Details

analyze257.0ms (7.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.5%	87.5%	0
0%	12.5%	87.5%	1
0%	12.5%	87.5%	2
3.1%	9.3%	87.5%	3
3.1%	6.2%	90.7%	4
4.7%	4.7%	90.7%	5
4.7%	3.5%	91.8%	6
5.6%	2.5%	91.8%	7
5.9%	1.8%	92.3%	8
6.4%	1.3%	92.3%	9
6.6%	0.9%	92.5%	10
6.8%	0.6%	92.5%	11
6.9%	0.5%	92.6%	12
7%	0.3%	92.6%	13
7.1%	0.2%	92.7%	14

Compiler

Compiled 23 to 18 computations (21.7% saved)

sample24.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
6.0ms	259×	pre	128	true
0.0ms	3×	body	128	invalid

Compiler

Compiled 36 to 31 computations (13.9% saved)

simplify260.0ms (7.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5013	19

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.1b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 m (-.f64 1 m))
0.0b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
0.1b	(/.f64 (*.f64 m (-.f64 1 m)) v)

rewrite50.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
12×	`associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-l_binary64`
9×	`add-cube-cbrt_binary64`
8×	`flip3--_binary64` `flip--_binary64`
7×	`pow1_binary64`
6×	`associate-*r/_binary64` `difference-of-squares_binary64`
4×	`sub-neg_binary64` `frac-times_binary64`
3×	`associate-/r*_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `times-frac_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `div-exp_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`difference-of-sqr-1_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

3 → 83

Calls

3 calls:

18.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
10.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
8.0ms	(*.f64 m (-.f64 1 m))

series171.0ms (5.2%)

Counts

3 → 9

Calls

3 calls:

65.0ms	(*.f64 m (-.f64 1 m))
60.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
46.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))

simplify58.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4959	1544
1	4959	1544

prune102.0ms (3.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	89	4	93

Merged error: 0b

Counts

93 → 4

Compiler

Compiled 1847 to 1278 computations (30.8% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 m (*.f64 m (neg.f64 m)))
0.0b	(.f64 (-.f64 (/.f64 (+.f64 m (.f64 m (neg.f64 m))) v) 1) (-.f64 1 m))
0.1b	(/.f64 (+.f64 m (*.f64 m (neg.f64 m))) v)

rewrite35.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
10×	`associate-l_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`flip3--_binary64` `associate-r_binary64` `difference-of-squares_binary64` `flip--_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
4×	`frac-times_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `sub-neg_binary64` `distribute-rgt-neg-out_binary64` `associate-r/_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64` `flip-+_binary64` `unsub-neg_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

3 → 80

Calls

3 calls:

19.0ms	(.f64 (-.f64 (/.f64 (+.f64 m (.f64 m (neg.f64 m))) v) 1) (-.f64 1 m))
6.0ms	(/.f64 (+.f64 m (*.f64 m (neg.f64 m))) v)
3.0ms	(+.f64 m (*.f64 m (neg.f64 m)))

series166.0ms (5%)

Counts

3 → 9

Calls

3 calls:

72.0ms	(+.f64 m (*.f64 m (neg.f64 m)))
47.0ms	(/.f64 (+.f64 m (*.f64 m (neg.f64 m))) v)
46.0ms	(.f64 (-.f64 (/.f64 (+.f64 m (.f64 m (neg.f64 m))) v) 1) (-.f64 1 m))

simplify60.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5526	1755

prune88.0ms (2.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	89	4	93

Merged error: 0b

Counts

93 → 4

Compiler

Compiled 1943 to 1077 computations (44.6% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 m (+.f64 m -1))
0.0b	(+.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 m (/.f64 (.f64 m (+.f64 m -1)) (/.f64 v m))))
0.1b	(/.f64 (*.f64 m (-.f64 1 m)) v)
0.2b	(/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m))

rewrite61.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64`
34×	`times-frac_binary64`
25×	`add-sqr-sqrt_binary64`
23×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64` `add-log-exp_binary64`
8×	`cbrt-undiv_binary64` `div-exp_binary64`
7×	`distribute-lft-out_binary64`
6×	`pow1_binary64` `associate-*r/_binary64` `sum-log_binary64`
5×	`flip3-+_binary64` `associate-r_binary64` `flip-+_binary64`
4×	`associate-/l/_binary64` `cbrt-unprod_binary64` `frac-add_binary64` `prod-exp_binary64` `div-inv_binary64`
3×	`flip3--_binary64` `associate-l_binary64` `flip--_binary64`
2×	`diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `associate-+l+_binary64` `distribute-lft-in_binary64` `associate-/r/_binary64` `associate-+l-_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `difference-of-sqr--1_binary64` `+-commutative_binary64` `associate-+r+_binary64` `*-commutative_binary64`

