Details

analyze228.0ms (6.1%)

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
12.5%	87.4%	0.1%	4
12.5%	87.4%	0.1%	5
15.6%	84.3%	0.1%	6
32.8%	67.1%	0.1%	7
38.2%	61.6%	0.1%	8
46%	53.8%	0.1%	9
62.6%	37.3%	0.1%	10
67.2%	32.7%	0.1%	11
71.1%	28.8%	0.1%	12
81.6%	18.2%	0.1%	13
84.1%	15.7%	0.1%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample15.0ms (0.4%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify207.0ms (5.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (197.0ms)

Iter	Nodes	Cost
0	3020	13
1	3020	13

prune4.0ms (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: 7.9b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 1 (/.f64 y z))
7.9b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

rewrite23.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`add-sqr-sqrt_binary64`
58×	`*-un-lft-identity_binary64`
44×	`times-frac_binary64`
24×	`difference-of-squares_binary64`
16×	`add-cube-cbrt_binary64`
9×	`distribute-lft-out_binary64`
8×	`associate-/r*_binary64`
6×	`distribute-lft-out--_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
2×	`associate-/l/_binary64` `pow1_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

2 → 76

Calls

2 calls:

12.0ms	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
7.0ms	(-.f64 1 (/.f64 y z))

series18.0ms (0.5%)

Counts

2 → 6

Calls

2 calls:

14.0ms	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
3.0ms	(-.f64 1 (/.f64 y z))

simplify73.0ms (2%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5311	1688

prune76.0ms (2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	10	83

Merged error: 5.2b

Counts

83 → 10

Compiler

Compiled 1596 to 681 computations (57.3% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 1 (/.f64 y z))
0.2b	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
7.9b	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))

rewrite57.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

318×	`times-frac_binary64`
284×	`add-sqr-sqrt_binary64`
278×	`*-un-lft-identity_binary64`
108×	`add-cube-cbrt_binary64`
88×	`difference-of-squares_binary64`
42×	`associate-/r*_binary64`
41×	`distribute-lft-out_binary64`
22×	`distribute-lft-out--_binary64`
16×	`add-exp-log_binary64`
11×	`associate-/r/_binary64` `associate-/l*_binary64`
10×	`add-cbrt-cube_binary64`
8×	`div-exp_binary64`
6×	`div-inv_binary64`
5×	`flip3-+_binary64` `add-log-exp_binary64` `flip-+_binary64`
4×	`pow1_binary64` `cbrt-undiv_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `div-sub_binary64` `inv-pow_binary64` `pow-flip_binary64`

Counts

3 → 253

Calls

3 calls:

18.0ms	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
12.0ms	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))
7.0ms	(-.f64 1 (/.f64 y z))

series31.0ms (0.8%)

Counts

3 → 9

Calls

3 calls:

17.0ms	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
10.0ms	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))
3.0ms	(-.f64 1 (/.f64 y z))

simplify135.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5525	6697

prune192.0ms (5.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	260	2	262
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	261	11	272

Merged error: 5.2b

Counts

272 → 11

Compiler

Compiled 5663 to 2534 computations (55.3% saved)

localize28.0ms (0.8%)

Local error

Found 4 expressions with local error:

1.8b	(/.f64 (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y))) (.f64 (cbrt.f64 (-.f64 1 (/.f64 y z))) (cbrt.f64 (-.f64 1 (/.f64 y z)))))
8.1b	(cbrt.f64 (-.f64 1 (/.f64 y z)))
8.1b	(cbrt.f64 (-.f64 1 (/.f64 y z)))
8.1b	(cbrt.f64 (-.f64 1 (/.f64 y z)))

rewrite57.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
30×	`cbrt-div_binary64`
24×	`cbrt-prod_binary64`
19×	`*-un-lft-identity_binary64`
16×	`add-exp-log_binary64`
12×	`difference-of-squares_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`associate-/l/_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64` `frac-times_binary64`
7×	`add-cube-cbrt_binary64` `times-frac_binary64`
6×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `prod-exp_binary64` `div-exp_binary64` `associate-l/_binary64`
3×	`pow1/3_binary64` `distribute-lft-out--_binary64`
1×	`associate-/r_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64`

Counts

4 → 91

Calls

4 calls:

