Details

analyze472.0ms (5.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	93.6%	6.4%	7
3.1%	84.2%	12.7%	8
12.5%	67.1%	20.5%	9
16%	63.5%	20.5%	10
17.9%	57.7%	24.4%	11
22.6%	48.7%	28.7%	12
28.7%	37.8%	33.6%	13
30.4%	35.9%	33.7%	14

Compiler

Compiled 9 to 9 computations (0% saved)

sample25.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
3.0ms	87×	body	128	nan
1.0ms	29×	body	128	invalid

Compiler

Compiled 17 to 21 computations (-23.5% saved)

simplify101.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	12
1	15	12

prune2.0ms (0%)

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

Error

22.1b

Counts

2 → 1

Compiler

Compiled 16 to 16 computations (0% saved)

localize6.0ms (0.1%)

Local error

Found 6 expressions with local error:

17.6b	(sqrt.f64 (/.f64 A (*.f64 V l)))
6.3b	(/.f64 A (*.f64 V l))
1.5b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
1.5b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
6.3b	(/.f64 A (*.f64 V l))
17.6b	(sqrt.f64 (/.f64 A (*.f64 V l)))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_759`
15×	`sqrt-prod_binary64_753`
11×	`add-cube-cbrt_binary64_772` `*-un-lft-identity_binary64_737`
10×	`add-cbrt-cube_binary64_773` `add-exp-log_binary64_775` `associate-r_binary64_677`
9×	`times-frac_binary64_743`
6×	`pow1_binary64_798`
3×	`add-log-exp_binary64_776` `associate-/l_binary64_682` `div-inv_binary64_734` `associate-l*_binary64_678`
2×	`unswap-sqr_binary64_705` `cbrt-unprod_binary64_770` `prod-exp_binary64_786` `sqrt-div_binary64_754` `cbrt-undiv_binary64_771` `div-exp_binary64_788`
1×	`frac-2neg_binary64_748` `clear-num_binary64_736` `pow1/2_binary64_817` `rem-sqrt-square_binary64_750` `associate-/r_binary64_681` `sqrt-pow1_binary64_755` `pow-prod-down_binary64_808` `-commutative_binary64_668` `associate-*r/_binary64_679`

Counts

3 → 66

Calls

6 calls:

8.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
4.0ms	(/.f64 A (*.f64 V l))
4.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
0.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
0.0ms	(/.f64 A (*.f64 V l))

series326.0ms (3.6%)

Counts

3 → 30

Calls

3 calls:

156.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
100.0ms	(/.f64 A (*.f64 V l))
70.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))

Compiler

Compiled 782 to 717 computations (8.3% saved)

simplify78.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4894	1105
1	4894	1105

prune109.0ms (1.2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	80	16	96
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	80	17	97

Error

5.5b

Counts

97 → 17

Compiler

Compiled 1300 to 395 computations (69.6% saved)

localize14.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.6b	(cbrt.f64 A)
0.5b	(*.f64 (cbrt.f64 A) (cbrt.f64 A))
0.2b	(/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V)
0.2b	(/.f64 (cbrt.f64 A) l)
0.6b	(cbrt.f64 A)
1.5b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
2.5b	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
17.6b	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))

rewrite45.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64_759`
28×	`times-frac_binary64_743`
27×	`add-exp-log_binary64_775`
26×	`associate-r_binary64_677`
22×	`add-cube-cbrt_binary64_772` `*-un-lft-identity_binary64_737`
20×	`add-cbrt-cube_binary64_773`
14×	`cbrt-prod_binary64_768`
11×	`pow1_binary64_798`
10×	`associate-l_binary64_678`
9×	`cbrt-unprod_binary64_770` `prod-exp_binary64_786`
7×	`unswap-sqr_binary64_705` `cbrt-undiv_binary64_771` `div-exp_binary64_788`
6×	`sqrt-div_binary64_754` `associate-*r/_binary64_679`
4×	`add-log-exp_binary64_776`
3×	`frac-times_binary64_747` `associate-*l/_binary64_680` `pow-prod-down_binary64_808`
2×	`div-inv_binary64_734` `sqrt-pow1_binary64_755` `sqrt-prod_binary64_753` `*-commutative_binary64_668`
1×	`pow1/3_binary64_819` `pow1/2_binary64_817`

Counts

4 → 106

Calls

8 calls:

15.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
12.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
8.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))
1.0ms	(cbrt.f64 A)
0.0ms	(/.f64 (cbrt.f64 A) l)

series470.0ms (5.1%)

Counts

4 → 33

Calls

4 calls:

179.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
131.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
90.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))
69.0ms	(cbrt.f64 A)

Compiler

Compiled 932 to 849 computations (8.9% saved)

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5074	1761

prune110.0ms (1.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	135	4	139
Fresh	4	11	15
Picked	0	1	1
Done	1	0	1
Total	140	16	156

Error

3.7b

Counts

156 → 16

Compiler

Compiled 2239 to 731 computations (67.4% saved)

localize6.0ms (0.1%)

Local error

Found 6 expressions with local error:

