Details

analyze363.0ms (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)

sample36.0ms (0.4%)

Algorithm

1×

intervals

Results

13.0ms	240×	body	128	valid
9.0ms	282×	pre	128	true
2.0ms	16×	body	256	valid
1.0ms	26×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify283.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (88.0ms)

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: 30.7b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(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))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
30.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite49.0ms (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:

15.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
13.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series716.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

302.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
159.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
149.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
106.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify82.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5031	1979

prune151.0ms (1.6%)

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: 0.4b

Counts

87 → 5

Compiler

Compiled 2086 to 1241 computations (40.5% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite78.0ms (0.9%)

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:

22.0ms	(/.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))
8.0ms	(+.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 (12.9%)

Counts

4 → 12

Calls

4 calls:

549.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
416.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
148.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify109.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4960	3037
1	4960	3037

prune200.0ms (2.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	101	10	111
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	106	10	116

Merged error: 0.0b

Counts

116 → 10

Compiler

Compiled 3362 to 2083 computations (38% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite44.0ms (0.5%)

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 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
9.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series741.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

407.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
129.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
124.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
81.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify110.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5087	1969

prune153.0ms (1.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	81	3	84
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	87	7	94

Merged error: 0b

Counts

94 → 7

Compiler

Compiled 2363 to 1475 computations (37.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite63.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64_84`
96×	`*-un-lft-identity_binary64_78`
62×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113`
19×	`associate-/r*_binary64_22`
17×	`add-exp-log_binary64_116` `distribute-lft-out_binary64_29`
11×	`add-cbrt-cube_binary64_114`
8×	`add-log-exp_binary64_117` `div-exp_binary64_129`
7×	`associate-/l*_binary64_23`
6×	`div-inv_binary64_75`
5×	`pow1_binary64_139`
4×	`cbrt-undiv_binary64_112`
2×	`flip-+_binary64_52` `frac-2neg_binary64_89` `1-exp_binary64_122` `rec-exp_binary64_128` `clear-num_binary64_77` `associate-/l/_binary64_25` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `inv-pow_binary64_163` `flip3--_binary64_82` `diff-log_binary64_170` `pow-flip_binary64_152` `flip--_binary64_53` `associate-/r/_binary64_24` `cancel-sign-sub-inv_binary64_44` `sub-neg_binary64_71` `sum-log_binary64_169`

Counts

4 → 145

Calls

4 calls:

12.0ms	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c))
9.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c)
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)))

series739.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

296.0ms	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c))
204.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c)
174.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
66.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify116.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4978	4909
1	4978	4909

prune293.0ms (3.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	157	7	164

Merged error: 0b

Counts

164 → 7

Compiler

Compiled 4701 to 2935 computations (37.6% saved)

regimes575.0ms (6.3%)

Compiler: Compiled 6264 to 4714 computations (24.7% 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%)

sample3.0s (33%)

Algorithm

1×

intervals

Results

556.0ms	7668×	body	128	valid
371.0ms	8806×	pre	128	true
55.0ms	806×	body	128	nan
51.0ms	332×	body	256	valid

Compiler

Compiled 1602 to 1207 computations (24.7% saved)

Details

analyze363.0ms (4%)

sample36.0ms (0.4%)

simplify283.0ms (3.1%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite49.0ms (0.5%)

series716.0ms (7.8%)

simplify82.0ms (0.9%)

prune151.0ms (1.6%)

localize16.0ms (0.2%)

rewrite78.0ms (0.9%)

series1.2s (12.9%)

simplify109.0ms (1.2%)

prune200.0ms (2.2%)

localize13.0ms (0.1%)

rewrite44.0ms (0.5%)

series741.0ms (8.1%)

simplify110.0ms (1.2%)

prune153.0ms (1.7%)

localize13.0ms (0.1%)

rewrite63.0ms (0.7%)

series739.0ms (8.1%)

simplify116.0ms (1.3%)

prune293.0ms (3.2%)

regimes575.0ms (6.3%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample3.0s (33%)

Profiling