Details

analyze284.0ms (11.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
6.2%	93.6%	0.1%	6
15.6%	84.3%	0.1%	7
31.2%	68.6%	0.1%	8
39%	56.2%	4.8%	9
50.7%	43.7%	5.6%	10
60.3%	33.7%	6%	11
64.6%	26.5%	8.9%	12
70.5%	20.3%	9.2%	13
74.6%	16.1%	9.4%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample17.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	80	valid
0.0ms	7×	body	80	invalid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify13.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	20	13
1	20	13

prune4.0ms (0.2%)

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: 0.0b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)
0.0b	(+.f64 (/.f64 x 2) (*.f64 y x))

rewrite22.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64` `sum-log_binary64`
2×	`flip3-+_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `+-commutative_binary64` `flip-+_binary64`
1×	`distribute-lft-out_binary64` `associate-+l+_binary64`

Counts

2 → 25

Calls

2 calls:

14.0ms	(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)
7.0ms	(+.f64 (/.f64 x 2) (*.f64 y x))

series21.0ms (0.9%)

Counts

2 → 6

Calls

2 calls:

11.0ms	(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)
10.0ms	(+.f64 (/.f64 x 2) (*.f64 y x))

simplify85.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5160	490

prune41.0ms (1.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	29	2	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	2	32

Merged error: 0.0b

Counts

32 → 2

Compiler

Compiled 475 to 265 computations (44.2% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 (*.f64 x (+.f64 y 1/2)) z)

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64`
2×	`associate-+l+_binary64`
1×	`flip3-+_binary64` `*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `add-sqr-sqrt_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

1 → 13

Calls

1 calls:

7.0ms

(+.f64 (*.f64 x (+.f64 y 1/2)) z)

series7.0ms (0.3%)

Counts

1 → 3

Calls

1 calls:

7.0ms

(+.f64 (*.f64 x (+.f64 y 1/2)) z)

simplify73.0ms (3%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4742	228
1	4742	228

prune15.0ms (0.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	15	1	16
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	16	2	18

Merged error: 0.0b

Counts

18 → 2

Compiler

Compiled 219 to 143 computations (34.7% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (*.f64 x (+.f64 y 1/2)) z)
0.1b	(.f64 (.f64 x (+.f64 y 1/2)) (*.f64 x (+.f64 y 1/2)))
2.6b	(-.f64 (.f64 (.f64 x (+.f64 y 1/2)) (.f64 x (+.f64 y 1/2))) (.f64 z z))
31.7b	(/.f64 (-.f64 (.f64 (.f64 x (+.f64 y 1/2)) (.f64 x (+.f64 y 1/2))) (.f64 z z)) (-.f64 (*.f64 x (+.f64 y 1/2)) z))

rewrite58.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`pow1_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
17×	`pow-prod-down_binary64`
14×	`associate-*r/_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`times-frac_binary64`
9×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
8×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
6×	`flip3-+_binary64` `flip-+_binary64` `associate--l+_binary64`
5×	`difference-of-squares_binary64`
4×	`flip3--_binary64` `pow-prod-up_binary64` `associate-/l*_binary64` `pow-sqr_binary64` `flip--_binary64` `frac-times_binary64`
3×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64` `pow-plus_binary64` `associate-*l/_binary64`
1×	`swap-sqr_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 111

Calls

4 calls:

22.0ms	(/.f64 (-.f64 (.f64 (.f64 x (+.f64 y 1/2)) (.f64 x (+.f64 y 1/2))) (.f64 z z)) (-.f64 (*.f64 x (+.f64 y 1/2)) z))
14.0ms	(-.f64 (.f64 (.f64 x (+.f64 y 1/2)) (.f64 x (+.f64 y 1/2))) (.f64 z z))
12.0ms	(.f64 (.f64 x (+.f64 y 1/2)) (*.f64 x (+.f64 y 1/2)))
6.0ms	(-.f64 (*.f64 x (+.f64 y 1/2)) z)

series71.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

36.0ms	(/.f64 (-.f64 (.f64 (.f64 x (+.f64 y 1/2)) (.f64 x (+.f64 y 1/2))) (.f64 z z)) (-.f64 (*.f64 x (+.f64 y 1/2)) z))
21.0ms	(-.f64 (.f64 (.f64 x (+.f64 y 1/2)) (.f64 x (+.f64 y 1/2))) (.f64 z z))
7.0ms	(.f64 (.f64 x (+.f64 y 1/2)) (*.f64 x (+.f64 y 1/2)))
7.0ms	(-.f64 (*.f64 x (+.f64 y 1/2)) z)