17.6b	(sqrt.f64 (/.f64 (/.f64 A V) l))
3.9b	(/.f64 (/.f64 A V) l)
1.5b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
1.5b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
3.9b	(/.f64 (/.f64 A V) l)
17.6b	(sqrt.f64 (/.f64 (/.f64 A V) l))

rewrite50.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

213×	`times-frac_binary64_743`
134×	`add-sqr-sqrt_binary64_759`
117×	`add-cube-cbrt_binary64_772` `*-un-lft-identity_binary64_737`
89×	`sqrt-prod_binary64_753`
46×	`associate-r_binary64_677`
13×	`associate-/l*_binary64_682` `div-inv_binary64_734`
10×	`add-cbrt-cube_binary64_773` `add-exp-log_binary64_775`
6×	`pow1_binary64_798`
4×	`unswap-sqr_binary64_705`
3×	`add-log-exp_binary64_776` `rem-sqrt-square_binary64_750` `associate-/r_binary64_681` `cbrt-undiv_binary64_771` `div-exp_binary64_788` `associate-l*_binary64_678`
2×	`sqrt-div_binary64_754`
1×	`cbrt-unprod_binary64_770` `frac-2neg_binary64_748` `prod-exp_binary64_786` `clear-num_binary64_736` `pow1/2_binary64_817` `sqrt-pow1_binary64_755` `associate-/l/_binary64_684` `pow-prod-down_binary64_808` `-commutative_binary64_668` `associate-r/_binary64_679`

Counts

3 → 191

Calls

6 calls:

17.0ms	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
7.0ms	(sqrt.f64 (/.f64 (/.f64 A V) l))
6.0ms	(/.f64 (/.f64 A V) l)
0.0ms	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
0.0ms	(/.f64 (/.f64 A V) l)

series326.0ms (3.6%)

Counts

3 → 30

Calls

3 calls:

150.0ms	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
110.0ms	(/.f64 (/.f64 A V) l)
66.0ms	(sqrt.f64 (/.f64 (/.f64 A V) l))

Compiler

Compiled 782 to 717 computations (8.3% saved)

simplify124.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4917	3725
1	4917	3725

prune190.0ms (2.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	210	11	221
Fresh	7	7	14
Picked	1	0	1
Done	1	0	1
Total	219	18	237

Error

0.1b

Counts

237 → 18

Compiler

Compiled 3723 to 983 computations (73.6% saved)

localize17.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.3b	(/.f64 (cbrt.f64 A) (cbrt.f64 V))
0.3b	(.f64 (.f64 (fabs.f64 (/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)) (cbrt.f64 l))) c0) (sqrt.f64 (/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)) (cbrt.f64 l))))
0.2b	(*.f64 (fabs.f64 (/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)) (cbrt.f64 l))) c0)
0.2b	(sqrt.f64 (/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)) (cbrt.f64 l)))
0.6b	(cbrt.f64 V)
0.6b	(cbrt.f64 V)
0.6b	(cbrt.f64 l)
0.6b	(cbrt.f64 l)

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64_768`
8×	`add-cube-cbrt_binary64_772` `add-sqr-sqrt_binary64_759` `*-un-lft-identity_binary64_737`
4×	`add-cbrt-cube_binary64_773` `pow1/3_binary64_819` `add-log-exp_binary64_776` `add-exp-log_binary64_775` `pow1_binary64_798`

Counts

4 → 44

Calls

8 calls:

1.0ms	(cbrt.f64 l)
1.0ms	(cbrt.f64 V)
1.0ms	(cbrt.f64 l)
1.0ms	(cbrt.f64 V)
0.0ms	(sqrt.f64 (/.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)) (cbrt.f64 l)))

series293.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

76.0ms	(cbrt.f64 l)
75.0ms	(cbrt.f64 l)
73.0ms	(cbrt.f64 V)
68.0ms	(cbrt.f64 V)

Compiler

Compiled 568 to 436 computations (23.2% saved)

simplify82.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4832	324
1	4832	324

prune54.0ms (0.6%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	53	3	56
Fresh	0	17	17
Picked	0	1	1
Done	0	0	0
Total	53	21	74

Error

0.0b

Counts

74 → 21

Compiler

Compiled 1340 to 266 computations (80.1% saved)

simplify27.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	417	1815
1	417	1815

regimes980.0ms (10.7%)

Accuracy

Total 1.1b remaining (95.7%)

Threshold costs 0b (0%)

Compiler

Compiled 10054 to 7649 computations (23.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	35
1	16	35

end0.0ms (0%)

sample5.1s (56%)

Algorithm

1×

intervals

Results

305.0ms	8000×	body	128	valid
104.0ms	2992×	body	128	nan
31.0ms	870×	body	128	invalid

Compiler

Compiled 3408 to 2596 computations (23.8% saved)

Pareto

0.17991746729009364

Details

analyze472.0ms (5.2%)

sample25.0ms (0.3%)

simplify101.0ms (1.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite19.0ms (0.2%)

series326.0ms (3.6%)

simplify78.0ms (0.9%)

prune109.0ms (1.2%)

localize14.0ms (0.2%)

rewrite45.0ms (0.5%)

series470.0ms (5.1%)

simplify77.0ms (0.8%)

prune110.0ms (1.2%)

localize6.0ms (0.1%)

rewrite50.0ms (0.6%)

series326.0ms (3.6%)

simplify124.0ms (1.4%)

prune190.0ms (2.1%)

localize17.0ms (0.2%)

rewrite8.0ms (0.1%)

series293.0ms (3.2%)

simplify82.0ms (0.9%)

prune54.0ms (0.6%)

simplify27.0ms (0.3%)

regimes980.0ms (10.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample5.1s (56%)

Profiling