Details

analyze361.0ms (9.8%)

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
21.8%	78%	0.1%	6
26.5%	73.3%	0.1%	7
32%	67.9%	0.1%	8
46.4%	52.7%	0.9%	9
50.9%	47.2%	1.9%	10
54.3%	43.3%	2.4%	11
62.1%	32.5%	5.4%	12
64.3%	28.1%	7.6%	13
66.3%	24.6%	9.2%	14

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample20.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	37×	body	128	invalid

Compiler

Compiled 25 to 24 computations (4% saved)

simplify143.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	738	15
1	738	15

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

Error

0.1b

Counts

2 → 2

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
0.0b	(/.f64 (+.f64 x 4) y)
3.4b	(*.f64 (/.f64 x y) z)

rewrite26.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64_78`
25×	`add-sqr-sqrt_binary64_100`
22×	`times-frac_binary64_84`
20×	`add-cube-cbrt_binary64_113`
13×	`associate-l_binary64_19`
10×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
5×	`add-log-exp_binary64_117` `pow1_binary64_139`
4×	`associate-/l*_binary64_23` `distribute-lft-out_binary64_29`
3×	`associate-r_binary64_18` `associate-l/_binary64_21` `associate-/r_binary64_22`
2×	`cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `div-inv_binary64_75` `unswap-sqr_binary64_46` `associate-/l/_binary64_25`
1×	`*-commutative_binary64_9` `flip-+_binary64_52` `frac-sub_binary64_87` `flip3--_binary64_82` `diff-log_binary64_170` `frac-2neg_binary64_89` `flip--_binary64_53` `pow-prod-down_binary64_149` `clear-num_binary64_77` `cancel-sign-sub-inv_binary64_44` `sub-div_binary64_85` `sub-neg_binary64_71` `flip3-+_binary64_81`

Counts

3 → 79

Calls

3 calls:

9.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
6.0ms	(*.f64 (/.f64 x y) z)
5.0ms	(/.f64 (+.f64 x 4) y)

series76.0ms (2.1%)

Counts

3 → 9

Calls

3 calls:

37.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
21.0ms	(*.f64 (/.f64 x y) z)
17.0ms	(/.f64 (+.f64 x 4) y)

simplify85.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4926	1165
1	4926	1165

prune85.0ms (2.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	82	6	88
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	83	7	90

Error

Counts

90 → 7

Compiler

Compiled 1674 to 835 computations (50.1% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 y (+.f64 x 4))
0.0b	(-.f64 (/.f64 1 (/.f64 y (+.f64 x 4))) (*.f64 (/.f64 x y) z))
0.1b	(/.f64 1 (/.f64 y (+.f64 x 4)))
3.4b	(*.f64 (/.f64 x y) z)

rewrite57.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

124×	`times-frac_binary64_84`
104×	`*-un-lft-identity_binary64_78`
77×	`add-sqr-sqrt_binary64_100`
72×	`add-cube-cbrt_binary64_113`
22×	`associate-/r*_binary64_22` `add-exp-log_binary64_116`
16×	`add-cbrt-cube_binary64_114` `distribute-lft-out_binary64_29`
13×	`associate-l_binary64_19`
11×	`associate-/r/_binary64_24`
9×	`div-exp_binary64_129`
7×	`div-inv_binary64_75` `pow1_binary64_139`
6×	`add-log-exp_binary64_117` `associate-/l*_binary64_23`
5×	`cbrt-undiv_binary64_112` `flip-+_binary64_52` `flip3-+_binary64_81`
3×	`associate-r_binary64_18`
2×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `frac-2neg_binary64_89` `1-exp_binary64_122` `rec-exp_binary64_128` `associate-*l/_binary64_21` `unswap-sqr_binary64_46` `clear-num_binary64_77`
1×	`*-commutative_binary64_9` `inv-pow_binary64_163` `frac-sub_binary64_87` `flip3--_binary64_82` `diff-log_binary64_170` `pow-flip_binary64_152` `flip--_binary64_53` `pow-prod-down_binary64_149` `cancel-sign-sub-inv_binary64_44` `sub-neg_binary64_71`

Counts

4 → 174

Calls

4 calls:

20.0ms	(-.f64 (/.f64 1 (/.f64 y (+.f64 x 4))) (*.f64 (/.f64 x y) z))
8.0ms	(*.f64 (/.f64 x y) z)
8.0ms	(/.f64 1 (/.f64 y (+.f64 x 4)))
5.0ms	(/.f64 y (+.f64 x 4))

series104.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(-.f64 (/.f64 1 (/.f64 y (+.f64 x 4))) (*.f64 (/.f64 x y) z))
24.0ms	(/.f64 y (+.f64 x 4))
21.0ms	(*.f64 (/.f64 x y) z)
18.0ms	(/.f64 1 (/.f64 y (+.f64 x 4)))

simplify105.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4962	2889
1	4962	2889

prune177.0ms (4.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	185	1	186
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	186	7	193

