Details

analyze450.0ms (4.9%)

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)

sample67.0ms (0.7%)

Algorithm

1×

intervals

Results

23.0ms	143×	body	256	valid
14.0ms	291×	pre	128	true
8.0ms	36×	body	512	valid
6.0ms	77×	body	128	valid
3.0ms	35×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify292.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune4.0ms (0%)

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: 53.8b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
26.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite43.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_100`
14×	`*-un-lft-identity_binary64_78`
9×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
8×	`add-log-exp_binary64_117` `add-cube-cbrt_binary64_113`
6×	`sqrt-prod_binary64_94` `times-frac_binary64_84` `associate-/l*_binary64_23` `difference-of-squares_binary64_47`
5×	`pow1_binary64_139`
4×	`flip3--_binary64_82` `flip--_binary64_53` `cancel-sign-sub-inv_binary64_44`
3×	`distribute-lft-out--_binary64_30`
2×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `diff-log_binary64_170` `sqrt-div_binary64_95` `associate-/l/_binary64_25` `sub-neg_binary64_71`
1×	`sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `rem-sqrt-square_binary64_91` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/r*_binary64_22` `clear-num_binary64_77` `div-sub_binary64_83` `pow1/2_binary64_158`

Counts

4 → 74

Calls

4 calls:

14.0ms	(/.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)))

series719.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

319.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
182.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
146.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
73.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify95.0ms (1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5031	1979

prune124.0ms (1.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	2	87

Merged error: 0.1b

Counts

87 → 2

Compiler

Compiled 2001 to 1179 computations (41.1% saved)

localize30.0ms (0.3%)

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)))))

rewrite76.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
22×	`times-frac_binary64_84`
20×	`*-un-lft-identity_binary64_78`
17×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
13×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
11×	`associate-/l*_binary64_23`
10×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113`
8×	`add-log-exp_binary64_117`
6×	`associate-/r/_binary64_24`
5×	`associate-/r*_binary64_22` `distribute-lft-out_binary64_29`
4×	`flip-+_binary64_52` `div-inv_binary64_75` `pow1_binary64_139` `flip3-+_binary64_81`
2×	`frac-2neg_binary64_89` `clear-num_binary64_77`
1×	`+-commutative_binary64_8` `flip3--_binary64_82` `diff-log_binary64_170` `flip--_binary64_53` `cancel-sign-sub-inv_binary64_44` `associate-/l/_binary64_25` `sub-neg_binary64_71` `sum-log_binary64_169`

Counts

4 → 99

Calls

4 calls:

18.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
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))
14.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series1.2s (13.4%)

Counts

4 → 12

Calls

4 calls:

505.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
469.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
200.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
69.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify148.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4960	3037
1	4960	3037

prune199.0ms (2.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	103	8	111
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	105	8	113

Merged error: 0b

Counts

113 → 8

Compiler

Compiled 3285 to 2025 computations (38.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(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 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_78`
15×	`add-sqr-sqrt_binary64_100`
14×	`add-cube-cbrt_binary64_113`
12×	`times-frac_binary64_84`
8×	`add-log-exp_binary64_117`
6×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
5×	`distribute-lft-out_binary64_29` `pow1_binary64_139`
4×	`associate-/r*_binary64_22`
3×	`sqrt-prod_binary64_94` `associate-/l*_binary64_23`
2×	`flip-+_binary64_52` `flip3--_binary64_82` `flip--_binary64_53` `sqrt-div_binary64_95` `associate-/r/_binary64_24` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `diff-log_binary64_170` `frac-2neg_binary64_89` `div-inv_binary64_75` `clear-num_binary64_77` `cancel-sign-sub-inv_binary64_44` `pow1/2_binary64_158` `sub-neg_binary64_71` `sum-log_binary64_169`

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))))

series674.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

356.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
127.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
120.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
71.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify89.0ms (1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5087	1969

prune158.0ms (1.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	81	3	84
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	86	6	92

Merged error: 0b

Counts

92 → 6

Compiler

Compiled 2312 to 1439 computations (37.8% saved)

localize14.0ms (0.2%)

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

rewrite56.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
16×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
14×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
11×	`*-un-lft-identity_binary64_78`
10×	`associate-r_binary64_18`
9×	`add-sqr-sqrt_binary64_100`
8×	`add-log-exp_binary64_117`
7×	`add-cube-cbrt_binary64_113`
6×	`pow1_binary64_139`
5×	`times-frac_binary64_84`
3×	`associate-l_binary64_19`
2×	`flip-+_binary64_52` `div-inv_binary64_75` `associate-/r/_binary64_24` `associate-*r/_binary64_20` `distribute-lft-out_binary64_29` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `-commutative_binary64_9` `flip3--_binary64_82` `diff-log_binary64_170` `frac-2neg_binary64_89` `flip--_binary64_53` `associate-/l_binary64_23` `associate-/r*_binary64_22` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `clear-num_binary64_77` `cancel-sign-sub-inv_binary64_44` `associate-/l/_binary64_25` `sub-neg_binary64_71` `sum-log_binary64_169`

Counts

4 → 84

Calls

4 calls:

20.0ms	(/.f64 (.f64 a (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))) (.f64 a 2))
14.0ms	(.f64 a (/.f64 (.f64 c -4) (+.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)))

series1.4s (14.8%)

Counts

4 → 12

Calls

4 calls:

515.0ms	(.f64 a (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
479.0ms	(/.f64 (.f64 a (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))) (.f64 a 2))
238.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
138.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify122.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4989	2293
1	4989	2293

prune177.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	96	6	102

Merged error: 0b

Counts

102 → 6

Compiler

Compiled 2463 to 1499 computations (39.1% saved)

regimes421.0ms (4.6%)

Compiler: Compiled 4008 to 3014 computations (24.8% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	63	24
1	63	24

end0.0ms (0%)

sample2.6s (28.2%)

Algorithm

1×

intervals

Results

473.0ms	3857×	body	256	valid
336.0ms	8874×	pre	128	true
268.0ms	1462×	body	512	valid
167.0ms	2681×	body	128	valid
51.0ms	874×	body	128	nan

Compiler

Compiled 1038 to 782 computations (24.7% saved)

Details

analyze450.0ms (4.9%)

sample67.0ms (0.7%)

simplify292.0ms (3.2%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite43.0ms (0.5%)

series719.0ms (7.8%)

simplify95.0ms (1%)

prune124.0ms (1.3%)

localize30.0ms (0.3%)

rewrite76.0ms (0.8%)

series1.2s (13.4%)

simplify148.0ms (1.6%)

prune199.0ms (2.2%)

localize12.0ms (0.1%)

rewrite32.0ms (0.3%)

series674.0ms (7.3%)

simplify89.0ms (1%)

prune158.0ms (1.7%)

localize14.0ms (0.2%)

rewrite56.0ms (0.6%)

series1.4s (14.8%)

simplify122.0ms (1.3%)

prune177.0ms (1.9%)

regimes421.0ms (4.6%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.6s (28.2%)

Profiling