Details

analyze818.0ms (14.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	28
1	28	28
0	3	3
1	3	3

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
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
31.2%	68.6%	0.1%	9
46.8%	44.5%	8.7%	10
51.5%	39%	9.5%	11
57.3%	32.6%	10.1%	12
63.8%	21.6%	14.7%	13
66.2%	18.7%	15.1%	14

Symmetry

(sort x y)

Compiler

Compiled 6 to 6 computations (0% saved)

sample26.0ms (0.5%)

Algorithm

1×

intervals

Results

5.0ms	256×	body	128	valid
1.0ms	22×	body	128	invalid

Compiler

Compiled 11 to 14 computations (-27.3% saved)

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	14	7
1	14	7

prune7.0ms (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

0.0b

Counts

2 → 1

Compiler

Compiled 10 to 10 computations (0% saved)

localize9.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

5×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
4×	`associate-l_binary64`
3×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `associate-r_binary64`
2×	`associate-*l/_binary64`
1×	`pow-prod-down_binary64` `prod-exp_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `flip3-+_binary64` `flip-+_binary64` `distribute-lft-out_binary64` `*-commutative_binary64`

Counts

1 → 21

Calls

1 calls:

9.0ms

(*.f64 (+.f64 x y) z)

Compiler

Compiled 235 to 73 computations (68.9% saved)

series112.0ms (2%)

Error

0.0b

Counts

1 → 15

Calls

1 calls:

104.0ms

(*.f64 (+.f64 x y) z)

Compiler

Compiled 207 to 134 computations (35.3% saved)

simplify104.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	5403	295

prune33.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	33	3	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	4	37

Error

0.0b

Counts

37 → 4

Compiler

Compiled 315 to 95 computations (69.8% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(.f64 (cbrt.f64 (.f64 z (+.f64 y x))) (cbrt.f64 (*.f64 z (+.f64 y x))))
3.0b	(cbrt.f64 (*.f64 z (+.f64 y x)))
3.0b	(cbrt.f64 (*.f64 z (+.f64 y x)))
3.0b	(cbrt.f64 (*.f64 z (+.f64 y x)))

rewrite113.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

20×	`associate-*r/_binary64`
18×	`cbrt-div_binary64`
11×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`pow1/3_binary64` `flip3-+_binary64` `flip-+_binary64`
8×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
7×	`cbrt-prod_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `frac-times_binary64` `swap-sqr_binary64` `associate-l_binary64` `associate-r_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64` `associate-*l/_binary64`
1×	`pow2_binary64` `pow-plus_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 72

Calls

4 calls:

11.0ms	(.f64 (cbrt.f64 (.f64 z (+.f64 y x))) (cbrt.f64 (*.f64 z (+.f64 y x))))
8.0ms	(cbrt.f64 (*.f64 z (+.f64 y x)))
5.0ms	(cbrt.f64 (*.f64 z (+.f64 y x)))
5.0ms	(cbrt.f64 (*.f64 z (+.f64 y x)))

Compiler

Compiled 2027 to 302 computations (85.1% saved)

series1.3s (23.3%)

Error

0.0b

Counts

4 → 60

Calls

4 calls:

405.0ms	(.f64 (cbrt.f64 (.f64 z (+.f64 y x))) (cbrt.f64 (*.f64 z (+.f64 y x))))
287.0ms	(cbrt.f64 (*.f64 z (+.f64 y x)))
271.0ms	(cbrt.f64 (*.f64 z (+.f64 y x)))
268.0ms	(cbrt.f64 (*.f64 z (+.f64 y x)))

Compiler

Compiled 5428 to 3582 computations (34% saved)

simplify104.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5096	2730

prune153.0ms (2.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	132	4	136

Error

0.0b

Counts

136 → 4

Compiler

Compiled 3528 to 971 computations (72.5% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 y x))
0.0b	(sqrt.f64 (+.f64 x y))
0.1b	(*.f64 z (sqrt.f64 (+.f64 y x)))
0.2b	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 z (sqrt.f64 (+.f64 y x))))

rewrite101.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

19×	`*-un-lft-identity_binary64`
18×	`sqrt-div_binary64`
17×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
13×	`pow1_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64`
10×	`associate-r/_binary64` `associate-l*_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`associate-r_binary64`
4×	`pow-prod-down_binary64` `prod-exp_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `frac-times_binary64` `distribute-lft-out_binary64`
2×	`associate-l/_binary64` `-commutative_binary64` `unswap-sqr_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 87

Calls

4 calls:

13.0ms	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 z (sqrt.f64 (+.f64 y x))))
8.0ms	(*.f64 z (sqrt.f64 (+.f64 y x)))
4.0ms	(sqrt.f64 (+.f64 y x))
3.0ms	(sqrt.f64 (+.f64 x y))

