Details

analyze653.0ms (10.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5132	96
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
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)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	40×	body	2048	valid
8.0ms	159×	body	128	valid
5.0ms	28×	body	1024	valid
3.0ms	10×	body	4096	valid
1.0ms	10×	body	512	valid
1.0ms	19×	body	128	nan
1.0ms	9×	body	256	valid
1.0ms	14×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify319.0ms (5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (314.0ms)

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

Merged error: 33.5b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
20.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite37.0ms (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:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
7.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series254.0ms (4%)

Counts

4 → 12

Calls

4 calls:

99.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
61.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
58.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
35.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify105.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4895	1979
1	4895	1979

prune120.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	79	7	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	8	87

Merged error: 4.9b

Counts

87 → 8

Compiler

Compiled 2167 to 1177 computations (45.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.5b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
9.0b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
20.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite48.0ms (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:

15.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series485.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

198.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
160.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
64.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
62.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify77.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4959	3121
1	4959	3121

prune146.0ms (2.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	113	9	122

Merged error: 4.8b

Counts

122 → 9

Compiler

Compiled 3356 to 1902 computations (43.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
20.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite29.0ms (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 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series331.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

173.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
62.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
62.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
34.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify109.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4896	1972
1	4896	1972

prune103.0ms (1.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	84	9	93

Merged error: 4.8b

Counts

93 → 9

Compiler

Compiled 2329 to 1331 computations (42.9% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
8.9b	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
20.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
20.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_799` `add-sqr-sqrt_binary64_782`
6×	`*-un-lft-identity_binary64_760` `sqrt-prod_binary64_776` `add-cube-cbrt_binary64_795` `pow1_binary64_821`
4×	`add-exp-log_binary64_798` `sqrt-div_binary64_777` `add-cbrt-cube_binary64_796`
3×	`flip--_binary64_735` `flip3--_binary64_764`
2×	`rem-sqrt-square_binary64_773` `sqrt-pow1_binary64_778` `pow1/2_binary64_840`
1×	`diff-log_binary64_852` `flip3-+_binary64_763` `cancel-sign-sub-inv_binary64_726` `flip-+_binary64_734` `+-commutative_binary64_690` `sum-log_binary64_851` `sub-neg_binary64_753`

Counts

4 → 53

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
3.0ms	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))

series209.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

65.0ms	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
57.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
56.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
31.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify85.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4924	1280
1	4924	1280

prune89.0ms (1.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	65	9	74

Merged error: 4.8b

Counts

74 → 9

Compiler

Compiled 2275 to 1282 computations (43.6% saved)

regimes784.0ms (12.3%)

Compiler: Compiled 4868 to 3656 computations (24.9% saved)

bsearch78.0ms (1.2%)

Steps

Iters	Range	Point
9	3.240667004624162e+54	6.900588731769942e+61	1.3389678122082543e+61
9	-2.8570170725650746e-224	-3.553196571313925e-229	-3.089056825403424e-228
0	-1.0331933023904229e+81	-1.0032634201183365e+81	-1.0182283612543797e+81

Iters

Range

Point

3.240667004624162e+54

6.900588731769942e+61

1.3389678122082543e+61

-2.8570170725650746e-224

-3.553196571313925e-229

-3.089056825403424e-228

-1.0331933023904229e+81

-1.0032634201183365e+81

-1.0182283612543797e+81

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%)

sample2.2s (34.2%)

Algorithm

1×

intervals

Results

279.0ms	1129×	body	2048	valid
269.0ms	5209×	body	128	valid
140.0ms	747×	body	1024	valid
118.0ms	382×	body	4096	valid
50.0ms	360×	body	512	valid
32.0ms	676×	body	128	nan
19.0ms	367×	body	128	invalid
16.0ms	173×	body	256	valid

Compiler

Compiled 1309 to 970 computations (25.9% saved)

Details

analyze653.0ms (10.3%)

sample39.0ms (0.6%)

simplify319.0ms (5%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite37.0ms (0.6%)

series254.0ms (4%)

simplify105.0ms (1.7%)

prune120.0ms (1.9%)

localize14.0ms (0.2%)

rewrite48.0ms (0.8%)

series485.0ms (7.6%)

simplify77.0ms (1.2%)

prune146.0ms (2.3%)

localize13.0ms (0.2%)

rewrite29.0ms (0.5%)

series331.0ms (5.2%)

simplify109.0ms (1.7%)

prune103.0ms (1.6%)

localize18.0ms (0.3%)

rewrite22.0ms (0.3%)

series209.0ms (3.3%)

simplify85.0ms (1.3%)

prune89.0ms (1.4%)

regimes784.0ms (12.3%)

bsearch78.0ms (1.2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.2s (34.2%)

Profiling