Details

analyze518.0ms (6.3%)

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
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)

sample41.0ms (0.5%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
4.0ms	24×	body	128	nan
1.0ms	7×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify458.0ms (5.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (368.0ms)

Iter	Nodes	Cost
0	4219	54
1	4219	54

prune10.0ms (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

21.0b

Counts

2 → 1

Compiler

Compiled 72 to 50 computations (30.6% saved)

localize29.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))) a)
0.1b	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b))
0.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.8b	(-.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))))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite28.0ms (0.3%)

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

8 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
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)))
0.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series590.0ms (7.2%)

Counts

4 → 65

Calls

4 calls:

157.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
154.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
140.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
138.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 4063 to 3021 computations (25.6% saved)

simplify83.0ms (1%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4969	2225
1	4969	2225

prune294.0ms (3.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	115	9	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	9	125

Error

7.0b

Counts

125 → 9

Compiler

Compiled 5206 to 3063 computations (41.2% saved)

localize26.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.0b	(sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
11.4b	(+.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))))))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite18.0ms (0.2%)

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

8 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	(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))))))
0.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series556.0ms (6.7%)

Counts

4 → 63

Calls

4 calls:

152.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
148.0ms	(+.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))))))
129.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
127.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 4810 to 3443 computations (28.4% saved)

simplify81.0ms (1%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4938	2090
1	4938	2090

prune267.0ms (3.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	119	9	128

Error

7.0b

Counts

128 → 9

Compiler

Compiled 6217 to 3729 computations (40% saved)

localize26.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.0b	(sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
8.2b	(-.f64 (.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))))) b)
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_100`
9×	`sqrt-prod_binary64_94`
8×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
7×	`pow1_binary64_139`
6×	`add-log-exp_binary64_117` `sqrt-div_binary64_95`
4×	`add-cbrt-cube_binary64_114` `flip3--_binary64_82` `flip--_binary64_53` `add-exp-log_binary64_116`
3×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `cancel-sign-sub-inv_binary64_44` `pow1/2_binary64_158`
1×	`diff-log_binary64_170` `difference-of-squares_binary64_47` `sub-neg_binary64_71`

Counts

4 → 60

Calls

8 calls:

19.0ms	(-.f64 (.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))))) b)
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)))
0.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series510.0ms (6.2%)

Counts

4 → 54

Calls

4 calls:

165.0ms	(-.f64 (.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))))) b)
151.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
97.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
96.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 4372 to 3132 computations (28.4% saved)

simplify40.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5201	1901

prune266.0ms (3.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	114	9	123

Error

7.0b

Counts

123 → 9

Compiler

Compiled 5873 to 3503 computations (40.4% saved)

localize28.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b))
0.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
8.5b	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
24.7b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
24.7b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_100`
7×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`add-log-exp_binary64_117` `cbrt-prod_binary64_109`
5×	`pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `cbrt-div_binary64_110` `add-exp-log_binary64_116`
3×	`sqrt-prod_binary64_94` `flip3--_binary64_82` `flip--_binary64_53`
2×	`pow1/3_binary64_160` `sqrt-div_binary64_95`
1×	`+-commutative_binary64_8` `sqrt-pow1_binary64_96` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `pow1/2_binary64_158` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

4 → 52

Calls

8 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	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
3.0ms	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
0.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series1.1s (13.6%)

Counts

4 → 78

Calls

4 calls:

406.0ms	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
288.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
286.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
144.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 7420 to 5576 computations (24.9% saved)

simplify70.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5030	4721

prune352.0ms (4.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	129	10	139

Error

7.0b

Counts

139 → 10

Compiler

Compiled 7882 to 4769 computations (39.5% saved)

simplify20.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	340	1436
1	340	1436

regimes313.0ms (3.8%)

Compiler: Compiled 2850 to 2031 computations (28.7% saved)

bsearch82.0ms (1%)

Steps

Iters	Range		Point
9	1.867706484167828e+108	9.890495663803595e+113	3.5283511614465457e+112
8	-3.959610459175091e+151	-1.5228555280189265e+149	-4.0455359245284925e+149

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes74.0ms (0.9%)

Compiler: Compiled 396 to 333 computations (15.9% saved)

bsearch40.0ms (0.5%)

Steps

Iters	Range		Point
9	1.867706484167828e+108	9.890495663803595e+113	1.6351325639831533e+113

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes54.0ms (0.7%)

Compiler: Compiled 288 to 258 computations (10.4% saved)

bsearch100.0ms (1.2%)

Steps

Iters	Range		Point
9	1.867706484167828e+108	9.890495663803595e+113	9.77616652260473e+113
11	-5.443972982579693e-148	-9.569361706695495e-169	-1.580524949699072e-162

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes41.0ms (0.5%)

Compiler: Compiled 192 to 186 computations (3.1% saved)

bsearch43.0ms (0.5%)

Steps

Iters	Range		Point
9	6.483886538216483e-41	1.2172249405601069e-32	1.0663126358646597e-38

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes30.0ms (0.4%)

Compiler: Compiled 96 to 114 computations (-18.8% saved)

bsearch0.0ms (0%)

regimes25.0ms (0.3%)

Accuracy

Total 1.1b remaining (16.3%)

Threshold costs 0b (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch15.0ms (0.2%)

Compiler: Compiled 352 to 239 computations (32.1% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	124	486
1	124	486

end0.0ms (0%)

sample1.9s (23.4%)

Algorithm

1×

intervals

Results

703.0ms	8000×	body	128	valid
59.0ms	668×	body	128	nan
38.0ms	433×	body	128	invalid

Compiler

Compiled 1313 to 927 computations (29.4% saved)

Pareto

-0.18235525091322452

Details

analyze518.0ms (6.3%)

sample41.0ms (0.5%)

simplify458.0ms (5.6%)

prune10.0ms (0.1%)

localize29.0ms (0.3%)

rewrite28.0ms (0.3%)

series590.0ms (7.2%)

simplify83.0ms (1%)

prune294.0ms (3.6%)

localize26.0ms (0.3%)

rewrite18.0ms (0.2%)

series556.0ms (6.7%)

simplify81.0ms (1%)

prune267.0ms (3.2%)

localize26.0ms (0.3%)

rewrite34.0ms (0.4%)

series510.0ms (6.2%)

simplify40.0ms (0.5%)

prune266.0ms (3.2%)

localize28.0ms (0.3%)

rewrite17.0ms (0.2%)

series1.1s (13.6%)

simplify70.0ms (0.9%)

prune352.0ms (4.3%)

simplify20.0ms (0.2%)

regimes313.0ms (3.8%)

bsearch82.0ms (1%)

regimes74.0ms (0.9%)

bsearch40.0ms (0.5%)

regimes54.0ms (0.7%)

bsearch100.0ms (1.2%)

regimes41.0ms (0.5%)

bsearch43.0ms (0.5%)

regimes30.0ms (0.4%)

bsearch0.0ms (0%)

regimes25.0ms (0.3%)

bsearch15.0ms (0.2%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample1.9s (23.4%)

Profiling