Details

analyze897.0ms (17.1%)

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%	99.8%	0.2%	7
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
9.4%	90.4%	0.2%	10
14%	83.4%	2.5%	11
18.7%	78.2%	3.1%	12
28.1%	65.5%	6.4%	13
30.7%	59.4%	9.9%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample39.0ms (0.7%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
8.0ms	189×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	49	22
1	49	22

prune3.0ms (0.1%)

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: 32.3b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (/.f64 (.f64 x x) (.f64 y y)) (/.f64 (.f64 z z) (.f64 t t)))
20.5b	(/.f64 (.f64 z z) (.f64 t t))
21.2b	(/.f64 (.f64 x x) (.f64 y y))

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
5×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
2×	`associate-/r_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64`
1×	`flip3-+_binary64` `distribute-lft-out_binary64` `frac-add_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

3 → 55

Calls

3 calls:

11.0ms	(+.f64 (/.f64 (.f64 x x) (.f64 y y)) (/.f64 (.f64 z z) (.f64 t t)))
7.0ms	(/.f64 (.f64 x x) (.f64 y y))
7.0ms	(/.f64 (.f64 z z) (.f64 t t))

series222.0ms (4.2%)

Counts

3 → 9

Calls

3 calls:

149.0ms	(+.f64 (/.f64 (.f64 x x) (.f64 y y)) (/.f64 (.f64 z z) (.f64 t t)))
37.0ms	(/.f64 (.f64 z z) (.f64 t t))
36.0ms	(/.f64 (.f64 x x) (.f64 y y))

simplify51.0ms (1%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4963	879
1	4963	879

prune183.0ms (3.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	53	11	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	11	65

Merged error: 4.8b

Counts

65 → 11

Compiler

Compiled 3331 to 1783 computations (46.5% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (/.f64 (.f64 z z) (*.f64 t t)))
0.4b	(*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))
20.5b	(/.f64 (.f64 z z) (.f64 t t))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
5×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-/r_binary64` `pow-prod-up_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64` `sqr-abs_binary64` `pow-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

3 → 58

Calls

3 calls:

7.0ms	(/.f64 (.f64 z z) (.f64 t t))
6.0ms	(+.f64 (.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (/.f64 (.f64 z z) (*.f64 t t)))
4.0ms	(*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))

series209.0ms (4%)

Counts

3 → 9

Calls

3 calls:

146.0ms	(+.f64 (.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (/.f64 (.f64 z z) (*.f64 t t)))
37.0ms	(/.f64 (.f64 z z) (.f64 t t))
26.0ms	(*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))

simplify73.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5024	835

prune155.0ms (3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	62	5	67
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	68	10	78

Merged error: 0.1b

Counts

78 → 10

Compiler

Compiled 3026 to 1550 computations (48.8% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (.f64 (/.f64 z t) (/.f64 z t)))
0.3b	(*.f64 (/.f64 z t) (/.f64 z t))
0.4b	(*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
17×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
5×	`add-log-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
4×	`cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-plus_binary64` `pow-sqr_binary64` `pow2_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `associate-r/_binary64` `sqr-abs_binary64` `+-commutative_binary64` `flip-+_binary64` `frac-times_binary64` `associate-l/_binary64` `sum-log_binary64`

Counts

3 → 104

Calls

3 calls:

12.0ms	(*.f64 (/.f64 z t) (/.f64 z t))
5.0ms	(+.f64 (.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (.f64 (/.f64 z t) (/.f64 z t)))
4.0ms	(*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))

series205.0ms (3.9%)

Counts

3 → 9

Calls

3 calls:

136.0ms	(+.f64 (.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y))) (.f64 (/.f64 z t) (/.f64 z t)))
39.0ms	(*.f64 (/.f64 z t) (/.f64 z t))
30.0ms	(*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))

simplify80.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4950	1350
1	4950	1350

prune432.0ms (8.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	105	8	113
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	108	15	123

Merged error: 0.0b

Counts

123 → 15

Compiler

Compiled 8578 to 4801 computations (44% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sqrt.f64 (fabs.f64 (/.f64 x y))) (pow.f64 (fabs.f64 (/.f64 x y)) 3/2))
0.2b	(pow.f64 (fabs.f64 (/.f64 x y)) 3/2)
0.3b	(*.f64 (/.f64 z t) (/.f64 z t))
8.6b	(sqrt.f64 (fabs.f64 (/.f64 x y)))

rewrite38.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
39×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
22×	`add-exp-log_binary64`
20×	`associate-r_binary64`
19×	`associate-l_binary64`
18×	`add-cbrt-cube_binary64`
14×	`pow1_binary64`
13×	`swap-sqr_binary64`
10×	`unswap-sqr_binary64`
9×	`sqrt-prod_binary64`
8×	`unpow-prod-down_binary64`
7×	`prod-exp_binary64`
5×	`cbrt-unprod_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `div-inv_binary64` `div-exp_binary64`
3×	`pow-unpow_binary64` `pow-prod-up_binary64`
2×	`pow-to-exp_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `pow-pow_binary64` `pow-plus_binary64` `rem-sqrt-square_binary64` `pow-sqr_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64`

Counts

4 → 130

Calls

4 calls:

12.0ms	(*.f64 (/.f64 z t) (/.f64 z t))
8.0ms	(*.f64 (sqrt.f64 (fabs.f64 (/.f64 x y))) (pow.f64 (fabs.f64 (/.f64 x y)) 3/2))
2.0ms	(pow.f64 (fabs.f64 (/.f64 x y)) 3/2)
2.0ms	(sqrt.f64 (fabs.f64 (/.f64 x y)))

series157.0ms (3%)

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow.f64 (fabs.f64 (/.f64 x y)) 3/2)
37.0ms	(*.f64 (/.f64 z t) (/.f64 z t))
32.0ms	(sqrt.f64 (fabs.f64 (/.f64 x y)))
25.0ms	(*.f64 (sqrt.f64 (fabs.f64 (/.f64 x y))) (pow.f64 (fabs.f64 (/.f64 x y)) 3/2))

simplify76.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5015	1768

prune337.0ms (6.4%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	137	5	142
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	137	20	157

Merged error: 0.0b

Counts

157 → 20

Compiler

Compiled 7186 to 3485 computations (51.5% saved)

regimes411.0ms (7.9%)

Compiler: Compiled 4454 to 3038 computations (31.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	13	21

end0.0ms (0%)

sample1.5s (29.2%)

Algorithm

1×

intervals

Results

511.0ms	8000×	body	128	valid
271.0ms	6066×	body	128	invalid

Compiler

Compiled 443 to 301 computations (32.1% saved)

Details

analyze897.0ms (17.1%)

sample39.0ms (0.7%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize11.0ms (0.2%)

rewrite30.0ms (0.6%)

series222.0ms (4.2%)

simplify51.0ms (1%)

prune183.0ms (3.5%)

localize10.0ms (0.2%)

rewrite23.0ms (0.4%)

series209.0ms (4%)

simplify73.0ms (1.4%)

prune155.0ms (3%)

localize9.0ms (0.2%)

rewrite32.0ms (0.6%)

series205.0ms (3.9%)

simplify80.0ms (1.5%)

prune432.0ms (8.2%)

localize16.0ms (0.3%)

rewrite38.0ms (0.7%)

series157.0ms (3%)

simplify76.0ms (1.4%)

prune337.0ms (6.4%)

regimes411.0ms (7.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.5s (29.2%)

Profiling