Details

analyze1.3s (8%)

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)

sample74.0ms (0.5%)

Algorithm

1×

intervals

Results

42.0ms	256×	body	128	valid
2.0ms	16×	body	128	nan
1.0ms	7×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify807.0ms (5.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (643.0ms)

Iter	Nodes	Cost
0	2977	54
1	2977	54

prune31.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

20.7b

Counts

2 → 1

Compiler

Compiled 74 to 51 computations (31.1% saved)

localize44.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.4b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.1b	(/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))
0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.0b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite48.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64` `sqrt-prod_binary64`
8×	`add-cube-cbrt_binary64`
7×	`cancel-sign-sub-inv_binary64`
6×	`pow1_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64` `sqrt-div_binary64`
3×	`diff-log_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
1×	`associate--l-_binary64` `neg-sub0_binary64` `distribute-rgt-neg-in_binary64` `neg-log_binary64`

Counts

4 → 65

Calls

8 calls:

16.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
10.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
8.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))

series1.0s (6.4%)

Counts

4 → 58

Calls

4 calls:

303.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
301.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
236.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
173.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 3691 to 2721 computations (26.3% saved)

simplify142.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	5243	1955

prune556.0ms (3.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	113	10	123
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	10	124

Error

6.5b

Counts

124 → 10

Compiler

Compiled 5306 to 3013 computations (43.2% saved)

localize52.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))))
0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
0.0b	(sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.0b	(sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
8.4b	(-.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite36.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
8×	`add-log-exp_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`sqrt-div_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
2×	`diff-log_binary64`
1×	`sub-neg_binary64` `associate--l-_binary64` `neg-sub0_binary64` `cancel-sign-sub-inv_binary64` `neg-log_binary64` `difference-of-squares_binary64`

Counts

4 → 60

Calls

8 calls:

9.0ms	(-.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.0ms	(sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

series889.0ms (5.6%)

Counts

4 → 51

Calls

4 calls:

292.0ms	(-.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
220.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
211.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
167.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 4300 to 3058 computations (28.9% saved)

simplify136.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	5212	1774

prune442.0ms (2.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	111	10	121

Error

6.5b

Counts

121 → 10

Compiler

Compiled 5871 to 3390 computations (42.3% saved)

localize56.0ms (0.4%)

Local error

Found 8 expressions with local error:

0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.3b	(.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
0.1b	(/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))
0.1b	(/.f64 (+.f64 (neg.f64 b) (.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
7.2b	(+.f64 (neg.f64 b) (.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
24.3b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite39.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow1_binary64` `sqrt-prod_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `flip--_binary64` `cbrt-prod_binary64`
2×	`cbrt-div_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `neg-sub0_binary64` `pow1/3_binary64` `associate-+l-_binary64` `neg-log_binary64` `+-commutative_binary64` `flip-+_binary64`

Counts

4 → 56

Calls

8 calls:

9.0ms	(+.f64 (neg.f64 b) (.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
8.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.0ms	(/.f64 (+.f64 (neg.f64 b) (.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))

series1.0s (6.6%)

Counts

4 → 52

Calls

4 calls:

355.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
293.0ms	(+.f64 (neg.f64 b) (.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
250.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
146.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 4551 to 3272 computations (28.1% saved)

simplify113.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4984	2143
1	4984	2143

prune408.0ms (2.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	108	10	118

Error

6.5b

Counts

118 → 10

Compiler

Compiled 5901 to 3361 computations (43% saved)

localize58.0ms (0.4%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))
0.1b	(/.f64 (+.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
0.0b	(sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.0b	(sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
10.9b	(+.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite39.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
8×	`add-log-exp_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`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`
2×	`sum-log_binary64`
1×	`flip3-+_binary64` `neg-sub0_binary64` `associate-+l-_binary64` `neg-log_binary64` `+-commutative_binary64` `flip-+_binary64`

Counts

4 → 58

Calls

8 calls:

10.0ms	(+.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.0ms	(sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

series841.0ms (5.3%)

Counts

4 → 49

Calls

4 calls:

264.0ms	(+.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
242.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
167.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
166.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 4212 to 2993 computations (28.9% saved)

simplify131.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	5043	1659

prune407.0ms (2.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	2	5	7
Picked	1	0	1
Done	0	2	2
Total	109	8	117

Error

6.5b

Counts

117 → 8

Compiler

Compiled 5341 to 3034 computations (43.2% saved)

simplify33.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	344	1298
1	344	1298

regimes557.0ms (3.5%)

Accuracy

Total 1.1b remaining (17.1%)

Threshold costs 0b (0%)

Compiler

Compiled 2571 to 1869 computations (27.3% saved)

bsearch135.0ms (0.9%)

Steps

Iters	Range		Point
8	4.270937452913649e+101	7.795859280107849e+104	6.946559789455752e+104
7	-3.252530031513093e+151	-1.3465950669058163e+150	-2.0262717151588954e+150

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	117	154
1	117	154

end0.0ms (0%)

sample6.4s (40.6%)

Algorithm

1×

intervals

Results

1.3s	8000×	body	128	valid
101.0ms	665×	body	128	nan
59.0ms	379×	body	128	invalid

Compiler

Compiled 2808 to 2007 computations (28.5% saved)

Pareto

0.3860850008941003

Details

analyze1.3s (8%)

sample74.0ms (0.5%)

simplify807.0ms (5.1%)

prune31.0ms (0.2%)

localize44.0ms (0.3%)

rewrite48.0ms (0.3%)

series1.0s (6.4%)

simplify142.0ms (0.9%)

prune556.0ms (3.5%)

localize52.0ms (0.3%)

rewrite36.0ms (0.2%)

series889.0ms (5.6%)

simplify136.0ms (0.9%)

prune442.0ms (2.8%)

localize56.0ms (0.4%)

rewrite39.0ms (0.2%)

series1.0s (6.6%)

simplify113.0ms (0.7%)

prune408.0ms (2.6%)

localize58.0ms (0.4%)

rewrite39.0ms (0.2%)

series841.0ms (5.3%)

simplify131.0ms (0.8%)

prune407.0ms (2.6%)

simplify33.0ms (0.2%)

regimes557.0ms (3.5%)

bsearch135.0ms (0.9%)

simplify7.0ms (0%)

end0.0ms (0%)

sample6.4s (40.6%)

Profiling