Details

analyze610.0ms (17%)

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
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
12.5%	85.8%	1.7%	9
16.4%	79.2%	4.4%	10
20.7%	72.4%	7%	11
32.6%	53.3%	14.1%	12
36%	45.5%	18.5%	13
38.3%	41.1%	20.6%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample26.0ms (0.7%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	80	valid
6.0ms	77×	body	80	invalid

Compiler

Compiled 31 to 26 computations (16.1% saved)

simplify75.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5009	19

prune8.0ms (0.2%)

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: 12.5b

Counts

2 → 2

Compiler

Compiled 41 to 31 computations (24.4% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
0.7b	(-.f64 (.f64 z z) (.f64 x x))
13.4b	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

rewrite23.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
13×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
7×	`add-log-exp_binary64` `difference-of-squares_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-/l*_binary64`
3×	`associate-/r*_binary64` `pow1_binary64` `flip3--_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `div-sub_binary64`
1×	`associate--l-_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

3 → 61

Calls

3 calls:

10.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
6.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
4.0ms	(-.f64 (.f64 z z) (.f64 x x))

series34.0ms (1%)

Counts

3 → 9

Calls

3 calls:

13.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
13.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
9.0ms	(-.f64 (.f64 z z) (.f64 x x))

simplify109.0ms (3%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4914	1367
1	4914	1367

prune64.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	68	4	72

Merged error: 0.0b

Counts

72 → 4

Compiler

Compiled 1458 to 423 computations (71% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 z x) y)
0.0b	(-.f64 (*.f64 (+.f64 z x) (/.f64 (-.f64 z x) y)) y)
0.2b	(*.f64 (+.f64 z x) (/.f64 (-.f64 z x) y))

rewrite33.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
19×	`associate-r_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `associate-/l*_binary64`
4×	`associate-l_binary64`
3×	`associate-/r*_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

3 → 92

Calls

3 calls:

12.0ms	(*.f64 (+.f64 z x) (/.f64 (-.f64 z x) y))
11.0ms	(-.f64 (*.f64 (+.f64 z x) (/.f64 (-.f64 z x) y)) y)
6.0ms	(/.f64 (-.f64 z x) y)

series31.0ms (0.9%)

Counts

3 → 9

Calls

3 calls:

12.0ms	(*.f64 (+.f64 z x) (/.f64 (-.f64 z x) y))
12.0ms	(-.f64 (*.f64 (+.f64 z x) (/.f64 (-.f64 z x) y)) y)
7.0ms	(/.f64 (-.f64 z x) y)

simplify94.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5078	1633

prune65.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	98	3	101
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	99	6	105

Merged error: 0b

Counts

105 → 6

Compiler

Compiled 2077 to 614 computations (70.4% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 y (-.f64 z x))
0.0b	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
0.2b	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))

rewrite66.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

177×	`times-frac_binary64`
164×	`*-un-lft-identity_binary64`
127×	`add-sqr-sqrt_binary64`
80×	`add-cube-cbrt_binary64`
26×	`associate-/r*_binary64`
22×	`distribute-lft-out_binary64` `difference-of-squares_binary64`
20×	`distribute-lft-out--_binary64`
13×	`associate-/r/_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`flip3--_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip--_binary64`
5×	`add-log-exp_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow1_binary64`
2×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `flip-+_binary64`

Counts

3 → 178

Calls

3 calls:

38.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
12.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
6.0ms	(/.f64 y (-.f64 z x))

series33.0ms (0.9%)

Counts

3 → 9

Calls

3 calls:

13.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
12.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
8.0ms	(/.f64 y (-.f64 z x))

simplify105.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5111	4382

prune101.0ms (2.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	186	1	187
Fresh	1	3	4
Picked	0	1	1
Done	1	0	1
Total	188	5	193

Merged error: 0b

Counts

193 → 5

Compiler

Compiled 4265 to 1048 computations (75.4% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (/.f64 (+.f64 z x) y) (/.f64 1 (-.f64 z x))) y)
0.0b	(/.f64 (+.f64 z x) y)
0.0b	(/.f64 1 (-.f64 z x))
0.2b	(/.f64 (/.f64 (+.f64 z x) y) (/.f64 1 (-.f64 z x)))

rewrite182.0ms (5.1%)

Algorithm

1×	rewrite-expression-head

Rules

895×	`times-frac_binary64`
606×	`*-un-lft-identity_binary64`
487×	`add-sqr-sqrt_binary64`
352×	`add-cube-cbrt_binary64`
70×	`distribute-lft-out_binary64`
62×	`difference-of-squares_binary64`
56×	`distribute-lft-out--_binary64`
42×	`div-inv_binary64`
37×	`associate-/r/_binary64`
32×	`add-exp-log_binary64`
29×	`associate-/r*_binary64`
23×	`associate-/l*_binary64`
20×	`add-cbrt-cube_binary64`
19×	`flip3--_binary64` `div-exp_binary64` `flip--_binary64`
10×	`cbrt-undiv_binary64`
6×	`add-log-exp_binary64`
5×	`pow1_binary64`
3×	`associate-/l/_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `inv-pow_binary64` `pow-flip_binary64` `flip-+_binary64`

Counts

4 → 490

Calls

4 calls:

106.0ms	(-.f64 (/.f64 (/.f64 (+.f64 z x) y) (/.f64 1 (-.f64 z x))) y)
20.0ms	(/.f64 (/.f64 (+.f64 z x) y) (/.f64 1 (-.f64 z x)))
6.0ms	(/.f64 1 (-.f64 z x))
6.0ms	(/.f64 (+.f64 z x) y)

series35.0ms (1%)

Counts

4 → 12

Calls

4 calls:

13.0ms	(-.f64 (/.f64 (/.f64 (+.f64 z x) y) (/.f64 1 (-.f64 z x))) y)
12.0ms	(/.f64 (/.f64 (+.f64 z x) y) (/.f64 1 (-.f64 z x)))
6.0ms	(/.f64 (+.f64 z x) y)
5.0ms	(/.f64 1 (-.f64 z x))

simplify211.0ms (5.9%)

Algorithm

1×	egg-herbie

Counts

502 → 502

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4973	15061
1	4973	15061

prune331.0ms (9.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	502	0	502
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	502	5	507

Merged error: 0b

Counts

507 → 5

Compiler

Compiled 13093 to 3829 computations (70.8% saved)

regimes206.0ms (5.7%)

Compiler: Compiled 582 to 422 computations (27.5% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	22
1	34	22

end0.0ms (0%)

sample1.1s (30.8%)

Algorithm

1×

intervals

Results

330.0ms	8000×	body	80	valid
115.0ms	2753×	body	80	invalid

Compiler

Compiled 135 to 100 computations (25.9% saved)

Details

analyze610.0ms (17%)

sample26.0ms (0.7%)

simplify75.0ms (2.1%)

prune8.0ms (0.2%)

localize8.0ms (0.2%)

rewrite23.0ms (0.6%)

series34.0ms (1%)

simplify109.0ms (3%)

prune64.0ms (1.8%)

localize10.0ms (0.3%)

rewrite33.0ms (0.9%)

series31.0ms (0.9%)

simplify94.0ms (2.6%)

prune65.0ms (1.8%)

localize8.0ms (0.2%)

rewrite66.0ms (1.8%)

series33.0ms (0.9%)

simplify105.0ms (2.9%)

prune101.0ms (2.8%)

localize9.0ms (0.3%)

rewrite182.0ms (5.1%)

series35.0ms (1%)

simplify211.0ms (5.9%)

prune331.0ms (9.2%)

regimes206.0ms (5.7%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.1s (30.8%)

Profiling