Details

analyze709.0ms (11.2%)

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)

sample40.0ms (0.6%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
1.0ms	12×	body	128	nan
1.0ms	10×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify255.0ms (4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (77.0ms)

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	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 20.8b

Counts

2 → 1

Compiler

Compiled 72 to 50 computations (30.6% saved)

localize31.0ms (0.5%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
1.5b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 53

Calls

4 calls:

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

series460.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

152.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
121.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
68.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))

simplify64.0ms (1%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4946	1288
1	4946	1288

prune138.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	58	7	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	7	66

Merged error: 10.1b

Counts

66 → 7

Compiler

Compiled 3034 to 1837 computations (39.5% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

9.0b	(+.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)))))))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite21.0ms (0.3%)

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

4 calls:

5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
3.0ms	(+.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)))))))

series492.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

132.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
130.0ms	(+.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)))))))
116.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify46.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5244	1361

prune155.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	68	7	75

Merged error: 10.1b

Counts

75 → 7

Compiler

Compiled 3865 to 2339 computations (39.5% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

10.3b	(-.f64 (.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)))))) b)
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`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×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `difference-of-squares_binary64`

Counts

4 → 57

Calls

4 calls:

19.0ms	(-.f64 (.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)))))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series497.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

138.0ms	(-.f64 (.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)))))) b)
127.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
112.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify76.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5502	1408

prune158.0ms (2.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	69	7	76

Merged error: 10.1b

Counts

76 → 7

Compiler

Compiled 3868 to 2336 computations (39.6% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

6.6b	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
24.6b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
24.6b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

7.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
3.0ms	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))

series687.0ms (10.9%)

Counts

4 → 12

Calls

4 calls:

221.0ms	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
173.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
163.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
130.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify73.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4966	1684
1	4966	1684

prune143.0ms (2.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	64	7	71

Merged error: 10.1b

Counts

71 → 7

Compiler

Compiled 3626 to 2198 computations (39.4% saved)

regimes382.0ms (6%)

Compiler: Compiled 3374 to 2358 computations (30.1% saved)

bsearch73.0ms (1.1%)

Steps

Iters	Range		Point
8	1.4848892700023645e+146	3.268889869395191e+149	2.468062116429859e+148
8	-2.605817302689682e+157	-1.5872384102599588e+153	-1.3305907505166363e+154

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	121	167
1	121	167

end0.0ms (0%)

sample1.6s (26.1%)

Algorithm

1×

intervals

Results

690.0ms	8000×	body	128	valid
58.0ms	677×	body	128	nan
32.0ms	389×	body	128	invalid

Compiler

Compiled 974 to 672 computations (31% saved)

Details

analyze709.0ms (11.2%)

sample40.0ms (0.6%)

simplify255.0ms (4%)

prune8.0ms (0.1%)

localize31.0ms (0.5%)

rewrite27.0ms (0.4%)

series460.0ms (7.3%)

simplify64.0ms (1%)

prune138.0ms (2.2%)

localize25.0ms (0.4%)

rewrite21.0ms (0.3%)

series492.0ms (7.8%)

simplify46.0ms (0.7%)

prune155.0ms (2.4%)

localize28.0ms (0.4%)

rewrite36.0ms (0.6%)

series497.0ms (7.9%)

simplify76.0ms (1.2%)

prune158.0ms (2.5%)

localize28.0ms (0.4%)

rewrite22.0ms (0.4%)

series687.0ms (10.9%)

simplify73.0ms (1.2%)

prune143.0ms (2.3%)

regimes382.0ms (6%)

bsearch73.0ms (1.1%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.6s (26.1%)

Profiling