simplify89.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5094	2466

prune132.0ms (5.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	123	2	125

Merged error: 0b

Counts

125 → 2

Compiler

Compiled 3273 to 1964 computations (40% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 (*.f64 x (+.f64 y 1/2)) z))
0.6b	(cbrt.f64 (-.f64 (*.f64 x (+.f64 y 1/2)) z))
2.6b	(-.f64 (.f64 (.f64 x (+.f64 y 1/2)) (.f64 x (+.f64 y 1/2))) (.f64 z z))
31.7b	(/.f64 (-.f64 (.f64 (.f64 x (+.f64 y 1/2)) (.f64 x (+.f64 y 1/2))) (.f64 z z)) (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x (+.f64 y 1/2)) z)) (cbrt.f64 (-.f64 (.f64 x (+.f64 y 1/2)) z))) (cbrt.f64 (-.f64 (*.f64 x (+.f64 y 1/2)) z))))

rewrite75.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`cbrt-div_binary64`
31×	`flip3--_binary64` `flip--_binary64`
28×	`frac-times_binary64`
26×	`associate-/r/_binary64`
14×	`associate-*l/_binary64`
13×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`-un-lft-identity_binary64` `associate-r/_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`add-log-exp_binary64` `cbrt-prod_binary64`
4×	`pow1_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-/l*_binary64` `times-frac_binary64` `associate--l+_binary64`
3×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `div-exp_binary64`
2×	`associate-/l/_binary64` `pow1/3_binary64`
1×	`associate-/r*_binary64` `sub-neg_binary64` `diff-log_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 96

Calls

4 calls:

43.0ms	(/.f64 (-.f64 (.f64 (.f64 x (+.f64 y 1/2)) (.f64 x (+.f64 y 1/2))) (.f64 z z)) (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x (+.f64 y 1/2)) z)) (cbrt.f64 (-.f64 (.f64 x (+.f64 y 1/2)) z))) (cbrt.f64 (-.f64 (*.f64 x (+.f64 y 1/2)) z))))
13.0ms	(-.f64 (.f64 (.f64 x (+.f64 y 1/2)) (.f64 x (+.f64 y 1/2))) (.f64 z z))
7.0ms	(cbrt.f64 (-.f64 (*.f64 x (+.f64 y 1/2)) z))
6.0ms	(cbrt.f64 (-.f64 (*.f64 x (+.f64 y 1/2)) z))

series124.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

35.0ms	(/.f64 (-.f64 (.f64 (.f64 x (+.f64 y 1/2)) (.f64 x (+.f64 y 1/2))) (.f64 z z)) (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x (+.f64 y 1/2)) z)) (cbrt.f64 (-.f64 (.f64 x (+.f64 y 1/2)) z))) (cbrt.f64 (-.f64 (*.f64 x (+.f64 y 1/2)) z))))
32.0ms	(cbrt.f64 (-.f64 (*.f64 x (+.f64 y 1/2)) z))
32.0ms	(cbrt.f64 (-.f64 (*.f64 x (+.f64 y 1/2)) z))
25.0ms	(-.f64 (.f64 (.f64 x (+.f64 y 1/2)) (.f64 x (+.f64 y 1/2))) (.f64 z z))

simplify79.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5688	4383

prune190.0ms (7.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	108	2	110

Merged error: 0b

Counts

110 → 2

Compiler

Compiled 5830 to 3676 computations (36.9% saved)

regimes126.0ms (5.1%)

Compiler: Compiled 153 to 129 computations (15.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	10
1	11	10

end0.0ms (0%)

sample887.0ms (36.1%)

Algorithm

1×

intervals

Results

298.0ms	7996×	body	80	valid
11.0ms	337×	body	80	invalid
0.0ms	2×	body	1280	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	160	valid

Compiler

Compiled 66 to 56 computations (15.2% saved)

Details

analyze284.0ms (11.6%)

sample17.0ms (0.7%)

simplify13.0ms (0.5%)

prune4.0ms (0.2%)

localize7.0ms (0.3%)

rewrite22.0ms (0.9%)

series21.0ms (0.9%)

simplify85.0ms (3.5%)

prune41.0ms (1.7%)

localize5.0ms (0.2%)

rewrite7.0ms (0.3%)

series7.0ms (0.3%)

simplify73.0ms (3%)

prune15.0ms (0.6%)

localize9.0ms (0.4%)

rewrite58.0ms (2.4%)

series71.0ms (2.9%)

simplify89.0ms (3.6%)

prune132.0ms (5.4%)

localize13.0ms (0.5%)

rewrite75.0ms (3.1%)

series124.0ms (5.1%)

simplify79.0ms (3.2%)

prune190.0ms (7.7%)

regimes126.0ms (5.1%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample887.0ms (36.1%)

Profiling