Details

analyze259.0ms (3.6%)

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)

sample32.0ms (0.4%)

Algorithm

1×

intervals

Results

12.0ms	244×	body	128	valid
8.0ms	282×	pre	128	true
1.0ms	26×	body	128	nan
1.0ms	12×	body	256	valid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify236.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 28.9b

Counts

2 → 1

Compiler

Compiled 66 to 54 computations (18.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
0.3b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
28.7b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

rewrite42.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_79`
10×	`add-log-exp_binary64_118`
9×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
8×	`add-sqr-sqrt_binary64_101`
7×	`add-cube-cbrt_binary64_114`
6×	`distribute-lft-out_binary64_30`
5×	`times-frac_binary64_85` `associate-/l*_binary64_24` `pow1_binary64_140`
3×	`sqrt-prod_binary64_95` `distribute-rgt-neg-in_binary64_37`
2×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `neg-sub0_binary64_74` `flip-+_binary64_53` `sum-log_binary64_170` `associate-+l-_binary64_14` `flip--_binary64_54` `sqrt-div_binary64_96` `flip3--_binary64_83` `associate-/l/_binary64_26` `flip3-+_binary64_82`
1×	`associate-/r*_binary64_23` `div-sub_binary64_84` `div-inv_binary64_76` `neg-log_binary64_172` `+-commutative_binary64_9` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `diff-log_binary64_171` `clear-num_binary64_78` `pow1/2_binary64_159` `cancel-sign-sub-inv_binary64_45` `sub-neg_binary64_72` `frac-2neg_binary64_90`

Counts

4 → 70

Calls

4 calls:

14.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
10.0ms	(+.f64 (neg.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)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series529.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

204.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
134.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
129.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
62.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify58.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5290	1826

prune173.0ms (2.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	76	6	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	6	83

Merged error: 0.4b

Counts

83 → 6

Compiler

Compiled 3489 to 2309 computations (33.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite66.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
34×	`times-frac_binary64_85`
32×	`add-sqr-sqrt_binary64_101` `*-un-lft-identity_binary64_79`
17×	`cbrt-undiv_binary64_113` `div-exp_binary64_130`
14×	`associate-/l*_binary64_24`
13×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128`
12×	`add-cube-cbrt_binary64_114`
10×	`distribute-lft-out--_binary64_31` `difference-of-squares_binary64_48` `add-log-exp_binary64_118`
8×	`sqrt-prod_binary64_95` `associate-/r*_binary64_23`
7×	`cancel-sign-sub-inv_binary64_45`
6×	`associate-/r/_binary64_25`
5×	`flip--_binary64_54` `distribute-rgt-neg-in_binary64_37` `flip3--_binary64_83`
4×	`div-inv_binary64_76` `pow1_binary64_140`
3×	`diff-log_binary64_171`
2×	`clear-num_binary64_78` `sub-neg_binary64_72` `frac-2neg_binary64_90`
1×	`associate--l-_binary64_17` `neg-sub0_binary64_74` `neg-log_binary64_172` `associate-/l/_binary64_26`

Counts

4 → 122

Calls

4 calls:

19.0ms	(/.f64 (/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
16.0ms	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
11.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series951.0ms (13.1%)

Counts

4 → 12

Calls

4 calls:

417.0ms	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
331.0ms	(/.f64 (/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
138.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
65.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify88.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4950	4144
1	4950	4144

prune807.0ms (11.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	123	11	134
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	129	11	140

Merged error: 0.0b

Counts

140 → 11

Compiler

Compiled 18319 to 12337 computations (32.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite63.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`add-sqr-sqrt_binary64_101` `*-un-lft-identity_binary64_79`
42×	`times-frac_binary64_85`
29×	`add-cube-cbrt_binary64_114`
27×	`associate-r_binary64_19`
18×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
16×	`distribute-lft-out--_binary64_31` `difference-of-squares_binary64_48`
11×	`sqrt-prod_binary64_95`
10×	`add-log-exp_binary64_118`
9×	`pow1_binary64_140`
8×	`distribute-rgt-neg-in_binary64_37`
7×	`associate-/r*_binary64_23` `cancel-sign-sub-inv_binary64_45`
6×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128`
4×	`flip--_binary64_54` `associate-/r/_binary64_25` `flip3--_binary64_83`
3×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `associate-/l*_binary64_24` `pow-prod-down_binary64_150` `diff-log_binary64_171`
2×	`div-inv_binary64_76` `sub-neg_binary64_72`
1×	`associate-l_binary64_20` `associate--l-_binary64_17` `neg-sub0_binary64_74` `neg-log_binary64_172` `associate-r/_binary64_21` `-commutative_binary64_10` `clear-num_binary64_78` `frac-2neg_binary64_90`

