Details

analyze347.0ms (4.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample49.0ms (0.6%)

Algorithm

1×

intervals

Results

13.0ms	118×	body	256	valid
10.0ms	276×	pre	128	true
8.0ms	45×	body	512	valid
5.0ms	93×	body	128	valid
1.0ms	20×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify592.0ms (7.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (495.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune7.0ms (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

51.9b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
26.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite68.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_441`
14×	`*-un-lft-identity_binary64_419`
9×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
8×	`add-log-exp_binary64_458` `add-cube-cbrt_binary64_454`
6×	`times-frac_binary64_425` `difference-of-squares_binary64_388` `sqrt-prod_binary64_435` `associate-/l*_binary64_364`
5×	`pow1_binary64_480`
4×	`flip3--_binary64_423` `flip--_binary64_394` `cancel-sign-sub-inv_binary64_385`
3×	`distribute-lft-out--_binary64_371`
2×	`sqrt-div_binary64_436` `sub-neg_binary64_412` `diff-log_binary64_511` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `pow1/2_binary64_499` `div-inv_binary64_416` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `associate-/r*_binary64_363` `rem-sqrt-square_binary64_432` `div-sub_binary64_424`

Counts

4 → 74

Calls

4 calls:

24.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
8.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series383.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
112.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
90.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
57.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify144.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune129.0ms (1.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	3	87

Error

0.1b

Counts

87 → 3

Compiler

Compiled 2001 to 1178 computations (41.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.2b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.3b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite48.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
22×	`times-frac_binary64_425`
20×	`*-un-lft-identity_binary64_419`
17×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
13×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
11×	`associate-/l*_binary64_364`
10×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
8×	`add-log-exp_binary64_458`
6×	`associate-/r/_binary64_365`
5×	`distribute-lft-out_binary64_370` `associate-/r*_binary64_363`
4×	`flip3-+_binary64_422` `div-inv_binary64_416` `flip-+_binary64_393` `pow1_binary64_480`
2×	`clear-num_binary64_418` `frac-2neg_binary64_430`
1×	`sub-neg_binary64_412` `sum-log_binary64_510` `flip3--_binary64_423` `diff-log_binary64_511` `flip--_binary64_394` `cancel-sign-sub-inv_binary64_385` `+-commutative_binary64_349` `associate-/l/_binary64_366`

Counts

4 → 99

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (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	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series566.0ms (7%)

Counts

4 → 12

Calls

4 calls:

214.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
190.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
98.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
64.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify71.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4982	3037
1	4982	3037

prune158.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	105	6	111
Fresh	0	1	1
Picked	1	0	1
Done	1	0	1
Total	107	7	114

Error

Counts

114 → 7

Compiler

Compiled 3206 to 1974 computations (38.4% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_419`
15×	`add-sqr-sqrt_binary64_441`
14×	`add-cube-cbrt_binary64_454`
12×	`times-frac_binary64_425`
8×	`add-log-exp_binary64_458`
6×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
5×	`distribute-lft-out_binary64_370` `pow1_binary64_480`
4×	`associate-/r*_binary64_363`
3×	`sqrt-prod_binary64_435` `associate-/l*_binary64_364`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `flip3--_binary64_423` `associate-/r/_binary64_365` `flip-+_binary64_393` `flip--_binary64_394`
1×	`clear-num_binary64_418` `sub-neg_binary64_412` `pow1/2_binary64_499` `div-inv_binary64_416` `sum-log_binary64_510` `frac-2neg_binary64_430` `diff-log_binary64_511` `sqrt-pow1_binary64_437` `cancel-sign-sub-inv_binary64_385` `rem-sqrt-square_binary64_432` `+-commutative_binary64_349` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 72

Calls

4 calls:

18.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

series339.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

175.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
68.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
61.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
34.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify121.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4905	1972
1	4905	1972

prune129.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	81	3	84
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	86	5	91

Error

Counts

91 → 5

Compiler

Compiled 2282 to 1416 computations (37.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3)))
0.1b	(/.f64 c (+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3))))
0.2b	(pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3)
0.5b	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3))

rewrite94.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64_419`
23×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
18×	`cbrt-prod_binary64_450`
12×	`times-frac_binary64_425` `unpow-prod-down_binary64_498` `cube-prod_binary64_447` `sqrt-prod_binary64_435`
7×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
6×	`add-log-exp_binary64_458` `pow1_binary64_480`
5×	`distribute-lft-out_binary64_370`
4×	`sqrt-div_binary64_436` `cube-div_binary64_448` `associate-/r*_binary64_363`
3×	`pow-pow_binary64_491` `pow-unpow_binary64_496` `associate-/l*_binary64_364`
2×	`flip3-+_binary64_422` `cbrt-div_binary64_451` `unpow3_binary64_485` `cube-mult_binary64_449` `sqr-pow_binary64_391` `flip3--_binary64_423` `associate-/r/_binary64_365` `flip-+_binary64_393` `flip--_binary64_394`
1×	`clear-num_binary64_418` `pow1/3_binary64_501` `pow1/2_binary64_499` `div-inv_binary64_416` `rem-cube-cbrt_binary64_442` `sqrt-pow2_binary64_438` `pow-exp_binary64_487` `sum-log_binary64_510` `rem-cbrt-cube_binary64_443` `pow-to-exp_binary64_488` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `+-commutative_binary64_349` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 108

Calls

4 calls:

27.0ms	(+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3)))
25.0ms	(/.f64 c (+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3))))
13.0ms	(pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3)
7.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3))

series616.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

320.0ms	(/.f64 c (+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3))))
112.0ms	(+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3)))
108.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3))
76.0ms	(pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3)

simplify104.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5050	2889

prune211.0ms (2.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	120	5	125

Error

Counts

125 → 5

Compiler

Compiled 3217 to 2038 computations (36.6% saved)

regimes456.0ms (5.6%)

Accuracy

Total 0.1b remaining (98.6%)

Threshold costs 0.1b (98.6%)

Compiler

Compiled 4144 to 3162 computations (23.7% saved)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	63	24
1	63	24

end0.0ms (0%)

sample3.3s (41.4%)

Algorithm

1×

intervals

Results

566.0ms	3747×	body	256	valid
430.0ms	8824×	pre	128	true
334.0ms	1470×	body	512	valid
220.0ms	2783×	body	128	valid
61.0ms	824×	body	128	nan

Compiler

Compiled 1072 to 819 computations (23.6% saved)

Details

analyze347.0ms (4.3%)

sample49.0ms (0.6%)

simplify592.0ms (7.3%)

prune7.0ms (0.1%)

localize21.0ms (0.3%)

rewrite68.0ms (0.8%)

series383.0ms (4.7%)

simplify144.0ms (1.8%)

prune129.0ms (1.6%)

localize14.0ms (0.2%)

rewrite48.0ms (0.6%)

series566.0ms (7%)

simplify71.0ms (0.9%)

prune158.0ms (1.9%)

localize20.0ms (0.2%)

rewrite39.0ms (0.5%)

series339.0ms (4.2%)

simplify121.0ms (1.5%)

prune129.0ms (1.6%)

localize15.0ms (0.2%)

rewrite94.0ms (1.2%)

series616.0ms (7.6%)

simplify104.0ms (1.3%)

prune211.0ms (2.6%)

regimes456.0ms (5.6%)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample3.3s (41.4%)

Profiling