Details

analyze285.0ms (4.1%)

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)

sample35.0ms (0.5%)

Algorithm

1×

intervals

Results

13.0ms	244×	body	128	valid
9.0ms	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)

simplify231.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

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	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 28.9b

Counts

2 → 1

Compiler

Compiled 65 to 53 computations (18.5% 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 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.3b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
28.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_101`
14×	`*-un-lft-identity_binary64_79`
9×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
8×	`add-cube-cbrt_binary64_114` `add-log-exp_binary64_118`
6×	`sqrt-prod_binary64_95` `times-frac_binary64_85` `associate-/l*_binary64_24` `difference-of-squares_binary64_48`
5×	`pow1_binary64_140`
4×	`flip--_binary64_54` `flip3--_binary64_83` `cancel-sign-sub-inv_binary64_45`
3×	`distribute-lft-out--_binary64_31`
2×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `sqrt-div_binary64_96` `diff-log_binary64_171` `associate-/l/_binary64_26` `sub-neg_binary64_72`
1×	`associate-/r*_binary64_23` `div-sub_binary64_84` `div-inv_binary64_76` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `clear-num_binary64_78` `pow1/2_binary64_159` `frac-2neg_binary64_90`

Counts

4 → 74

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series542.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

221.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
141.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
62.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify71.0ms (1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5031	1979

prune216.0ms (3.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	79	7	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	7	87

Merged error: 0.4b

Counts

87 → 7

Compiler

Compiled 4085 to 2779 computations (32% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

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))
0.2b	(+.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 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite52.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
22×	`times-frac_binary64_85`
20×	`*-un-lft-identity_binary64_79`
17×	`cbrt-undiv_binary64_113` `div-exp_binary64_130`
13×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128`
11×	`associate-/l*_binary64_24`
10×	`add-cube-cbrt_binary64_114` `add-sqr-sqrt_binary64_101`
8×	`add-log-exp_binary64_118`
6×	`associate-/r/_binary64_25`
5×	`associate-/r*_binary64_23` `distribute-lft-out_binary64_30`
4×	`flip-+_binary64_53` `div-inv_binary64_76` `flip3-+_binary64_82` `pow1_binary64_140`
2×	`clear-num_binary64_78` `frac-2neg_binary64_90`
1×	`sum-log_binary64_170` `+-commutative_binary64_9` `flip--_binary64_54` `diff-log_binary64_171` `flip3--_binary64_83` `cancel-sign-sub-inv_binary64_45` `associate-/l/_binary64_26` `sub-neg_binary64_72`

Counts

4 → 99

Calls

4 calls:

16.0ms	(/.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)))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series939.0ms (13.4%)

Counts

4 → 12

Calls

4 calls:

399.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
329.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
142.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
69.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify76.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4960	3037
1	4960	3037

prune780.0ms (11.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	100	11	111
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	107	11	118

Merged error: 0.0b

Counts

118 → 11

Compiler

Compiled 16414 to 11366 computations (30.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_79`
15×	`add-sqr-sqrt_binary64_101`
14×	`add-cube-cbrt_binary64_114`
12×	`times-frac_binary64_85`
8×	`add-log-exp_binary64_118`
6×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
5×	`distribute-lft-out_binary64_30` `pow1_binary64_140`
4×	`associate-/r*_binary64_23`
3×	`sqrt-prod_binary64_95` `associate-/l*_binary64_24`
2×	`flip-+_binary64_53` `flip--_binary64_54` `associate-/r/_binary64_25` `sqrt-div_binary64_96` `flip3--_binary64_83` `flip3-+_binary64_82`
1×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `div-inv_binary64_76` `sum-log_binary64_170` `+-commutative_binary64_9` `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 → 72

Calls

4 calls:

9.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

series653.0ms (9.3%)

Counts

4 → 12

Calls

4 calls:

342.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
120.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
72.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify73.0ms (1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5087	1969

prune324.0ms (4.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	86	9	95

Merged error: 0.0b

Counts

95 → 9

Compiler

Compiled 6611 to 4588 computations (30.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.2b	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
0.3b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

rewrite45.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64_79`
24×	`times-frac_binary64_85`
21×	`add-cube-cbrt_binary64_114` `add-sqr-sqrt_binary64_101`
18×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `associate-r_binary64_19`
9×	`pow1_binary64_140`
8×	`add-log-exp_binary64_118` `distribute-lft-out_binary64_30`
6×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128`
4×	`associate-/r*_binary64_23` `associate-/r/_binary64_25`
3×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `flip-+_binary64_53` `associate-/l*_binary64_24` `pow-prod-down_binary64_150` `flip3-+_binary64_82`
2×	`div-inv_binary64_76`
1×	`associate-l_binary64_20` `sum-log_binary64_170` `+-commutative_binary64_9` `flip--_binary64_54` `associate-r/_binary64_21` `-commutative_binary64_10` `diff-log_binary64_171` `clear-num_binary64_78` `flip3--_binary64_83` `cancel-sign-sub-inv_binary64_45` `sub-neg_binary64_72` `frac-2neg_binary64_90`

Counts

4 → 95

Calls

4 calls:

15.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
9.0ms	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series831.0ms (11.8%)

Counts

4 → 12

Calls

4 calls:

380.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
233.0ms	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
136.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
82.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify65.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4921	2612
1	4921	2612

prune290.0ms (4.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	0	7	7
Picked	1	0	1
Done	1	0	1
Total	107	9	116

Merged error: 0b

Counts

116 → 9

Compiler

Compiled 5937 to 4052 computations (31.8% saved)

regimes80.0ms (1.1%)

Compiler: Compiled 909 to 666 computations (26.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	24
1	60	24

end0.0ms (0%)

sample1.3s (18.6%)

Algorithm

1×

intervals

Results

425.0ms	7689×	body	128	valid
301.0ms	8823×	pre	128	true
42.0ms	823×	body	128	nan
32.0ms	311×	body	256	valid

Compiler

Compiled 347 to 256 computations (26.2% saved)

Details

analyze285.0ms (4.1%)

sample35.0ms (0.5%)

simplify231.0ms (3.3%)

prune6.0ms (0.1%)

localize11.0ms (0.2%)

rewrite41.0ms (0.6%)

series542.0ms (7.7%)

simplify71.0ms (1%)

prune216.0ms (3.1%)

localize16.0ms (0.2%)

rewrite52.0ms (0.7%)

series939.0ms (13.4%)

simplify76.0ms (1.1%)

prune780.0ms (11.1%)

localize13.0ms (0.2%)

rewrite31.0ms (0.4%)

series653.0ms (9.3%)

simplify73.0ms (1%)

prune324.0ms (4.6%)

localize12.0ms (0.2%)

rewrite45.0ms (0.6%)

series831.0ms (11.8%)

simplify65.0ms (0.9%)

prune290.0ms (4.1%)

regimes80.0ms (1.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.3s (18.6%)

Profiling