Counts

4 → 127

Calls

4 calls:

20.0ms	(.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
12.0ms	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
11.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))

series941.0ms (13%)

Counts

4 → 12

Calls

4 calls:

401.0ms	(.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
346.0ms	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
129.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
65.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))

simplify79.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4926	3820
1	4926	3820

prune478.0ms (6.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	139	11	150

Merged error: 0.0b

Counts

150 → 11

Compiler

Compiled 9346 to 5890 computations (37% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))) 3))))))
0.3b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
0.5b	(cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))) 3))
0.7b	(pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))) 3)

rewrite66.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-sqr-sqrt_binary64_101`
39×	`associate-r_binary64_19`
37×	`*-un-lft-identity_binary64_79`
33×	`times-frac_binary64_85`
25×	`add-cube-cbrt_binary64_114`
24×	`cbrt-prod_binary64_110`
18×	`difference-of-squares_binary64_48`
17×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
15×	`sqrt-prod_binary64_95`
10×	`pow1_binary64_140`
9×	`unpow-prod-down_binary64_158` `cube-prod_binary64_107`
6×	`distribute-lft-out--_binary64_31` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `add-log-exp_binary64_118`
5×	`sqr-pow_binary64_51`
4×	`cube-div_binary64_108` `flip--_binary64_54` `flip3--_binary64_83`
3×	`pow-unpow_binary64_156` `pow-prod-down_binary64_150` `distribute-rgt-neg-in_binary64_37`
2×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `cbrt-div_binary64_111` `cube-mult_binary64_109` `associate-/r/_binary64_25` `unpow3_binary64_145`
1×	`pow-exp_binary64_147` `associate-l_binary64_20` `pow-to-exp_binary64_148` `pow-pow_binary64_151` `div-inv_binary64_76` `rem-cbrt-cube_binary64_103` `rem-cube-cbrt_binary64_102` `associate-r/_binary64_21` `-commutative_binary64_10` `diff-log_binary64_171` `pow1/3_binary64_161` `cancel-sign-sub-inv_binary64_45` `sub-neg_binary64_72`

Counts

4 → 119

Calls

4 calls:

30.0ms	(.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))) 3))))))
8.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
6.0ms	(pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))) 3)
6.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))) 3))

series725.0ms (10%)

Counts

4 → 12

Calls

4 calls:

416.0ms	(.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))) 3))))))
181.0ms	(pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))) 3)
65.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))) 3))
64.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))

simplify82.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5097	3215

prune189.0ms (2.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	131	11	142

Merged error: 0.0b

Counts

142 → 11

Compiler

Compiled 4300 to 2446 computations (43.1% saved)

regimes92.0ms (1.3%)

Compiler: Compiled 1086 to 789 computations (27.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	85	32
1	85	32

end0.0ms (0%)

sample1.2s (16.8%)

Algorithm

1×

intervals

Results

375.0ms	7689×	body	128	valid
268.0ms	8823×	pre	128	true
37.0ms	823×	body	128	nan
29.0ms	311×	body	256	valid

Compiler

Compiled 411 to 300 computations (27% saved)

Details

analyze259.0ms (3.6%)

sample32.0ms (0.4%)

simplify236.0ms (3.3%)

prune6.0ms (0.1%)

localize11.0ms (0.2%)

rewrite42.0ms (0.6%)

series529.0ms (7.3%)

simplify58.0ms (0.8%)

prune173.0ms (2.4%)

localize15.0ms (0.2%)

rewrite66.0ms (0.9%)

series951.0ms (13.1%)

simplify88.0ms (1.2%)

prune807.0ms (11.1%)

localize14.0ms (0.2%)

rewrite63.0ms (0.9%)

series941.0ms (13%)

simplify79.0ms (1.1%)

prune478.0ms (6.6%)

localize17.0ms (0.2%)

rewrite66.0ms (0.9%)

series725.0ms (10%)

simplify82.0ms (1.1%)

prune189.0ms (2.6%)

regimes92.0ms (1.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.2s (16.8%)

Profiling