Details

analyze719.0ms (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)

sample41.0ms (0.6%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
1.0ms	16×	body	128	nan
1.0ms	10×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify250.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	1224	54
1	1224	54

prune14.0ms (0.2%)

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: 21.7b

Counts

2 → 1

Compiler

Compiled 72 to 50 computations (30.6% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
24.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
24.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64` `sqrt-prod_binary64`
6×	`pow1_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 59

Calls

4 calls:

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

series506.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

136.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
124.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
123.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
122.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5012	1454

prune138.0ms (2.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	66	5	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	5	72

Merged error: 7.7b

Counts

72 → 5

Compiler

Compiled 3189 to 1910 computations (40.1% saved)

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
3.2b	(/.f64 (.f64 2 (-.f64 (/.f64 (.f64 c a) b) b)) (*.f64 2 a))
5.1b	(/.f64 (*.f64 c a) b)
24.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
5×	`pow1_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`associate-/r*_binary64` `times-frac_binary64`
3×	`sqrt-prod_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `distribute-lft-out_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 71

Calls

4 calls:

14.0ms	(/.f64 (.f64 2 (-.f64 (/.f64 (.f64 c a) b) b)) (*.f64 2 a))
7.0ms	(+.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))))
5.0ms	(/.f64 (*.f64 c a) b)

series392.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

124.0ms	(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)))))
108.0ms	(/.f64 (.f64 2 (-.f64 (/.f64 (.f64 c a) b) b)) (*.f64 2 a))
39.0ms	(/.f64 (*.f64 c a) b)

simplify57.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4981	1297
1	4981	1297

prune126.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	79	4	83
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	81	7	88

Merged error: 7.1b

Counts

88 → 7

Compiler

Compiled 3294 to 1742 computations (47.1% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 c (.f64 4 a))
0.8b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
1.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
24.8b	(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

10×	`pow1_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `associate-r_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 57

Calls

4 calls:

10.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
6.0ms	(.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))))

series320.0ms (5%)

Counts

4 → 12

Calls

4 calls:

120.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
110.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
64.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
26.0ms	(.f64 c (.f64 4 a))

simplify41.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4873	1121
1	4873	1121

prune98.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	67	9	76

Merged error: 6.8b

Counts

76 → 9

Compiler

Compiled 2518 to 1291 computations (48.7% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 c 4) a)))))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 c 4) a))
1.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 c 4) a))))
24.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 c 4) a)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite31.0ms (0.5%)

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

4 calls:

9.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 c 4) a))))
9.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 c 4) a)))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 c 4) a))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 c 4) a)))

series632.0ms (9.8%)

Counts

4 → 12

Calls

4 calls:

317.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 c 4) a)))))
126.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 c 4) a)))
118.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 c 4) a))))
70.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 c 4) a))

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4989	1969
1	4989	1969

prune113.0ms (1.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	80	4	84
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	82	11	93

Merged error: 6.5b

Counts

93 → 11

Compiler

Compiled 2891 to 1397 computations (51.7% saved)

regimes551.0ms (8.5%)

Compiler: Compiled 5686 to 3914 computations (31.2% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 38 to 26 computations (31.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	159	455
1	159	455

end0.0ms (0%)

sample2.1s (32.3%)

Algorithm

1×

intervals

Results

710.0ms	8000×	body	128	valid
55.0ms	679×	body	128	nan
35.0ms	380×	body	128	invalid

Compiler

Compiled 1742 to 1167 computations (33% saved)

Details

analyze719.0ms (11.2%)

sample41.0ms (0.6%)

simplify250.0ms (3.9%)

prune14.0ms (0.2%)

localize24.0ms (0.4%)

rewrite32.0ms (0.5%)

series506.0ms (7.8%)

simplify71.0ms (1.1%)

prune138.0ms (2.1%)

localize29.0ms (0.4%)

rewrite34.0ms (0.5%)

series392.0ms (6.1%)

simplify57.0ms (0.9%)

prune126.0ms (1.9%)

localize21.0ms (0.3%)

rewrite27.0ms (0.4%)

series320.0ms (5%)

simplify41.0ms (0.6%)

prune98.0ms (1.5%)

localize21.0ms (0.3%)

rewrite31.0ms (0.5%)

series632.0ms (9.8%)

simplify70.0ms (1.1%)

prune113.0ms (1.8%)

regimes551.0ms (8.5%)

bsearch6.0ms (0.1%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample2.1s (32.3%)

Profiling