Details

analyze723.0ms (12.1%)

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)

sample42.0ms (0.7%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
2.0ms	21×	body	128	nan
1.0ms	15×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify446.0ms (7.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (347.0ms)

Iter	Nodes	Cost
0	2977	54
1	2977	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

Error

22.7b

Counts

2 → 1

Compiler

Compiled 72 to 50 computations (30.6% saved)

localize32.0ms (0.5%)

Local error

Found 4 expressions with local error:

1.4b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
2.5b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
25.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
25.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite23.0ms (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` `cancel-sign-sub-inv_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 54

Calls

4 calls:

6.0ms	(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)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))

series226.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

70.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
67.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
57.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
32.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))

simplify72.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5666	1295

prune136.0ms (2.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	59	7	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	7	67

Error

8.8b

Counts

67 → 7

Compiler

Compiled 3074 to 1861 computations (39.5% saved)

localize27.0ms (0.5%)

Local error

Found 4 expressions with local error:

1.4b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
3.9b	(/.f64 c (+.f64 b (-.f64 b (.f64 2 (/.f64 (.f64 c a) b)))))
7.2b	(/.f64 (*.f64 c a) b)
25.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
15×	`times-frac_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`associate-/r*_binary64`
6×	`add-log-exp_binary64`
5×	`pow1_binary64`
4×	`distribute-lft-out_binary64` `associate-/l*_binary64`
3×	`cbrt-undiv_binary64` `div-exp_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `flip-+_binary64`

Counts

4 → 81

Calls

4 calls:

7.0ms	(/.f64 c (+.f64 b (-.f64 b (.f64 2 (/.f64 (.f64 c a) b)))))
5.0ms	(/.f64 (*.f64 c a) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))

series237.0ms (4%)

Counts

4 → 12

Calls

4 calls:

116.0ms	(/.f64 c (+.f64 b (-.f64 b (.f64 2 (/.f64 (.f64 c a) b)))))
66.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
37.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
18.0ms	(/.f64 (*.f64 c a) b)

simplify86.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4913	1655
1	4913	1655

prune163.0ms (2.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	88	5	93
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	90	10	100

Error

7.4b

Counts

100 → 10

Compiler

Compiled 4179 to 2316 computations (44.6% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.4b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
3.5b	(*.f64 c (/.f64 a b))
3.9b	(/.f64 c (+.f64 b (-.f64 b (.f64 2 (.f64 c (/.f64 a b))))))
25.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64` `times-frac_binary64`
13×	`associate-r_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64`
4×	`associate-/r*_binary64` `distribute-lft-out_binary64`
3×	`associate-l_binary64` `associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-r/_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64` `-commutative_binary64`

Counts

4 → 92

Calls

4 calls:

10.0ms	(*.f64 c (/.f64 a b))
7.0ms	(/.f64 c (+.f64 b (-.f64 b (.f64 2 (.f64 c (/.f64 a b))))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))

series223.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

113.0ms	(/.f64 c (+.f64 b (-.f64 b (.f64 2 (.f64 c (/.f64 a b))))))
60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
32.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
19.0ms	(*.f64 c (/.f64 a b))

simplify75.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4939	1784
1	4939	1784

prune187.0ms (3.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	100	4	104
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	101	13	114

Error

6.0b

Counts

114 → 13

Compiler

Compiled 4802 to 2646 computations (44.9% saved)

localize31.0ms (0.5%)

Local error

Found 4 expressions with local error:

19.5b	(cbrt.f64 (*.f64 c (/.f64 a b)))
19.5b	(cbrt.f64 (*.f64 c (/.f64 a b)))
19.5b	(cbrt.f64 (*.f64 c (/.f64 a b)))
25.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 45

Calls

4 calls:

4.0ms	(cbrt.f64 (*.f64 c (/.f64 a b)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
4.0ms	(cbrt.f64 (*.f64 c (/.f64 a b)))
4.0ms	(cbrt.f64 (*.f64 c (/.f64 a b)))

series299.0ms (5%)

Counts

4 → 12

Calls

4 calls:

79.0ms	(cbrt.f64 (*.f64 c (/.f64 a b)))
78.0ms	(cbrt.f64 (*.f64 c (/.f64 a b)))
76.0ms	(cbrt.f64 (*.f64 c (/.f64 a b)))
65.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify58.0ms (1%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5168	780

prune96.0ms (1.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	57	13	70

Error

6.0b

Counts

70 → 13

Compiler

Compiled 3099 to 1277 computations (58.8% saved)

regimes565.0ms (9.5%)

Accuracy

Total 1.8b remaining (24.8%)

Threshold costs 0b (0%)

Compiler

Compiled 6146 to 4018 computations (34.6% saved)

bsearch5.0ms (0.1%)

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	207	515
1	207	515

end0.0ms (0%)

sample2.1s (35.3%)

Algorithm

1×

intervals

Results

706.0ms	8000×	body	128	valid
53.0ms	656×	body	128	nan
31.0ms	378×	body	128	invalid

Compiler

Compiled 1896 to 1219 computations (35.7% saved)

Details

analyze723.0ms (12.1%)

sample42.0ms (0.7%)

simplify446.0ms (7.5%)

prune8.0ms (0.1%)

localize32.0ms (0.5%)

rewrite23.0ms (0.4%)

series226.0ms (3.8%)

simplify72.0ms (1.2%)

prune136.0ms (2.3%)

localize27.0ms (0.5%)

rewrite23.0ms (0.4%)

series237.0ms (4%)

simplify86.0ms (1.4%)

prune163.0ms (2.7%)

localize26.0ms (0.4%)

rewrite28.0ms (0.5%)

series223.0ms (3.7%)

simplify75.0ms (1.3%)

prune187.0ms (3.1%)

localize31.0ms (0.5%)

rewrite17.0ms (0.3%)

series299.0ms (5%)

simplify58.0ms (1%)

prune96.0ms (1.6%)

regimes565.0ms (9.5%)

bsearch5.0ms (0.1%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample2.1s (35.3%)

Profiling