Details

analyze780.0ms (13.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4879	216
1	4879	216
0	3	3
1	3	3

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
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample39.0ms (0.7%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
2.0ms	27×	body	128	nan
1.0ms	13×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify366.0ms (6.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (360.0ms)

Iter	Nodes	Cost
0	4219	54
1	4219	54

prune6.0ms (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

20.5b

Counts

2 → 1

Compiler

Compiled 72 to 50 computations (30.6% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_100`
11×	`*-un-lft-identity_binary64_78`
8×	`add-log-exp_binary64_117`
7×	`sqrt-prod_binary64_94` `add-cube-cbrt_binary64_113`
6×	`pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `sqrt-div_binary64_95`
3×	`flip3--_binary64_82` `flip--_binary64_53` `cancel-sign-sub-inv_binary64_44`
2×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `difference-of-squares_binary64_47` `pow1/2_binary64_158`
1×	`+-commutative_binary64_8` `flip-+_binary64_52` `distribute-lft-out--_binary64_30` `diff-log_binary64_170` `distribute-lft-out_binary64_29` `sub-neg_binary64_71` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

4 → 59

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series237.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
61.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
58.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
54.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify93.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4936	1457
1	4936	1457

prune146.0ms (2.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	65	6	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	6	72

Error

7.5b

Counts

72 → 6

Compiler

Compiled 3268 to 1960 computations (40% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

10.7b	(+.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))))))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_100`
9×	`sqrt-prod_binary64_94`
7×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78` `pow1_binary64_139`
6×	`add-log-exp_binary64_117` `sqrt-div_binary64_95`
4×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
3×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `flip3--_binary64_82` `flip--_binary64_53` `pow1/2_binary64_158`
1×	`+-commutative_binary64_8` `flip-+_binary64_52` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

4 → 56

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
3.0ms	(+.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))))))

series233.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

63.0ms	(+.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))))))
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
56.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
55.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify105.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4930	1361
1	4930	1361

prune148.0ms (2.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	69	5	74

Error

7.5b

Counts

74 → 5

Compiler

Compiled 3839 to 2318 computations (39.6% saved)

localize29.0ms (0.5%)

Local error

Found 4 expressions with local error:

22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
22.9b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
22.9b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_100`
8×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`sqrt-prod_binary64_94` `cbrt-prod_binary64_109` `pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `cbrt-div_binary64_110` `add-log-exp_binary64_117` `flip3--_binary64_82` `flip--_binary64_53` `add-exp-log_binary64_116` `sqrt-div_binary64_95`
2×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `pow1/3_binary64_160` `pow1/2_binary64_158`

Counts

4 → 56

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series298.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
89.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
57.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
56.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify57.0ms (1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4934	1424
1	4934	1424

prune194.0ms (3.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	67	6	73

Error

7.5b

Counts

73 → 6

Compiler

Compiled 4923 to 3004 computations (39% saved)

localize33.0ms (0.6%)

Local error

Found 4 expressions with local error:

22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
22.9b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
22.9b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
22.9b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_100` `cbrt-prod_binary64_109`
8×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`cbrt-div_binary64_110`
5×	`pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `flip3--_binary64_82` `flip--_binary64_53` `add-exp-log_binary64_116`
3×	`sqrt-prod_binary64_94` `pow1/3_binary64_160`
2×	`sqrt-div_binary64_95`
1×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `pow1/2_binary64_158`

Counts

4 → 54

Calls

4 calls:

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

series329.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

94.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
92.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
89.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
54.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify58.0ms (1%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4934	1440
1	4934	1440

prune224.0ms (4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	66	6	72

Error

7.5b

Counts

72 → 6

Compiler

Compiled 5437 to 3313 computations (39.1% saved)

regimes360.0ms (6.4%)

Accuracy

Total 0.7b remaining (7.7%)

Threshold costs 0.7b (7.7%)

Compiler

Compiled 3674 to 2526 computations (31.2% saved)

bsearch84.0ms (1.5%)

Steps

Iters	Range		Point
9	1.184070874810778e+129	7.915678514483357e+135	6.861854509988867e+134
9	-2.8939307640831774e+161	-1.1654110119923588e+154	-1.3436054541167692e+154

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	163	172
1	163	172

end0.0ms (0%)

sample1.7s (30.2%)

Algorithm

1×

intervals

Results

720.0ms	8000×	body	128	valid
54.0ms	626×	body	128	nan
33.0ms	391×	body	128	invalid

Compiler

Compiled 1052 to 716 computations (31.9% saved)

Details

analyze780.0ms (13.8%)

sample39.0ms (0.7%)

simplify366.0ms (6.5%)

prune6.0ms (0.1%)

localize22.0ms (0.4%)

rewrite24.0ms (0.4%)

series237.0ms (4.2%)

simplify93.0ms (1.6%)

prune146.0ms (2.6%)

localize24.0ms (0.4%)

rewrite17.0ms (0.3%)

series233.0ms (4.1%)

simplify105.0ms (1.9%)

prune148.0ms (2.6%)

localize29.0ms (0.5%)

rewrite19.0ms (0.3%)

series298.0ms (5.3%)

simplify57.0ms (1%)

prune194.0ms (3.4%)

localize33.0ms (0.6%)

rewrite19.0ms (0.3%)

series329.0ms (5.8%)

simplify58.0ms (1%)

prune224.0ms (4%)

regimes360.0ms (6.4%)

bsearch84.0ms (1.5%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.7s (30.2%)

Profiling