Details

analyze267.0ms (3.7%)

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)

sample45.0ms (0.6%)

Algorithm

1×

intervals

Results

16.0ms	137×	body	256	valid
9.0ms	276×	pre	128	true
6.0ms	44×	body	512	valid
4.0ms	75×	body	128	valid
1.0ms	20×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify298.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (291.0ms)

Iter	Nodes	Cost
0	1706	24
1	1706	24

prune6.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 54.2b

Counts

2 → 2

Compiler

Compiled 82 to 67 computations (18.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
0.3b	(.f64 (.f64 3 a) c)
27.3b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))

rewrite45.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`add-log-exp_binary64`
9×	`pow1_binary64`
7×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`distribute-lft-out_binary64`
5×	`associate-/l*_binary64` `times-frac_binary64`
4×	`cbrt-unprod_binary64` `prod-exp_binary64`
3×	`pow-prod-down_binary64` `associate-r_binary64` `distribute-rgt-neg-in_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `associate-+l-_binary64` `div-exp_binary64` `flip-+_binary64` `sum-log_binary64`
1×	`associate-/r_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-l_binary64` `cancel-sign-sub-inv_binary64` `div-sub_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `+-commutative_binary64` `flip--_binary64` `-commutative_binary64`

Counts

4 → 73

Calls

4 calls:

17.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
10.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
6.0ms	(.f64 (.f64 3 a) c)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series468.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

237.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
132.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
71.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
28.0ms	(.f64 (.f64 3 a) c)

simplify59.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5037	1664

prune141.0ms (2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	84	3	87

Merged error: 0.1b

Counts

87 → 3

Compiler

Compiled 2741 to 1734 computations (36.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 3 a) c)
0.3b	(.f64 (.f64 3 a) c)
0.3b	(/.f64 (.f64 (.f64 3 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
0.4b	(/.f64 (/.f64 (.f64 (.f64 3 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))

rewrite71.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
34×	`times-frac_binary64`
28×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
19×	`cbrt-unprod_binary64` `prod-exp_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
14×	`pow1_binary64` `associate-/l*_binary64`
12×	`add-cube-cbrt_binary64`
8×	`associate-/r*_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
6×	`pow-prod-down_binary64` `associate-r_binary64` `associate-/r/_binary64`
4×	`add-log-exp_binary64` `distribute-rgt-neg-in_binary64` `div-inv_binary64` `sqrt-prod_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`associate-/l/_binary64`

Counts

4 → 123

Calls

4 calls:

21.0ms	(/.f64 (/.f64 (.f64 (.f64 3 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
19.0ms	(/.f64 (.f64 (.f64 3 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
7.0ms	(.f64 (.f64 3 a) c)
6.0ms	(.f64 (.f64 3 a) c)

series790.0ms (11%)

Counts

4 → 12

Calls

4 calls:

396.0ms	(/.f64 (.f64 (.f64 3 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
327.0ms	(/.f64 (/.f64 (.f64 (.f64 3 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
34.0ms	(.f64 (.f64 3 a) c)
34.0ms	(.f64 (.f64 3 a) c)

simplify93.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5015	3312

prune277.0ms (3.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	130	5	135
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	131	7	138

Merged error: 0b

Counts

138 → 7

Compiler

Compiled 5745 to 3603 computations (37.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 3 a))))))
0.2b	(/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 3 a)))))) a)
0.2b	(.f64 a (/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 3 a)))))) a))
0.3b	(.f64 c (.f64 3 a))

rewrite145.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

333×	`times-frac_binary64`
260×	`add-sqr-sqrt_binary64`
251×	`*-un-lft-identity_binary64`
151×	`add-cube-cbrt_binary64`
86×	`associate-r_binary64`
50×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
30×	`associate-/l*_binary64`
25×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-rgt-neg-in_binary64` `sqrt-prod_binary64`
16×	`associate-/r/_binary64`
11×	`pow1_binary64`
10×	`associate-/r*_binary64` `div-inv_binary64`
8×	`flip3--_binary64` `flip--_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64`
3×	`unswap-sqr_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`associate-/l/_binary64` `associate-*r/_binary64`

Counts

4 → 296

Calls

4 calls:

45.0ms	(.f64 a (/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 3 a)))))) a))
20.0ms	(/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 3 a)))))) a)
13.0ms	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 3 a))))))
6.0ms	(.f64 c (.f64 3 a))

series1.2s (17%)

Counts

4 → 12

Calls

4 calls:

489.0ms	(/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 3 a)))))) a)
368.0ms	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 3 a))))))
332.0ms	(.f64 a (/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 3 a)))))) a))
32.0ms	(.f64 c (.f64 3 a))

simplify155.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4935	10824
1	4935	10824

prune572.0ms (8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	304	4	308
Fresh	4	1	5
Picked	0	1	1
Done	0	1	1
Total	308	7	315

Merged error: 0b

Counts

315 → 7

Compiler

Compiled 12174 to 6147 computations (49.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 3 a)))))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 3 a)))
0.1b	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 3 a))))))
0.3b	(.f64 c (.f64 3 a))

rewrite47.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
21×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
9×	`pow1_binary64`
8×	`sqrt-prod_binary64`
7×	`associate-/r*_binary64` `cancel-sign-sub-inv_binary64`
5×	`distribute-rgt-neg-in_binary64`
3×	`pow-prod-down_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64` `associate-/l*_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `associate-/r/_binary64`
1×	`associate--l-_binary64` `associate-r_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`

Counts

4 → 98

Calls

4 calls:

13.0ms	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 3 a))))))
12.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 3 a)))))
6.0ms	(.f64 c (.f64 3 a))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 3 a)))

series608.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

370.0ms	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 3 a))))))
134.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 3 a)))))
71.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 3 a)))
32.0ms	(.f64 c (.f64 3 a))

simplify81.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4970	2689
1	4970	2689

prune196.0ms (2.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	110	7	117

Merged error: 0b

Counts

117 → 7

Compiler

Compiled 4010 to 2456 computations (38.8% saved)

regimes75.0ms (1%)

Compiler: Compiled 680 to 524 computations (22.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	81	23
1	81	23

end0.0ms (0%)

sample1.5s (20.4%)

Algorithm

1×

intervals

Results

391.0ms	3857×	body	256	valid
278.0ms	8825×	pre	128	true
218.0ms	1465×	body	512	valid
137.0ms	2678×	body	128	valid
39.0ms	825×	body	128	nan

Compiler

Compiled 212 to 163 computations (23.1% saved)

Details

analyze267.0ms (3.7%)

sample45.0ms (0.6%)

simplify298.0ms (4.2%)

prune6.0ms (0.1%)

localize11.0ms (0.1%)

rewrite45.0ms (0.6%)

series468.0ms (6.5%)

simplify59.0ms (0.8%)

prune141.0ms (2%)

localize14.0ms (0.2%)

rewrite71.0ms (1%)

series790.0ms (11%)

simplify93.0ms (1.3%)

prune277.0ms (3.9%)

localize13.0ms (0.2%)

rewrite145.0ms (2%)

series1.2s (17%)

simplify155.0ms (2.2%)

prune572.0ms (8%)

localize13.0ms (0.2%)

rewrite47.0ms (0.7%)

series608.0ms (8.5%)

simplify81.0ms (1.1%)

prune196.0ms (2.7%)

regimes75.0ms (1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.5s (20.4%)

Profiling