Details

analyze348.0ms (13.9%)

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
0%	99.9%	0.1%	9
46%	49.5%	4.4%	10
50.3%	44.9%	4.8%	11
55.6%	39.2%	5.2%	12
62.9%	25.7%	11.4%	13
65.2%	23.2%	11.7%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample19.0ms (0.8%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	80	valid
1.0ms	35×	body	80	invalid

Compiler

Compiled 23 to 24 computations (-4.3% saved)

simplify317.0ms (12.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (308.0ms)

Iter	Nodes	Cost
0	4649	13
1	4649	13

prune7.0ms (0.3%)

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: 0.0b

Counts

2 → 2

Compiler

Compiled 29 to 28 computations (3.4% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (-.f64 x y) (*.f64 z 1/2))
0.0b	(/.f64 (.f64 4 (-.f64 (-.f64 x y) (.f64 z 1/2))) z)

rewrite18.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
3×	`associate-/r*_binary64` `diff-log_binary64` `times-frac_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `pow1_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `div-exp_binary64` `flip--_binary64`
1×	`associate--l-_binary64` `cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `associate--l+_binary64`

Counts

2 → 37

Calls

2 calls:

10.0ms	(/.f64 (.f64 4 (-.f64 (-.f64 x y) (.f64 z 1/2))) z)
7.0ms	(-.f64 (-.f64 x y) (*.f64 z 1/2))

series16.0ms (0.6%)

Counts

2 → 6

Calls

2 calls:

10.0ms	(/.f64 (.f64 4 (-.f64 (-.f64 x y) (.f64 z 1/2))) z)
6.0ms	(-.f64 (-.f64 x y) (*.f64 z 1/2))

simplify62.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5415	667

prune35.0ms (1.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	41	2	43
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	41	4	45

Merged error: 0b

Counts

45 → 4

Compiler

Compiled 686 to 395 computations (42.4% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (-.f64 x y) (*.f64 z 1/2))
0.0b	(/.f64 z (-.f64 (-.f64 x y) (*.f64 z 1/2)))
0.2b	(/.f64 4 (/.f64 z (-.f64 (-.f64 x y) (*.f64 z 1/2))))

rewrite33.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`times-frac_binary64`
55×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
18×	`associate-/r*_binary64`
11×	`associate-/r/_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
6×	`flip3--_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip--_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow1_binary64` `diff-log_binary64`
2×	`sub-neg_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`associate--l-_binary64` `associate--l+_binary64`

Counts

3 → 121

Calls

3 calls:

12.0ms	(/.f64 4 (/.f64 z (-.f64 (-.f64 x y) (*.f64 z 1/2))))
8.0ms	(/.f64 z (-.f64 (-.f64 x y) (*.f64 z 1/2)))
7.0ms	(-.f64 (-.f64 x y) (*.f64 z 1/2))

series30.0ms (1.2%)

Counts

3 → 9

Calls

3 calls:

14.0ms	(/.f64 z (-.f64 (-.f64 x y) (*.f64 z 1/2)))
10.0ms	(/.f64 4 (/.f64 z (-.f64 (-.f64 x y) (*.f64 z 1/2))))
6.0ms	(-.f64 (-.f64 x y) (*.f64 z 1/2))

simplify64.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5189	3284

prune93.0ms (3.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	130	4	134

Merged error: 0b

Counts

134 → 4

Compiler

Compiled 2758 to 1569 computations (43.1% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.5b	(*.f64 (-.f64 x y) (/.f64 4 z))

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
11×	`*-un-lft-identity_binary64`
10×	`times-frac_binary64`
9×	`add-cube-cbrt_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-l_binary64`
3×	`pow1_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip--_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `-commutative_binary64`

Counts

1 → 38

Calls

1 calls:

9.0ms

(*.f64 (-.f64 x y) (/.f64 4 z))

series9.0ms (0.3%)

Counts

1 → 3

Calls

1 calls:

