Details

analyze267.0ms (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)

sample50.0ms (0.7%)

Algorithm

1×

intervals

Results

16.0ms	112×	body	320	valid
9.0ms	93×	body	160	valid
9.0ms	284×	pre	80	true
3.0ms	18×	body	640	valid
2.0ms	33×	body	80	valid
1.0ms	28×	body	80	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify112.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	928	24
1	928	24

prune4.0ms (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: 52.3b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

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))
25.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `insert-posit16` `flip--_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

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))
10.0ms	(-.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)))

series529.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

214.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
133.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
116.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify131.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	6773	2041

prune102.0ms (1.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	3	87

Merged error: 0.1b

Counts

87 → 3

Compiler

Compiled 2017 to 1197 computations (40.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite53.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`associate-/l*_binary64`
10×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
6×	`associate-/r/_binary64`
5×	`associate-/r*_binary64` `distribute-lft-out_binary64`
4×	`flip3-+_binary64` `pow1_binary64` `div-inv_binary64` `insert-posit16` `flip-+_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 102

Calls

4 calls:

18.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
15.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
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))

series894.0ms (13.1%)

Counts

4 → 12

Calls

4 calls:

374.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
314.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
130.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
76.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify120.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4929	3120
1	4929	3120

prune156.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	109	5	114
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	111	6	117

Merged error: 0b

Counts

117 → 6

Compiler

Compiled 3232 to 1986 computations (38.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.3b	(/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
0.3b	(/.f64 1 (/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))

rewrite71.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

319×	`times-frac_binary64`
161×	`*-un-lft-identity_binary64`
127×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
47×	`add-exp-log_binary64`
45×	`associate-/r*_binary64`
38×	`associate-/r/_binary64`
28×	`div-exp_binary64`
27×	`add-cbrt-cube_binary64`
22×	`div-inv_binary64`
17×	`flip3-+_binary64` `distribute-lft-out_binary64` `flip-+_binary64`
14×	`cbrt-undiv_binary64`
8×	`add-log-exp_binary64`
6×	`associate-/l*_binary64`
5×	`pow1_binary64`
4×	`1-exp_binary64` `prod-exp_binary64` `rec-exp_binary64` `insert-posit16`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `inv-pow_binary64` `+-commutative_binary64` `flip--_binary64` `pow-flip_binary64` `sum-log_binary64`

Counts

4 → 259

Calls

4 calls:

24.0ms	(/.f64 1 (/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
15.0ms	(/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
8.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
6.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series801.0ms (11.8%)

Counts

4 → 12

Calls

4 calls:

375.0ms	(/.f64 1 (/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
215.0ms	(/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
131.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
79.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify154.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

271 → 271

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5316	10553

prune488.0ms (7.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	270	1	271
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	271	6	277

Merged error: 0b

Counts

277 → 6

Compiler

Compiled 8757 to 5786 computations (33.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite46.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `distribute-lft-out_binary64`
6×	`pow1_binary64`
4×	`associate-/r*_binary64` `associate-/r/_binary64` `insert-posit16`
3×	`flip3-+_binary64` `associate-l_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 97

Calls

4 calls:

15.0ms	(.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
13.0ms	(/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
8.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series782.0ms (11.5%)

Counts

4 → 12

Calls

4 calls:

369.0ms	(.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
209.0ms	(/.f64 -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)))))
68.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify102.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4918	2676
1	4918	2676

prune129.0ms (1.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	109	6	115

Merged error: 0b

Counts

115 → 6

Compiler

Compiled 2655 to 1607 computations (39.5% saved)

regimes54.0ms (0.8%)

Compiler: Compiled 492 to 378 computations (23.2% saved)

bsearch0.0ms (0%)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	65	30
1	65	30

end0.0ms (0%)

sample1.7s (24.6%)

Algorithm

1×

intervals

Results

526.0ms	3676×	body	320	valid
278.0ms	2879×	body	160	valid
271.0ms	8848×	pre	80	true
96.0ms	497×	body	640	valid
48.0ms	948×	body	80	valid
43.0ms	848×	body	80	nan

Compiler

Compiled 212 to 164 computations (22.6% saved)

Details

analyze267.0ms (3.9%)

sample50.0ms (0.7%)

simplify112.0ms (1.6%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite38.0ms (0.6%)

series529.0ms (7.8%)

simplify131.0ms (1.9%)

prune102.0ms (1.5%)

localize14.0ms (0.2%)

rewrite53.0ms (0.8%)

series894.0ms (13.1%)

simplify120.0ms (1.8%)

prune156.0ms (2.3%)

localize14.0ms (0.2%)

rewrite71.0ms (1%)

series801.0ms (11.8%)

simplify154.0ms (2.3%)

prune488.0ms (7.2%)

localize11.0ms (0.2%)

rewrite46.0ms (0.7%)

series782.0ms (11.5%)

simplify102.0ms (1.5%)

prune129.0ms (1.9%)

regimes54.0ms (0.8%)

bsearch0.0ms (0%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample1.7s (24.6%)

Profiling