Error

Counts

193 → 7

Compiler

Compiled 3873 to 2091 computations (46% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (/.f64 1 y) (/.f64 1 (+.f64 x 4))) (*.f64 (/.f64 x y) z))
0.0b	(/.f64 1 (+.f64 x 4))
0.1b	(/.f64 (/.f64 1 y) (/.f64 1 (+.f64 x 4)))
3.4b	(*.f64 (/.f64 x y) z)

rewrite142.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Rules

595×	`times-frac_binary64_84`
358×	`*-un-lft-identity_binary64_78`
271×	`add-sqr-sqrt_binary64_100`
266×	`add-cube-cbrt_binary64_113`
53×	`add-exp-log_binary64_116`
46×	`distribute-lft-out_binary64_29`
36×	`div-inv_binary64_75`
35×	`div-exp_binary64_129`
31×	`associate-/r/_binary64_24`
23×	`add-cbrt-cube_binary64_114`
22×	`associate-/r*_binary64_22`
16×	`associate-/l*_binary64_23`
15×	`flip-+_binary64_52` `flip3-+_binary64_81`
13×	`associate-l_binary64_19`
10×	`cbrt-undiv_binary64_112`
9×	`1-exp_binary64_122` `rec-exp_binary64_128`
7×	`pow1_binary64_139`
6×	`add-log-exp_binary64_117`
3×	`associate-r_binary64_18`
2×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `frac-2neg_binary64_89` `associate-*l/_binary64_21` `unswap-sqr_binary64_46` `clear-num_binary64_77`
1×	`*-commutative_binary64_9` `inv-pow_binary64_163` `frac-sub_binary64_87` `flip3--_binary64_82` `diff-log_binary64_170` `pow-flip_binary64_152` `flip--_binary64_53` `pow-prod-down_binary64_149` `cancel-sign-sub-inv_binary64_44` `associate-/l/_binary64_25` `sub-neg_binary64_71`

Counts

4 → 379

Calls

4 calls:

67.0ms	(-.f64 (/.f64 (/.f64 1 y) (/.f64 1 (+.f64 x 4))) (*.f64 (/.f64 x y) z))
17.0ms	(/.f64 (/.f64 1 y) (/.f64 1 (+.f64 x 4)))
7.0ms	(*.f64 (/.f64 x y) z)
5.0ms	(/.f64 1 (+.f64 x 4))

series92.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(-.f64 (/.f64 (/.f64 1 y) (/.f64 1 (+.f64 x 4))) (*.f64 (/.f64 x y) z))
22.0ms	(*.f64 (/.f64 x y) z)
19.0ms	(/.f64 (/.f64 1 y) (/.f64 1 (+.f64 x 4)))
8.0ms	(/.f64 1 (+.f64 x 4))

simplify152.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

391 → 391

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4931	8307
1	4931	8307

prune547.0ms (14.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	391	0	391
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	391	7	398

Error

Counts

398 → 7

Compiler

Compiled 9228 to 5486 computations (40.6% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.7b	(.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 z (cbrt.f64 (/.f64 x y))))
11.4b	(cbrt.f64 (/.f64 x y))
11.4b	(cbrt.f64 (/.f64 x y))
11.4b	(cbrt.f64 (/.f64 x y))

rewrite29.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`cbrt-prod_binary64_109`
27×	`times-frac_binary64_84`
25×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
16×	`add-exp-log_binary64_116` `pow1_binary64_139`
15×	`cbrt-div_binary64_110`
10×	`add-cbrt-cube_binary64_114`
8×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-prod-down_binary64_149`
7×	`associate-*r/_binary64_20`
5×	`frac-times_binary64_88` `associate-*l/_binary64_21`
4×	`add-log-exp_binary64_117`
3×	`pow1/3_binary64_160` `div-inv_binary64_75`
1×	`-commutative_binary64_9` `associate-l_binary64_19` `associate-r*_binary64_18`

Counts

4 → 95

Calls

4 calls:

14.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 z (cbrt.f64 (/.f64 x y))))
2.0ms	(cbrt.f64 (/.f64 x y))
2.0ms	(cbrt.f64 (/.f64 x y))
2.0ms	(cbrt.f64 (/.f64 x y))

series175.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

51.0ms	(cbrt.f64 (/.f64 x y))
49.0ms	(cbrt.f64 (/.f64 x y))
49.0ms	(cbrt.f64 (/.f64 x y))
26.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 z (cbrt.f64 (/.f64 x y))))

simplify65.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5024	1313

prune97.0ms (2.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	107	7	114

Error

Counts

114 → 7

Compiler

Compiled 2694 to 886 computations (67.1% saved)

regimes199.0ms (5.4%)

Accuracy

Total 0.8b remaining (99.1%)

Threshold costs 0.8b (99.1%)

Compiler

Compiled 1572 to 1166 computations (25.8% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 11 to 9 computations (18.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	80	80
1	80	80

end0.0ms (0%)

sample898.0ms (24.3%)

Algorithm

1×

intervals

Results

330.0ms	8000×	body	128	valid
46.0ms	1147×	body	128	invalid

Compiler

Compiled 370 to 268 computations (27.6% saved)

Details

analyze361.0ms (9.8%)

sample20.0ms (0.5%)

simplify143.0ms (3.9%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite26.0ms (0.7%)

series76.0ms (2.1%)

simplify85.0ms (2.3%)

prune85.0ms (2.3%)

localize10.0ms (0.3%)

rewrite57.0ms (1.5%)

series104.0ms (2.8%)

simplify105.0ms (2.8%)

prune177.0ms (4.8%)

localize11.0ms (0.3%)

rewrite142.0ms (3.9%)

series92.0ms (2.5%)

simplify152.0ms (4.1%)

prune547.0ms (14.8%)

localize13.0ms (0.4%)

rewrite29.0ms (0.8%)

series175.0ms (4.7%)

simplify65.0ms (1.8%)

prune97.0ms (2.6%)

regimes199.0ms (5.4%)

bsearch2.0ms (0.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample898.0ms (24.3%)

Profiling