9.0ms

(*.f64 (-.f64 x y) (/.f64 4 z))

simplify67.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5329	554

prune29.0ms (1.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	40	1	41
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	42	3	45

Merged error: 0b

Counts

45 → 3

Compiler

Compiled 614 to 361 computations (41.2% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 x y) z)
0.0b	(*.f64 64 (pow.f64 (/.f64 (-.f64 x y) z) 3))
0.3b	(pow.f64 (/.f64 (-.f64 x y) z) 3)
32.4b	(cbrt.f64 (*.f64 64 (pow.f64 (/.f64 (-.f64 x y) z) 3)))

rewrite49.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`add-sqr-sqrt_binary64`
85×	`*-un-lft-identity_binary64`
77×	`times-frac_binary64`
53×	`add-cube-cbrt_binary64`
44×	`associate-r_binary64`
40×	`unpow-prod-down_binary64` `cube-prod_binary64`
17×	`add-exp-log_binary64`
16×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
11×	`add-cbrt-cube_binary64`
6×	`unswap-sqr_binary64`
5×	`pow1_binary64` `associate-/l*_binary64` `div-inv_binary64`
4×	`add-log-exp_binary64` `prod-exp_binary64` `pow-exp_binary64`
3×	`pow-unpow_binary64` `associate-/r_binary64` `sqr-pow_binary64` `associate-l*_binary64` `cube-div_binary64` `div-exp_binary64`
2×	`pow-to-exp_binary64` `associate-/l/_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `rem-cube-cbrt_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `pow1/3_binary64` `pow-pow_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `cbrt-prod_binary64` `*-commutative_binary64`

Counts

4 → 173

Calls

4 calls:

16.0ms	(*.f64 64 (pow.f64 (/.f64 (-.f64 x y) z) 3))
9.0ms	(cbrt.f64 (*.f64 64 (pow.f64 (/.f64 (-.f64 x y) z) 3)))
8.0ms	(/.f64 (-.f64 x y) z)
7.0ms	(pow.f64 (/.f64 (-.f64 x y) z) 3)

series60.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(*.f64 64 (pow.f64 (/.f64 (-.f64 x y) z) 3))
17.0ms	(pow.f64 (/.f64 (-.f64 x y) z) 3)
15.0ms	(cbrt.f64 (*.f64 64 (pow.f64 (/.f64 (-.f64 x y) z) 3)))
7.0ms	(/.f64 (-.f64 x y) z)

simplify99.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5342	2931

prune126.0ms (5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	185	3	188

Merged error: 0b

Counts

188 → 3

Compiler

Compiled 3518 to 1890 computations (46.3% saved)

regimes150.0ms (6%)

Compiler: Compiled 204 to 206 computations (-1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	16
1	47	16

end0.0ms (0%)

sample837.0ms (33.4%)

Algorithm

1×

intervals

Results

249.0ms	8000×	body	80	valid
32.0ms	995×	body	80	invalid

Compiler

Compiled 70 to 68 computations (2.9% saved)

Details

analyze348.0ms (13.9%)

sample19.0ms (0.8%)

simplify317.0ms (12.6%)

prune7.0ms (0.3%)

localize7.0ms (0.3%)

rewrite18.0ms (0.7%)

series16.0ms (0.6%)

simplify62.0ms (2.5%)

prune35.0ms (1.4%)

localize7.0ms (0.3%)

rewrite33.0ms (1.3%)

series30.0ms (1.2%)

simplify64.0ms (2.6%)

prune93.0ms (3.7%)

localize6.0ms (0.2%)

rewrite11.0ms (0.4%)

series9.0ms (0.3%)

simplify67.0ms (2.7%)

prune29.0ms (1.2%)

localize9.0ms (0.4%)

rewrite49.0ms (1.9%)

series60.0ms (2.4%)

simplify99.0ms (3.9%)

prune126.0ms (5%)

regimes150.0ms (6%)

bsearch0.0ms (0%)

simplify4.0ms (0.2%)

end0.0ms (0%)

sample837.0ms (33.4%)

Profiling