Counts

4 → 120

Calls

4 calls:

23.0ms	(+.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 m (/.f64 (.f64 m (+.f64 m -1)) (/.f64 v m))))
10.0ms	(/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m))
8.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
7.0ms	(*.f64 m (+.f64 m -1))

series218.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

57.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
57.0ms	(*.f64 m (+.f64 m -1))
53.0ms	(/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m))
50.0ms	(+.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 m (/.f64 (.f64 m (+.f64 m -1)) (/.f64 v m))))

simplify73.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4958	2717
1	4958	2717

prune155.0ms (4.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	132	4	136

Merged error: 0b

Counts

136 → 4

Compiler

Compiled 3665 to 2062 computations (43.7% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) (-.f64 1 m))
0.2b	(/.f64 m (sqrt.f64 v))
0.3b	(/.f64 (-.f64 1 m) (sqrt.f64 v))
0.4b	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))

rewrite93.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`add-sqr-sqrt_binary64`
120×	`times-frac_binary64`
116×	`*-un-lft-identity_binary64`
74×	`add-cube-cbrt_binary64`
66×	`sqrt-prod_binary64`
46×	`associate-r_binary64`
28×	`difference-of-squares_binary64`
25×	`associate-l_binary64`
22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`distribute-lft-out--_binary64`
12×	`associate-/r*_binary64`
10×	`unswap-sqr_binary64`
9×	`associate-/l*_binary64`
8×	`pow1_binary64`
7×	`flip3--_binary64` `flip--_binary64`
6×	`cbrt-undiv_binary64` `div-exp_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64` `frac-times_binary64`
4×	`add-log-exp_binary64` `div-inv_binary64`
3×	`associate-r/_binary64` `associate-l/_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `sub-neg_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-sub_binary64`

Counts

4 → 224

Calls

4 calls:

34.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))
21.0ms	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) (-.f64 1 m))
8.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))
4.0ms	(/.f64 m (sqrt.f64 v))

series277.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

86.0ms	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) (-.f64 1 m))
74.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))
73.0ms	(/.f64 m (sqrt.f64 v))
44.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))

simplify105.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4950	4541
1	4950	4541

prune260.0ms (7.9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	236	0	236
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	236	4	240

Merged error: 0b

Counts

240 → 4

Compiler

Compiled 5733 to 2819 computations (50.8% saved)

regimes38.0ms (1.2%)

Compiler: Compiled 225 to 180 computations (20% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	19
1	31	19

end0.0ms (0%)

sample696.0ms (21.1%)

Algorithm

1×

intervals

Results

273.0ms	8000×	body	128	valid
162.0ms	8067×	pre	128	true
2.0ms	67×	body	128	invalid

Compiler

Compiled 101 to 81 computations (19.8% saved)

Details

analyze257.0ms (7.8%)

sample24.0ms (0.7%)

simplify260.0ms (7.9%)

prune4.0ms (0.1%)

localize8.0ms (0.3%)

rewrite50.0ms (1.5%)

series171.0ms (5.2%)

simplify58.0ms (1.7%)

prune102.0ms (3.1%)

localize11.0ms (0.3%)

rewrite35.0ms (1.1%)

series166.0ms (5%)

simplify60.0ms (1.8%)

prune88.0ms (2.7%)

localize15.0ms (0.5%)

rewrite61.0ms (1.8%)

series218.0ms (6.6%)

simplify73.0ms (2.2%)

prune155.0ms (4.7%)

localize9.0ms (0.3%)

rewrite93.0ms (2.8%)

series277.0ms (8.4%)

simplify105.0ms (3.2%)

prune260.0ms (7.9%)

regimes38.0ms (1.2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample696.0ms (21.1%)

Profiling