Details

analyze256.0ms (3.9%)

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)

sample36.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	293×	pre	128	true
8.0ms	172×	body	128	valid
8.0ms	84×	body	256	valid
2.0ms	37×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify234.0ms (3.6%)

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

Merged error: 41.9b

Counts

2 → 1

Compiler

Compiled 65 to 53 computations (18.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.1b	(-.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))
36.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite39.0ms (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)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series545.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

218.0ms	(/.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)))
68.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify68.0ms (1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5031	1979

prune171.0ms (2.6%)

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

Merged error: 0.2b

Counts

87 → 5

Compiler

Compiled 3585 to 2332 computations (35% 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))
0.2b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite52.0ms (0.8%)

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))

series907.0ms (13.9%)

Counts

4 → 12

Calls

4 calls:

395.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
322.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
122.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
68.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify76.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4960	3037
1	4960	3037

prune517.0ms (7.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	104	7	111
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	109	7	116

Merged error: 0b

Counts

116 → 7

Compiler

Compiled 11026 to 7651 computations (30.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite34.0ms (0.5%)

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:

11.0ms	(/.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))))

series676.0ms (10.3%)

Counts

4 → 12

Calls

4 calls:

352.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
132.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
124.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
68.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5087	1969

prune209.0ms (3.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	84	7	91

Merged error: 0b

Counts

91 → 7

Compiler

Compiled 4416 to 3048 computations (31% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))) 3))))) (.f64 a 2))
0.2b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)))))
0.6b	(cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))
0.8b	(pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)

rewrite69.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
24×	`*-un-lft-identity_binary64_79`
22×	`times-frac_binary64_85`
17×	`cbrt-undiv_binary64_113` `div-exp_binary64_130`
16×	`add-cube-cbrt_binary64_114` `add-sqr-sqrt_binary64_101`
13×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128`
12×	`cbrt-prod_binary64_110`
11×	`associate-/l*_binary64_24`
6×	`associate-/r/_binary64_25` `unpow-prod-down_binary64_158` `cube-prod_binary64_107`
5×	`associate-/r*_binary64_23` `pow1_binary64_140`
4×	`cube-div_binary64_108` `div-inv_binary64_76` `add-log-exp_binary64_118` `distribute-lft-out_binary64_30`
3×	`pow-unpow_binary64_156` `flip-+_binary64_53` `flip3-+_binary64_82`
2×	`sqr-pow_binary64_51` `flip--_binary64_54` `cbrt-div_binary64_111` `cube-mult_binary64_109` `clear-num_binary64_78` `flip3--_binary64_83` `frac-2neg_binary64_90` `unpow3_binary64_145`
1×	`pow-exp_binary64_147` `pow-to-exp_binary64_148` `pow-pow_binary64_151` `rem-cbrt-cube_binary64_103` `rem-cube-cbrt_binary64_102` `pow1/3_binary64_161` `associate-/l/_binary64_26`

Counts

4 → 123

Calls

4 calls:

21.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))) 3))))) (.f64 a 2))
20.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)))))
6.0ms	(pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)
6.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))

series931.0ms (14.2%)

Counts

4 → 12

Calls

4 calls:

383.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)))))
305.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))) 3))))) (.f64 a 2))
177.0ms	(pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)
66.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))

simplify91.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4934	3631
1	4934	3631

prune176.0ms (2.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	135	7	142

Merged error: 0b

Counts

142 → 7

Compiler

Compiled 3971 to 2475 computations (37.7% saved)

regimes57.0ms (0.9%)

Compiler: Compiled 582 to 453 computations (22.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	24
1	63	24

end0.0ms (0%)

sample1.3s (19.3%)

Algorithm

1×

intervals

Results

279.0ms	2923×	body	256	valid
265.0ms	8920×	pre	128	true
251.0ms	5076×	body	128	valid
41.0ms	920×	body	128	nan
0.0ms	1×	body	512	valid

Compiler

Compiled 238 to 185 computations (22.3% saved)

Details

analyze256.0ms (3.9%)

sample36.0ms (0.6%)

simplify234.0ms (3.6%)

prune6.0ms (0.1%)

localize10.0ms (0.2%)

rewrite39.0ms (0.6%)

series545.0ms (8.3%)

simplify68.0ms (1%)

prune171.0ms (2.6%)

localize16.0ms (0.2%)

rewrite52.0ms (0.8%)

series907.0ms (13.9%)

simplify76.0ms (1.2%)

prune517.0ms (7.9%)

localize12.0ms (0.2%)

rewrite34.0ms (0.5%)

series676.0ms (10.3%)

simplify70.0ms (1.1%)

prune209.0ms (3.2%)

localize17.0ms (0.3%)

rewrite69.0ms (1.1%)

series931.0ms (14.2%)

simplify91.0ms (1.4%)

prune176.0ms (2.7%)

regimes57.0ms (0.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.3s (19.3%)

Profiling