Details

analyze462.0ms (7.6%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample40.0ms (0.7%)

Algorithm

1×

intervals

Results

10.0ms	33×	body	2048	valid
9.0ms	172×	body	128	valid
5.0ms	24×	body	1024	valid
3.0ms	9×	body	4096	valid
2.0ms	14×	body	512	valid
1.0ms	25×	body	128	nan
1.0ms	10×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify399.0ms (6.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (306.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (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

32.7b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
21.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_782`
14×	`*-un-lft-identity_binary64_760`
9×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
8×	`add-cube-cbrt_binary64_795` `add-log-exp_binary64_799`
6×	`sqrt-prod_binary64_776` `difference-of-squares_binary64_729` `associate-/l*_binary64_705` `times-frac_binary64_766`
5×	`pow1_binary64_821`
4×	`cancel-sign-sub-inv_binary64_726` `flip--_binary64_735` `flip3--_binary64_764`
3×	`distribute-lft-out--_binary64_712`
2×	`diff-log_binary64_852` `cbrt-undiv_binary64_794` `associate-/l/_binary64_707` `sqrt-div_binary64_777` `div-exp_binary64_811` `sub-neg_binary64_753`
1×	`rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `prod-exp_binary64_809` `sqrt-pow1_binary64_778` `associate-/r*_binary64_704` `div-inv_binary64_757` `div-sub_binary64_765` `cbrt-unprod_binary64_793` `pow1/2_binary64_840` `clear-num_binary64_759`

Counts

4 → 74

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series260.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

102.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
63.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
57.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
36.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify91.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune120.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	78	8	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	78	9	87

Error

6.0b

Counts

87 → 9

Compiler

Compiled 2157 to 1290 computations (40.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
3.3b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
10.4b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
21.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite50.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
22×	`times-frac_binary64_766`
21×	`*-un-lft-identity_binary64_760`
17×	`cbrt-undiv_binary64_794` `div-exp_binary64_811`
13×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
12×	`add-sqr-sqrt_binary64_782`
11×	`add-cube-cbrt_binary64_795` `associate-/l*_binary64_705`
6×	`associate-/r/_binary64_706` `add-log-exp_binary64_799`
5×	`distribute-lft-out_binary64_711` `associate-/r*_binary64_704` `pow1_binary64_821`
4×	`flip3-+_binary64_763` `div-inv_binary64_757` `flip-+_binary64_734`
3×	`sqrt-prod_binary64_776`
2×	`frac-2neg_binary64_771` `sqrt-div_binary64_777` `clear-num_binary64_759`
1×	`rem-sqrt-square_binary64_773` `associate-/l/_binary64_707` `sqrt-pow1_binary64_778` `+-commutative_binary64_690` `sum-log_binary64_851` `pow1/2_binary64_840` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 102

Calls

4 calls:

14.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
11.0ms	(/.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))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series467.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

187.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
154.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
66.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify99.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4956	3121
1	4956	3121

prune143.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	116	7	123

Error

5.9b

Counts

123 → 7

Compiler

Compiled 3241 to 1987 computations (38.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
21.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_760`
15×	`add-sqr-sqrt_binary64_782`
14×	`add-cube-cbrt_binary64_795`
12×	`times-frac_binary64_766`
8×	`add-log-exp_binary64_799`
6×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
5×	`distribute-lft-out_binary64_711` `pow1_binary64_821`
4×	`associate-/r*_binary64_704`
3×	`sqrt-prod_binary64_776` `associate-/l*_binary64_705`
2×	`associate-/r/_binary64_706` `flip3-+_binary64_763` `sqrt-div_binary64_777` `flip-+_binary64_734` `flip--_binary64_735` `flip3--_binary64_764`
1×	`diff-log_binary64_852` `rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `cancel-sign-sub-inv_binary64_726` `sqrt-pow1_binary64_778` `div-inv_binary64_757` `+-commutative_binary64_690` `sum-log_binary64_851` `pow1/2_binary64_840` `div-exp_binary64_811` `clear-num_binary64_759` `sub-neg_binary64_753`

