Details

analyze718.0ms (12.9%)

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)

sample41.0ms (0.7%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
5.0ms	21×	body	128	nan
1.0ms	12×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify252.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	1224	54
1	1224	54

prune8.0ms (0.1%)

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

Merged error: 22.6b

Counts

2 → 1

Compiler

Compiled 74 to 51 computations (31.1% saved)

localize32.0ms (0.6%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (neg.f64 b) (sqrt.f64 (-.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))))
26.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
26.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64`
12×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
7×	`sqrt-prod_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `distribute-rgt-neg-in_binary64` `rem-sqrt-square_binary64` `neg-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `associate--l-_binary64` `associate-+l-_binary64` `+-commutative_binary64` `flip-+_binary64`

Counts

4 → 62

Calls

4 calls:

11.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
10.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series509.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

140.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
126.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
123.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify72.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4963	1613
1	4963	1613

prune165.0ms (3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	68	6	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	6	75

Merged error: 8.6b

Counts

75 → 6

Compiler

Compiled 3528 to 2040 computations (42.2% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

7.6b	(-.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))))))
26.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
26.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
26.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite22.0ms (0.4%)

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` `neg-log_binary64` `difference-of-squares_binary64`

Counts

4 → 59

Calls

4 calls:

5.0ms	(-.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))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series470.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

134.0ms	(-.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))))))
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
111.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
105.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify72.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4989	1489
1	4989	1489

prune160.0ms (2.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	71	6	77

Merged error: 8.6b

Counts

77 → 6

Compiler

Compiled 4107 to 2394 computations (41.7% saved)

localize29.0ms (0.5%)

Local error

Found 4 expressions with local error:

26.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
26.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
26.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
26.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `pow1/2_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`

Counts

4 → 60

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series468.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
116.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
111.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify65.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4993	1404
1	4993	1404

prune232.0ms (4.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	72	6	78

Merged error: 8.6b

Counts

78 → 6

Compiler

Compiled 5378 to 3156 computations (41.3% saved)

localize27.0ms (0.5%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.1b	(/.f64 (*.f64 a c) b)
5.3b	(/.f64 (+.f64 (neg.f64 b) (-.f64 (.f64 2 (/.f64 (.f64 a c) b)) b)) (*.f64 2 a))
26.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite42.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
8×	`add-log-exp_binary64` `times-frac_binary64`
6×	`associate-/l*_binary64`
5×	`pow1_binary64`
4×	`associate-/r*_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-prod_binary64`
3×	`distribute-rgt-neg-in_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `neg-sub0_binary64` `div-sub_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `associate-+r-_binary64` `pow1/2_binary64` `associate--l-_binary64` `associate-+l-_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `neg-log_binary64` `flip-+_binary64`

Counts

4 → 82

Calls

4 calls:

15.0ms	(/.f64 (+.f64 (neg.f64 b) (-.f64 (.f64 2 (/.f64 (.f64 a c) b)) b)) (*.f64 2 a))
13.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(/.f64 (*.f64 a c) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series356.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

120.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
85.0ms	(/.f64 (+.f64 (neg.f64 b) (-.f64 (.f64 2 (/.f64 (.f64 a c) b)) b)) (*.f64 2 a))
37.0ms	(/.f64 (*.f64 a c) b)

simplify65.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	6786	1776

prune151.0ms (2.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	90	4	94
Fresh	2	1	3
Picked	1	0	1
Done	0	2	2
Total	93	7	100

Merged error: 7.5b

Counts

100 → 7

Compiler

Compiled 3906 to 2041 computations (47.7% saved)

regimes143.0ms (2.6%)

Compiler: Compiled 930 to 642 computations (31% saved)

bsearch84.0ms (1.5%)

Steps

Iters	Range		Point
8	1.8257074873285927e+99	1.175239160178683e+104	6.4417367273105074e+103
9	-430611.2890384929	-1.1707958582698768	-425882.49394125835

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	158	178
1	158	178

end0.0ms (0%)

sample1.3s (23.1%)

Algorithm

1×

intervals

Results

688.0ms	8000×	body	128	valid
53.0ms	643×	body	128	nan
31.0ms	383×	body	128	invalid

Compiler

Compiled 465 to 311 computations (33.1% saved)

Details

analyze718.0ms (12.9%)

sample41.0ms (0.7%)

simplify252.0ms (4.5%)

prune8.0ms (0.1%)

localize32.0ms (0.6%)

rewrite36.0ms (0.6%)

series509.0ms (9.2%)

simplify72.0ms (1.3%)

prune165.0ms (3%)

localize25.0ms (0.4%)

rewrite22.0ms (0.4%)

series470.0ms (8.5%)

simplify72.0ms (1.3%)

prune160.0ms (2.9%)

localize29.0ms (0.5%)

rewrite21.0ms (0.4%)

series468.0ms (8.4%)

simplify65.0ms (1.2%)

prune232.0ms (4.2%)

localize27.0ms (0.5%)

rewrite42.0ms (0.8%)

series356.0ms (6.4%)

simplify65.0ms (1.2%)

prune151.0ms (2.7%)

regimes143.0ms (2.6%)

bsearch84.0ms (1.5%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.3s (23.1%)

Profiling