28.0ms	(/.f64 (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y))) (.f64 (cbrt.f64 (-.f64 1 (/.f64 y z))) (cbrt.f64 (-.f64 1 (/.f64 y z)))))
10.0ms	(cbrt.f64 (-.f64 1 (/.f64 y z)))
9.0ms	(cbrt.f64 (-.f64 1 (/.f64 y z)))
7.0ms	(cbrt.f64 (-.f64 1 (/.f64 y z)))

series213.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

122.0ms	(/.f64 (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y))) (.f64 (cbrt.f64 (-.f64 1 (/.f64 y z))) (cbrt.f64 (-.f64 1 (/.f64 y z)))))
32.0ms	(cbrt.f64 (-.f64 1 (/.f64 y z)))
29.0ms	(cbrt.f64 (-.f64 1 (/.f64 y z)))
29.0ms	(cbrt.f64 (-.f64 1 (/.f64 y z)))

simplify138.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	5330	2089

prune286.0ms (7.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	103	11	114

Merged error: 5.2b

Counts

114 → 11

Compiler

Compiled 4310 to 1869 computations (56.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (/.f64 y z))
0.2b	(*.f64 (/.f64 y z) (/.f64 y z))
4.9b	(/.f64 (+.f64 x y) (-.f64 1 (*.f64 (/.f64 y z) (/.f64 y z))))
12.3b	(.f64 (/.f64 (+.f64 x y) (-.f64 1 (.f64 (/.f64 y z) (/.f64 y z)))) (+.f64 1 (/.f64 y z)))

rewrite55.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`*-un-lft-identity_binary64`
81×	`times-frac_binary64`
80×	`add-sqr-sqrt_binary64`
54×	`add-cube-cbrt_binary64`
39×	`associate-l_binary64`
23×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`difference-of-squares_binary64`
17×	`associate-r_binary64`
13×	`pow1_binary64` `swap-sqr_binary64` `distribute-lft-out_binary64`
6×	`add-log-exp_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64`
5×	`associate-/r*_binary64`
4×	`flip3-+_binary64` `associate-/r/_binary64` `associate-/l*_binary64` `flip-+_binary64`
3×	`associate-*r/_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `flip3--_binary64` `flip--_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`pow-prod-up_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-plus_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-sqr_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64`

Counts

4 → 176

Calls

4 calls:

19.0ms	(.f64 (/.f64 (+.f64 x y) (-.f64 1 (.f64 (/.f64 y z) (/.f64 y z)))) (+.f64 1 (/.f64 y z)))
13.0ms	(*.f64 (/.f64 y z) (/.f64 y z))
9.0ms	(/.f64 (+.f64 x y) (-.f64 1 (*.f64 (/.f64 y z) (/.f64 y z))))
7.0ms	(+.f64 1 (/.f64 y z))

series62.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

31.0ms	(.f64 (/.f64 (+.f64 x y) (-.f64 1 (.f64 (/.f64 y z) (/.f64 y z)))) (+.f64 1 (/.f64 y z)))
22.0ms	(/.f64 (+.f64 x y) (-.f64 1 (*.f64 (/.f64 y z) (/.f64 y z))))
6.0ms	(*.f64 (/.f64 y z) (/.f64 y z))
3.0ms	(+.f64 1 (/.f64 y z))

simplify124.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5050	3515

prune131.0ms (3.5%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	188	11	199

Merged error: 5.2b

Counts

199 → 11

Compiler

Compiled 4656 to 2042 computations (56.1% saved)

regimes241.0ms (6.4%)

Compiler: Compiled 976 to 696 computations (28.7% saved)

bsearch1.0ms (0%)

Compiler: Compiled 9 to 8 computations (11.1% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	63	91
1	63	91

end0.0ms (0%)

sample1.3s (35.6%)

Algorithm

1×

intervals

Results

242.0ms

8000×

body

valid

Compiler

Compiled 328 to 218 computations (33.5% saved)

Details

analyze228.0ms (6.1%)

sample15.0ms (0.4%)

simplify207.0ms (5.5%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

rewrite23.0ms (0.6%)

series18.0ms (0.5%)

simplify73.0ms (2%)

prune76.0ms (2%)

localize7.0ms (0.2%)

rewrite57.0ms (1.5%)

series31.0ms (0.8%)

simplify135.0ms (3.6%)

prune192.0ms (5.1%)

localize28.0ms (0.8%)

rewrite57.0ms (1.5%)

series213.0ms (5.7%)

simplify138.0ms (3.7%)

prune286.0ms (7.6%)

localize9.0ms (0.2%)

rewrite55.0ms (1.5%)

series62.0ms (1.7%)

simplify124.0ms (3.3%)

prune131.0ms (3.5%)

regimes241.0ms (6.4%)

bsearch1.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.3s (35.6%)

Profiling