Details

analyze254.0ms (5%)

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 21 to 16 computations (23.8% saved)

sample24.0ms (0.5%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
6.0ms	261×	pre	128	true
0.0ms	5×	body	128	invalid

Compiler

Compiled 32 to 27 computations (15.6% saved)

simplify337.0ms (6.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (152.0ms)

Iter	Nodes	Cost
0	4809	16
1	4809	16

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 22 to 18 computations (18.2% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 47

Calls

2 calls:

17.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
9.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

series122.0ms (2.4%)

Counts

2 → 6

Calls

2 calls:

70.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
52.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

simplify81.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4955	817
1	4955	817

prune67.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	46	7	53
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	8	54

Merged error: 0.0b

Counts

54 → 8

Compiler

Compiled 1031 to 696 computations (32.5% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite46.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
48×	`*-un-lft-identity_binary64`
37×	`times-frac_binary64`
27×	`add-cube-cbrt_binary64`
25×	`associate-r_binary64`
14×	`difference-of-squares_binary64`
12×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64` `distribute-lft-out--_binary64`
6×	`associate-l_binary64` `associate-/l*_binary64`
3×	`associate-/r*_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`associate-*r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

3 → 103

Calls

3 calls:

15.0ms	(*.f64 m (/.f64 (-.f64 1 m) v))
13.0ms	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) m)
7.0ms	(/.f64 (-.f64 1 m) v)

series146.0ms (2.8%)

Counts

3 → 9

Calls

3 calls:

50.0ms	(*.f64 m (/.f64 (-.f64 1 m) v))
48.0ms	(/.f64 (-.f64 1 m) v)
47.0ms	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) m)

simplify76.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5854	1591

prune105.0ms (2.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	112	8	120

Merged error: 0.0b

Counts

120 → 8

Compiler

Compiled 2075 to 1322 computations (36.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
0.3b	(/.f64 (-.f64 1 m) (sqrt.f64 v))
0.3b	(/.f64 m (sqrt.f64 v))
0.4b	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))

rewrite93.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 213

Calls

4 calls:

33.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))
19.0ms	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
9.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))
5.0ms	(/.f64 m (sqrt.f64 v))

series290.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

92.0ms	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
75.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))
75.0ms	(/.f64 m (sqrt.f64 v))
47.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))

simplify99.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4952	4078
1	4952	4078

prune239.0ms (4.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	223	2	225
Fresh	2	3	5
Picked	1	0	1
Done	1	1	2
Total	227	6	233

Merged error: 0b

Counts

233 → 6

Compiler

Compiled 5071 to 2489 computations (50.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite359.0ms (7%)

Algorithm

1×	rewrite-expression-head

Rules

1132×	`times-frac_binary64`
842×	`sqrt-prod_binary64`
741×	`add-sqr-sqrt_binary64`
599×	`*-un-lft-identity_binary64`
560×	`add-cube-cbrt_binary64`
245×	`associate-l_binary64`
52×	`associate-/r*_binary64`
40×	`associate-r_binary64`
34×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
33×	`unswap-sqr_binary64`
26×	`difference-of-squares_binary64`
18×	`associate-/l*_binary64` `div-inv_binary64`
14×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`distribute-lft-out--_binary64`
6×	`pow1_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64`
3×	`sqrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `associate-r/_binary64` `div-sub_binary64` `flip--_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 768

Calls

4 calls:

176.0ms	(*.f64 (/.f64 (sqrt.f64 m) (/.f64 (sqrt.f64 v) (sqrt.f64 m))) (/.f64 (-.f64 1 m) (sqrt.f64 v)))
17.0ms	(/.f64 (sqrt.f64 m) (/.f64 (sqrt.f64 v) (sqrt.f64 m)))
8.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))
6.0ms	(/.f64 (sqrt.f64 v) (sqrt.f64 m))

series254.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

83.0ms	(*.f64 (/.f64 (sqrt.f64 m) (/.f64 (sqrt.f64 v) (sqrt.f64 m))) (/.f64 (-.f64 1 m) (sqrt.f64 v)))
64.0ms	(/.f64 (sqrt.f64 m) (/.f64 (sqrt.f64 v) (sqrt.f64 m)))
61.0ms	(/.f64 (sqrt.f64 v) (sqrt.f64 m))
46.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))

simplify214.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

780 → 780

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4972	19076
1	4972	19076

prune1.1s (20.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	780	0	780
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	780	6	786

Merged error: 0b

Counts

786 → 6

Compiler

Compiled 22663 to 8056 computations (64.5% saved)

regimes151.0ms (2.9%)

Compiler: Compiled 1544 to 1160 computations (24.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	18
1	38	18

end0.0ms (0%)

sample1.0s (20.3%)

Algorithm

1×

intervals

Results

254.0ms	8000×	body	128	valid
169.0ms	8065×	pre	128	true
2.0ms	65×	body	128	invalid

Compiler

Compiled 539 to 405 computations (24.9% saved)

Details

analyze254.0ms (5%)

sample24.0ms (0.5%)

simplify337.0ms (6.6%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite31.0ms (0.6%)

series122.0ms (2.4%)

simplify81.0ms (1.6%)

prune67.0ms (1.3%)

localize7.0ms (0.1%)

rewrite46.0ms (0.9%)

series146.0ms (2.8%)

simplify76.0ms (1.5%)

prune105.0ms (2.1%)

localize10.0ms (0.2%)

rewrite93.0ms (1.8%)

series290.0ms (5.7%)

simplify99.0ms (1.9%)

prune239.0ms (4.7%)

localize12.0ms (0.2%)

rewrite359.0ms (7%)

series254.0ms (4.9%)

simplify214.0ms (4.2%)

prune1.1s (20.5%)

regimes151.0ms (2.9%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.0s (20.3%)

Profiling