Details

analyze698.0ms (12.2%)

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)

sample28.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	80	valid
4.0ms	91×	body	80	nan
1.0ms	24×	body	80	invalid

Compiler

Compiled 17 to 21 computations (-23.5% saved)

simplify20.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

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

Merged error: 19.3b

Counts

2 → 1

Compiler

Compiled 16 to 16 computations (0% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

1.4b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
6.1b	(/.f64 A (*.f64 V l))
15.0b	(sqrt.f64 (/.f64 A (*.f64 V l)))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
15×	`sqrt-prod_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`times-frac_binary64`
6×	`pow1_binary64`
3×	`add-log-exp_binary64` `associate-l_binary64` `associate-/l*_binary64` `div-inv_binary64` `insert-posit16`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`

Counts

3 → 69

Calls

3 calls:

9.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
5.0ms	(/.f64 A (*.f64 V l))
4.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))

series188.0ms (3.3%)

Counts

3 → 9

Calls

3 calls:

91.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
61.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
37.0ms	(/.f64 A (*.f64 V l))

simplify183.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (156.0ms)

Iter	Nodes	Cost
0	4794	891
1	4794	891

prune81.0ms (1.4%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	63	15	78
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	63	16	79

Merged error: 7.5b

Counts

79 → 16

Compiler

Compiled 1128 to 385 computations (65.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 A)
1.4b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
4.2b	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
15.0b	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))

rewrite53.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
28×	`times-frac_binary64`
27×	`add-exp-log_binary64`
26×	`associate-r_binary64`
22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
20×	`add-cbrt-cube_binary64`
14×	`cbrt-prod_binary64`
11×	`pow1_binary64`
10×	`associate-l_binary64`
9×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`cbrt-undiv_binary64` `unswap-sqr_binary64` `div-exp_binary64`
6×	`associate-*r/_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`pow-prod-down_binary64` `frac-times_binary64` `associate-*l/_binary64`
2×	`sqrt-pow1_binary64` `div-inv_binary64` `sqrt-prod_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `pow1/3_binary64`

Counts

4 → 110

Calls

4 calls:

21.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
16.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
10.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))
1.0ms	(cbrt.f64 A)

series389.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

154.0ms	(cbrt.f64 A)
109.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
72.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))
53.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))

simplify198.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (167.0ms)

Iter	Nodes	Cost
0	4948	1542
1	4948	1542

prune105.0ms (1.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	118	4	122
Fresh	4	10	14
Picked	0	1	1
Done	1	0	1
Total	123	15	138

Merged error: 4.5b

Counts

138 → 15

Compiler

Compiled 2066 to 730 computations (64.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.9b	(/.f64 1 (/.f64 V (/.f64 A l)))
1.4b	(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))
3.8b	(/.f64 V (/.f64 A l))
15.0b	(sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l))))

rewrite165.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

1155×	`times-frac_binary64`
574×	`add-sqr-sqrt_binary64`
539×	`*-un-lft-identity_binary64`
533×	`add-cube-cbrt_binary64`
281×	`sqrt-prod_binary64`
140×	`associate-r_binary64`
57×	`associate-/r*_binary64`
48×	`div-inv_binary64`
32×	`add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`
18×	`div-exp_binary64`
14×	`associate-/r/_binary64`
9×	`pow1_binary64` `cbrt-undiv_binary64`
8×	`unswap-sqr_binary64`
7×	`rem-sqrt-square_binary64`
6×	`associate-/l*_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`1-exp_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rec-exp_binary64`
2×	`clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `prod-exp_binary64` `-commutative_binary64`

Counts

4 → 597

Calls

4 calls:

54.0ms	(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))
24.0ms	(sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l))))
15.0ms	(/.f64 1 (/.f64 V (/.f64 A l)))
7.0ms	(/.f64 V (/.f64 A l))

series284.0ms (5%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))
94.0ms	(sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l))))
39.0ms	(/.f64 V (/.f64 A l))
33.0ms	(/.f64 1 (/.f64 V (/.f64 A l)))

simplify318.0ms (5.6%)

Algorithm

1×	egg-herbie

Counts

609 → 609

Iterations

Useful iterations: 0 (184.0ms)

Iter	Nodes	Cost
0	4983	12620
1	4983	12620

prune588.0ms (10.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	598	11	609
Fresh	7	6	13
Picked	1	0	1
Done	1	0	1
Total	607	17	624

Merged error: 0.1b

Counts

624 → 17

Compiler

Compiled 12100 to 4044 computations (66.6% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 V)
0.5b	(cbrt.f64 V)
0.6b	(cbrt.f64 A)
0.6b	(cbrt.f64 A)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `pow1/3_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16`

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt.f64 A)
1.0ms	(cbrt.f64 A)
1.0ms	(cbrt.f64 V)
1.0ms	(cbrt.f64 V)

series614.0ms (10.7%)

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt.f64 A)
154.0ms	(cbrt.f64 V)
153.0ms	(cbrt.f64 A)
151.0ms	(cbrt.f64 V)

simplify93.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4900	360
1	4900	360

prune63.0ms (1.1%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	55	5	60
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	57	20	77

Merged error: 0.0b

Counts

77 → 20

Compiler

Compiled 1564 to 488 computations (68.8% saved)

regimes303.0ms (5.3%)

Compiler: Compiled 3073 to 2325 computations (24.3% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	26	54
1	26	54

end0.0ms (0%)

sample1.3s (22.2%)

Algorithm

1×

intervals

Results

341.0ms	8000×	body	80	valid
122.0ms	2892×	body	80	nan
35.0ms	855×	body	80	invalid

Compiler

Compiled 470 to 351 computations (25.3% saved)

Details

analyze698.0ms (12.2%)

sample28.0ms (0.5%)

simplify20.0ms (0.3%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite21.0ms (0.4%)

series188.0ms (3.3%)

simplify183.0ms (3.2%)

prune81.0ms (1.4%)

localize11.0ms (0.2%)

rewrite53.0ms (0.9%)

series389.0ms (6.8%)

simplify198.0ms (3.5%)

prune105.0ms (1.8%)

localize8.0ms (0.1%)

rewrite165.0ms (2.9%)

series284.0ms (5%)

simplify318.0ms (5.6%)

prune588.0ms (10.3%)

localize16.0ms (0.3%)

rewrite7.0ms (0.1%)

series614.0ms (10.7%)

simplify93.0ms (1.6%)

prune63.0ms (1.1%)

regimes303.0ms (5.3%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.3s (22.2%)

Profiling