Details

analyze41.0ms (1.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
0%	6.2%	93.8%	2
1.6%	3.1%	95.3%	3
1.6%	3.1%	95.3%	4
2.3%	1.6%	96.1%	5
2.3%	1.6%	96.1%	6
2.7%	0.8%	96.5%	7
2.7%	0.8%	96.5%	8
2.9%	0.4%	96.7%	9
2.9%	0.4%	96.7%	10
3%	0.2%	96.8%	11
3%	0.2%	96.8%	12
3.1%	0.1%	96.8%	13
3.1%	0.1%	96.8%	14

Compiler

Compiled 18 to 11 computations (38.9% saved)

sample22.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true
0.0ms	2×	pre	128	false

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify96.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4853	17
1	4853	17

prune6.0ms (0.2%)

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: 15.1b

Counts

2 → 2

Compiler

Compiled 59 to 43 computations (27.1% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 a a) (.f64 b b))
0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
14.6b	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

rewrite19.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

9.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
4.0ms	(-.f64 (.f64 a a) (.f64 b b))
1.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

series188.0ms (6%)

Counts

3 → 9

Calls

3 calls:

78.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
64.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
46.0ms	(-.f64 (.f64 a a) (.f64 b b))

simplify63.0ms (2%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5114	1000

prune88.0ms (2.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	58	3	61
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	60	3	63

Merged error: 0.0b

Counts

63 → 3

Compiler

Compiled 1639 to 699 computations (57.4% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)
0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)))
0.1b	(*.f64 b (/.f64 b a))

rewrite28.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`times-frac_binary64`
13×	`associate-r_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64`
3×	`associate-/r_binary64` `add-log-exp_binary64` `associate-l_binary64` `associate-/l_binary64` `sqrt-prod_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `-commutative_binary64`

Counts

3 → 75

Calls

3 calls:

10.0ms	(*.f64 b (/.f64 b a))
8.0ms	(/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)
2.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)))

series158.0ms (5.1%)

Counts

3 → 9

Calls

3 calls:

71.0ms	(/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)
61.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)))
26.0ms	(*.f64 b (/.f64 b a))

simplify57.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4961	1284
1	4961	1284

prune74.0ms (2.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	83	4	87

Merged error: 0b

Counts

87 → 4

Compiler

Compiled 1567 to 585 computations (62.7% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 a (-.f64 a (*.f64 b (/.f64 b a))))
0.0b	(sqrt.f64 (fabs.f64 (/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))))
0.1b	(/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))
0.1b	(*.f64 b (/.f64 b a))

rewrite46.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`times-frac_binary64`
71×	`add-sqr-sqrt_binary64`
65×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`add-exp-log_binary64`
18×	`associate-/r*_binary64`
16×	`add-cbrt-cube_binary64`
13×	`associate-r_binary64`
11×	`associate-/r/_binary64`
8×	`pow1_binary64`
7×	`div-inv_binary64`
6×	`associate-/l*_binary64` `div-exp_binary64`
5×	`flip3--_binary64` `cbrt-undiv_binary64` `flip--_binary64`
4×	`add-log-exp_binary64`
3×	`associate-l_binary64` `sqrt-prod_binary64`
2×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `inv-pow_binary64` `pow-flip_binary64` `-commutative_binary64`

Counts

4 → 156

Calls

4 calls:

12.0ms	(/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))
9.0ms	(*.f64 b (/.f64 b a))
6.0ms	(/.f64 a (-.f64 a (*.f64 b (/.f64 b a))))
1.0ms	(sqrt.f64 (fabs.f64 (/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))))

series230.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

77.0ms	(/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))
72.0ms	(/.f64 a (-.f64 a (*.f64 b (/.f64 b a))))
56.0ms	(sqrt.f64 (fabs.f64 (/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))))
24.0ms	(*.f64 b (/.f64 b a))

simplify95.0ms (3%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5732	3517

prune141.0ms (4.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	168	4	172

Merged error: 0b

Counts

172 → 4

Compiler

Compiled 3525 to 1205 computations (65.8% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))))
0.0b	(/.f64 (-.f64 a b) a)
0.0b	(/.f64 a (/.f64 (-.f64 a b) a))
0.0b	(/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))

rewrite143.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Rules

890×	`times-frac_binary64`
617×	`*-un-lft-identity_binary64`
492×	`add-sqr-sqrt_binary64`
369×	`add-cube-cbrt_binary64`
84×	`associate-/r*_binary64`
63×	`distribute-lft-out_binary64`
61×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
27×	`div-inv_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-/l*_binary64`
10×	`cbrt-undiv_binary64` `div-exp_binary64`
7×	`associate-/r/_binary64`
5×	`pow1_binary64`
4×	`associate-/l/_binary64` `add-log-exp_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64` `sqrt-prod_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 478

Calls

4 calls:

29.0ms	(/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))
11.0ms	(/.f64 a (/.f64 (-.f64 a b) a))
7.0ms	(/.f64 (-.f64 a b) a)
1.0ms	(sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))))

series272.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

85.0ms	(sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))))
80.0ms	(/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))
54.0ms	(/.f64 (-.f64 a b) a)
53.0ms	(/.f64 a (/.f64 (-.f64 a b) a))

simplify186.0ms (5.9%)

Algorithm

1×	egg-herbie

Counts

490 → 490

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4981	13838
1	4981	13838

prune405.0ms (13%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	490	0	490
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	490	4	494

Merged error: 0b

Counts

494 → 4

Compiler

Compiled 11853 to 2159 computations (81.8% saved)

regimes28.0ms (0.9%)

Compiler: Compiled 154 to 119 computations (22.7% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	17
1	37	17

end0.0ms (0%)

sample699.0ms (22.4%)

Algorithm

1×

intervals

Results

280.0ms	8000×	body	128	valid
165.0ms	8000×	pre	128	true
2.0ms	122×	pre	128	false

Compiler

Compiled 77 to 56 computations (27.3% saved)

Details

analyze41.0ms (1.3%)

sample22.0ms (0.7%)

simplify96.0ms (3.1%)

prune6.0ms (0.2%)

localize8.0ms (0.2%)

rewrite19.0ms (0.6%)

series188.0ms (6%)

simplify63.0ms (2%)

prune88.0ms (2.8%)

localize8.0ms (0.3%)

rewrite28.0ms (0.9%)

series158.0ms (5.1%)

simplify57.0ms (1.8%)

prune74.0ms (2.4%)

localize9.0ms (0.3%)

rewrite46.0ms (1.5%)

series230.0ms (7.4%)

simplify95.0ms (3%)

prune141.0ms (4.5%)

localize9.0ms (0.3%)

rewrite143.0ms (4.6%)

series272.0ms (8.7%)

simplify186.0ms (5.9%)

prune405.0ms (13%)

regimes28.0ms (0.9%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample699.0ms (22.4%)

Profiling