Counts

4 → 72

Calls

4 calls:

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

series317.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

167.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
58.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
33.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify77.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4891	1972
1	4891	1972

prune98.0ms (1.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	84	7	91

Error

5.9b

Counts

91 → 7

Compiler

Compiled 2239 to 1384 computations (38.2% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

10.1b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
21.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
21.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
21.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
12×	`add-sqr-sqrt_binary64_782`
9×	`*-un-lft-identity_binary64_760` `sqrt-prod_binary64_776` `add-cube-cbrt_binary64_795`
7×	`pow1_binary64_821`
6×	`sqrt-div_binary64_777`
4×	`add-log-exp_binary64_799`
3×	`rem-sqrt-square_binary64_773` `cbrt-undiv_binary64_794` `prod-exp_binary64_809` `sqrt-pow1_binary64_778` `associate-/r*_binary64_704` `cbrt-unprod_binary64_793` `pow1/2_binary64_840` `div-exp_binary64_811` `times-frac_binary64_766` `flip--_binary64_735` `flip3--_binary64_764`
2×	`associate-/r/_binary64_706`
1×	`frac-2neg_binary64_771` `flip3-+_binary64_763` `div-inv_binary64_757` `flip-+_binary64_734` `associate-/l*_binary64_705` `clear-num_binary64_759`

Counts

4 → 70

Calls

4 calls:

8.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
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)))

series367.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

197.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
56.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
54.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify64.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4973	1823
1	4973	1823

prune152.0ms (2.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	82	7	89

Error

5.9b

Counts

89 → 7

Compiler

Compiled 3894 to 2357 computations (39.5% saved)

regimes557.0ms (9.2%)

Accuracy

Total 1.0b remaining (14.9%)

Threshold costs 1.0b (14.9%)

Compiler

Compiled 3744 to 2880 computations (23.1% saved)

bsearch110.0ms (1.8%)

Steps

Iters	Range	Point
7	6.1964526172169535e+134	1.9152122692699513e+136	8.912861377839782e+134
10	-1.1228739214406659e-236	-7.143985414855799e-248	-3.3856076934378627e-242
9	-1.4477785457512157e+153	-5.651711623551278e+145	-6.97667166683124e+151

Iters

Range

Point

6.1964526172169535e+134

1.9152122692699513e+136

8.912861377839782e+134

-1.1228739214406659e-236

-7.143985414855799e-248

-3.3856076934378627e-242

-1.4477785457512157e+153

-5.651711623551278e+145

-6.97667166683124e+151

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	105	82
1	105	82

end0.0ms (0%)

sample2.0s (33.2%)

Algorithm

1×

intervals

Results

283.0ms	5208×	body	128	valid
283.0ms	1099×	body	2048	valid
146.0ms	733×	body	1024	valid
132.0ms	430×	body	4096	valid
55.0ms	362×	body	512	valid
34.0ms	674×	body	128	nan
19.0ms	168×	body	256	valid
19.0ms	364×	body	128	invalid

Compiler

Compiled 1028 to 778 computations (24.3% saved)

Details

analyze462.0ms (7.6%)

sample40.0ms (0.7%)

simplify399.0ms (6.6%)

prune4.0ms (0.1%)

localize14.0ms (0.2%)

rewrite34.0ms (0.6%)

series260.0ms (4.3%)

simplify91.0ms (1.5%)

prune120.0ms (2%)

localize14.0ms (0.2%)

rewrite50.0ms (0.8%)

series467.0ms (7.7%)

simplify99.0ms (1.6%)

prune143.0ms (2.4%)

localize12.0ms (0.2%)

rewrite31.0ms (0.5%)

series317.0ms (5.2%)

simplify77.0ms (1.3%)

prune98.0ms (1.6%)

localize19.0ms (0.3%)

rewrite32.0ms (0.5%)

series367.0ms (6.1%)

simplify64.0ms (1.1%)

prune152.0ms (2.5%)

regimes557.0ms (9.2%)

bsearch110.0ms (1.8%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.0s (33.2%)

Profiling