Details

analyze331.0ms (4%)

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)

sample70.0ms (0.8%)

Algorithm

1×

intervals

Results

17.0ms	93×	body	256	valid
16.0ms	283×	pre	128	true
16.0ms	163×	body	128	valid
2.0ms	27×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify523.0ms (6.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (394.0ms)

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

44.3b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
39.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite67.0ms (0.8%)

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:

23.0ms	(/.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	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
8.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series335.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
91.0ms	(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)
37.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify108.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune171.0ms (2.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	81	5	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	5	87

Error

0.2b

Counts

87 → 5

Compiler

Compiled 2097 to 1244 computations (40.7% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite61.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
22×	`times-frac_binary64_766`
20×	`*-un-lft-identity_binary64_760`
17×	`cbrt-undiv_binary64_794` `div-exp_binary64_811`
13×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
11×	`associate-/l*_binary64_705`
10×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
8×	`add-log-exp_binary64_799`
6×	`associate-/r/_binary64_706`
5×	`distribute-lft-out_binary64_711` `associate-/r*_binary64_704`
4×	`flip3-+_binary64_763` `div-inv_binary64_757` `flip-+_binary64_734` `pow1_binary64_821`
2×	`frac-2neg_binary64_771` `clear-num_binary64_759`
1×	`diff-log_binary64_852` `associate-/l/_binary64_707` `cancel-sign-sub-inv_binary64_726` `+-commutative_binary64_690` `sum-log_binary64_851` `sub-neg_binary64_753` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 99

Calls

4 calls:

26.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
13.0ms	(/.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	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series692.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

311.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
252.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
79.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
50.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify78.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4982	3037
1	4982	3037

prune273.0ms (3.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	102	9	111
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	107	9	116

Error

Counts

116 → 9

Compiler

Compiled 3339 to 2062 computations (38.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.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 (.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))))))

rewrite28.0ms (0.3%)

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 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))))

series490.0ms (6%)

Counts

4 → 12

Calls

4 calls:

253.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
111.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
66.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
59.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify141.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	4905	1972
1	4905	1972

prune142.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	85	8	93

Error

Counts

93 → 8

Compiler

Compiled 2360 to 1470 computations (37.7% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c)
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.3b	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c))

rewrite77.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64_766`
96×	`*-un-lft-identity_binary64_760`
62×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
19×	`associate-/r*_binary64_704`
17×	`distribute-lft-out_binary64_711` `add-exp-log_binary64_798`
11×	`add-cbrt-cube_binary64_796`
8×	`add-log-exp_binary64_799` `div-exp_binary64_811`
7×	`associate-/l*_binary64_705`
6×	`div-inv_binary64_757`
5×	`pow1_binary64_821`
4×	`cbrt-undiv_binary64_794`
2×	`frac-2neg_binary64_771` `flip3-+_binary64_763` `associate-/l/_binary64_707` `flip-+_binary64_734` `rec-exp_binary64_810` `clear-num_binary64_759` `1-exp_binary64_804`
1×	`diff-log_binary64_852` `associate-/r/_binary64_706` `cancel-sign-sub-inv_binary64_726` `inv-pow_binary64_845` `+-commutative_binary64_690` `sum-log_binary64_851` `sub-neg_binary64_753` `flip--_binary64_735` `pow-flip_binary64_834` `flip3--_binary64_764`

Counts

4 → 145

Calls

4 calls:

25.0ms	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c))
18.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c)
10.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
9.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series387.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

183.0ms	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c))
108.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c)
61.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
35.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify114.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5148	4909

prune340.0ms (4.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	157	8	165

Error

Counts

165 → 8

Compiler

Compiled 4701 to 2935 computations (37.6% saved)

regimes614.0ms (7.5%)

Accuracy

Total 0.2b remaining (99.8%)

Threshold costs 0.2b (99.8%)

Compiler

Compiled 5800 to 4346 computations (25.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	24
1	63	24

end0.0ms (0%)

sample3.1s (37.6%)

Algorithm

1×

intervals

Results

403.0ms	2902×	body	256	valid
390.0ms	8894×	pre	128	true
369.0ms	5098×	body	128	valid
62.0ms	894×	body	128	nan

Compiler

Compiled 1486 to 1115 computations (25% saved)

Details

analyze331.0ms (4%)

sample70.0ms (0.8%)

simplify523.0ms (6.4%)

prune7.0ms (0.1%)

localize25.0ms (0.3%)

rewrite67.0ms (0.8%)

series335.0ms (4.1%)

simplify108.0ms (1.3%)

prune171.0ms (2.1%)

localize16.0ms (0.2%)

rewrite61.0ms (0.7%)

series692.0ms (8.4%)

simplify78.0ms (0.9%)

prune273.0ms (3.3%)

localize12.0ms (0.1%)

rewrite28.0ms (0.3%)

series490.0ms (6%)

simplify141.0ms (1.7%)

prune142.0ms (1.7%)

localize26.0ms (0.3%)

rewrite77.0ms (0.9%)

series387.0ms (4.7%)

simplify114.0ms (1.4%)

prune340.0ms (4.1%)

regimes614.0ms (7.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.1s (37.6%)

Profiling