Compiler

Compiled 1662 to 347 computations (79.1% saved)

series290.0ms (5.1%)

Error

0.0b

Counts

4 → 42

Calls

4 calls:

91.0ms	(*.f64 z (sqrt.f64 (+.f64 y x)))
86.0ms	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 z (sqrt.f64 (+.f64 y x))))
49.0ms	(sqrt.f64 (+.f64 x y))
41.0ms	(sqrt.f64 (+.f64 y x))

Compiler

Compiled 1280 to 830 computations (35.2% saved)

simplify107.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4987	1394
1	4987	1394

prune88.0ms (1.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	129	4	133

Error

Counts

133 → 4

Compiler

Compiled 1768 to 389 computations (78% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (*.f64 z (fabs.f64 (cbrt.f64 (+.f64 y x)))) (sqrt.f64 (cbrt.f64 (+.f64 y x)))))
0.3b	(*.f64 z (fabs.f64 (cbrt.f64 (+.f64 y x))))
0.5b	(cbrt.f64 (+.f64 y x))
0.5b	(cbrt.f64 (+.f64 y x))

rewrite138.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

16×	`*-un-lft-identity_binary64`
15×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64` `sqrt-div_binary64`
10×	`add-cube-cbrt_binary64` `cbrt-div_binary64` `associate-l_binary64`
8×	`flip3-+_binary64` `flip-+_binary64` `cbrt-prod_binary64` `associate-*r/_binary64`
7×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64`
4×	`add-log-exp_binary64` `associate-r_binary64` `frac-times_binary64` `sqrt-prod_binary64`
3×	`distribute-lft-out_binary64`
2×	`pow1/3_binary64` `-commutative_binary64` `associate-l/_binary64`
1×	`unswap-sqr_binary64`

Counts

4 → 79

Calls

4 calls:

28.0ms	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (*.f64 z (fabs.f64 (cbrt.f64 (+.f64 y x)))) (sqrt.f64 (cbrt.f64 (+.f64 y x)))))
7.0ms	(*.f64 z (fabs.f64 (cbrt.f64 (+.f64 y x))))
6.0ms	(cbrt.f64 (+.f64 y x))
6.0ms	(cbrt.f64 (+.f64 y x))

Compiler

Compiled 2183 to 405 computations (81.4% saved)

series753.0ms (13.4%)

Error

Counts

4 → 44

Calls

4 calls:

398.0ms	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (*.f64 z (fabs.f64 (cbrt.f64 (+.f64 y x)))) (sqrt.f64 (cbrt.f64 (+.f64 y x)))))
108.0ms	(cbrt.f64 (+.f64 y x))
100.0ms	(cbrt.f64 (+.f64 y x))
94.0ms	(*.f64 z (fabs.f64 (cbrt.f64 (+.f64 y x))))

Compiler

Compiled 2993 to 2133 computations (28.7% saved)

simplify101.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4953	2413
1	4953	2413

prune132.0ms (2.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	123	4	127

Error

Counts

127 → 4

Compiler

Compiled 2778 to 545 computations (80.4% saved)

regimes166.0ms (2.9%)

Accuracy

Total 0.0b remaining (83.9%)

Threshold costs 0.0b (83.9%)

Compiler

Compiled 1162 to 771 computations (33.6% saved)

bsearch0.0ms (0%)

simplify16.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	7
1	8	7

Remove

(sort x y)

Compiler

Compiled 10 to 10 computations (0% saved)

end0.0ms (0%)

sample865.0ms (15.4%)

Algorithm

1×

intervals

Results

200.0ms	8000×	body	128	valid
15.0ms	632×	body	128	invalid

Compiler

Compiled 239 to 161 computations (32.6% saved)

Details

analyze818.0ms (14.5%)

sample26.0ms (0.5%)

simplify14.0ms (0.3%)

prune7.0ms (0.1%)

localize9.0ms (0.2%)

rewrite26.0ms (0.5%)

series112.0ms (2%)

simplify104.0ms (1.8%)

prune33.0ms (0.6%)

localize8.0ms (0.1%)

rewrite113.0ms (2%)

series1.3s (23.3%)

simplify104.0ms (1.8%)

prune153.0ms (2.7%)

localize15.0ms (0.3%)

rewrite101.0ms (1.8%)

series290.0ms (5.1%)

simplify107.0ms (1.9%)

prune88.0ms (1.6%)

localize19.0ms (0.3%)

rewrite138.0ms (2.5%)

series753.0ms (13.4%)

simplify101.0ms (1.8%)

prune132.0ms (2.4%)

regimes166.0ms (2.9%)

bsearch0.0ms (0%)

simplify16.0ms (0.3%)

end0.0ms (0%)

sample865.0ms (15.4%)

Profiling