplify70.0ms (0.4%)

prune345.0ms (2.2%)

localize25.0ms (0.2%)

rewrite39.0ms (0.2%)

series837.0ms (5.3%)

simplify97.0ms (0.6%)

prune381.0ms (2.4%)

localize41.0ms (0.3%)

rewrite43.0ms (0.3%)

series949.0ms (6%)

simplify106.0ms (0.7%)

prune243.0ms (1.5%)

simplify47.0ms (0.3%)

regimes815.0ms (5.1%)

bsearch111.0ms (0.7%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample7.6s (47.8%)

Profiling