Details

analyze280.0ms (7.5%)

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
12.5%	87.4%	0.1%	5
31.2%	68.7%	0.1%	6
46.8%	53.1%	0.1%	7
60.9%	39%	0.1%	8
67.9%	31.2%	0.9%	9
74.5%	22.2%	3.2%	10
77.9%	17.2%	5%	11
81.1%	11.8%	7.1%	12
82.7%	9%	8.3%	13
84.3%	6.1%	9.7%	14

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample19.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
0.0ms	10×	body	128	invalid

Compiler

Compiled 29 to 21 computations (27.6% saved)

simplify101.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

985×	`distribute-rgt-in_binary64`
960×	`distribute-lft-in_binary64`
653×	`associate-/l*_binary64`
602×	`cube-prod_binary64`
535×	`associate-/l/_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	22	16
2	28	16
3	69	16
4	100	16
5	206	16
6	379	16
7	360	16
8	684	16
9	768	16
10	860	16
11	1008	16
12	1175	16
13	1412	16
14	2748	16
15	3005	16
16	4321	16
17	5574	16

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

5.6b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	5.6b	(/.f64 (*.f64 x (+.f64 (/.f64 x y) 1)) (+.f64 x 1))

Compiler

Compiled 26 to 18 computations (30.8% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.1b	(*.f64 x (+.f64 (/.f64 x y) 1))
5.2b	(/.f64 (*.f64 x (+.f64 (/.f64 x y) 1)) (+.f64 x 1))

rewrite58.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

12×	`*-un-lft-identity_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 50

Calls

2 calls:

8.0ms	(/.f64 (*.f64 x (+.f64 (/.f64 x y) 1)) (+.f64 x 1))
7.0ms	(*.f64 x (+.f64 (/.f64 x y) 1))

Compiler

Compiled 890 to 521 computations (41.5% saved)

series52.0ms (1.4%)

Error

0.0b

Counts

2 → 30

Calls

2 calls:

23.0ms	(/.f64 (*.f64 x (+.f64 (/.f64 x y) 1)) (+.f64 x 1))
15.0ms	(*.f64 x (+.f64 (/.f64 x y) 1))

Compiler

Compiled 737 to 510 computations (30.8% saved)

simplify108.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

697×	`associate-/l*_binary64`
349×	`associate-l_binary64`
324×	`distribute-rgt-in_binary64`
311×	`associate-*l/_binary64`
282×	`distribute-lft-in_binary64`

Counts

80 → 61

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	129	1377
1	359	1231
2	1317	1205
3	3995	1202
4	4565	1202
5	4993	1202
6	4943	1202

prune33.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	56	5	61
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	56	6	62

Error

0.0b

Counts

62 → 6

Alt Table

Status	Error	Program
	41.7b	(-.f64 (+.f64 (/.f64 x y) 1) (/.f64 1 y))
▶	6.9b	(/.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (+.f64 (/.f64 x y) 1) (cbrt.f64 x))) (+.f64 x 1))
	24.9b	(/.f64 (/.f64 (-.f64 (/.f64 (pow.f64 x 3) (*.f64 y y)) x) (-.f64 (/.f64 x y) 1)) (+.f64 x 1))
✓	5.6b	(/.f64 (*.f64 x (+.f64 (/.f64 x y) 1)) (+.f64 x 1))
	12.2b	(.f64 (/.f64 (+.f64 x (/.f64 (.f64 x x) y)) (-.f64 (*.f64 x x) 1)) (-.f64 x 1))
	29.6b	(.f64 (sqrt.f64 (.f64 (+.f64 (/.f64 x y) 1) (/.f64 x (+.f64 x 1)))) (sqrt.f64 (*.f64 (+.f64 (/.f64 x y) 1) (/.f64 x (+.f64 x 1)))))

Compiler

Compiled 844 to 452 computations (46.4% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 x)
0.7b	(cbrt.f64 x)
0.7b	(cbrt.f64 x)
5.2b	(/.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (+.f64 (/.f64 x y) 1) (cbrt.f64 x))) (+.f64 x 1))

rewrite47.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

22×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`
13×	`*-un-lft-identity_binary64`
9×	`cbrt-prod_binary64`
9×	`add-sqr-sqrt_binary64`

Counts

4 → 66

Calls

4 calls:

14.0ms	(/.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (+.f64 (/.f64 x y) 1) (cbrt.f64 x))) (+.f64 x 1))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

Compiler

Compiled 1679 to 738 computations (56% saved)

series86.0ms (2.3%)

Error

0.0b

Counts

4 → 27

Calls

4 calls:

41.0ms	(/.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (+.f64 (/.f64 x y) 1) (cbrt.f64 x))) (+.f64 x 1))
12.0ms	(cbrt.f64 x)
12.0ms	(cbrt.f64 x)
11.0ms	(cbrt.f64 x)

Compiler

Compiled 1219 to 862 computations (29.3% saved)

simplify67.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

529×	`associate-/l/_binary64`
468×	`distribute-rgt-in_binary64`
429×	`distribute-lft-in_binary64`
156×	`sub-neg_binary64`
144×	`associate-l_binary64`

Counts

93 → 66

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	164	1941
1	462	1257
2	1911	1225
3	5114	1225

prune25.0ms (0.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	66	6	72

Error

0.0b

Counts

72 → 6

Alt Table

Status	Error	Program
	41.7b	(-.f64 (+.f64 (/.f64 x y) 1) (/.f64 1 y))
✓	6.9b	(/.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (+.f64 (/.f64 x y) 1) (cbrt.f64 x))) (+.f64 x 1))
	24.9b	(/.f64 (/.f64 (-.f64 (/.f64 (pow.f64 x 3) (*.f64 y y)) x) (-.f64 (/.f64 x y) 1)) (+.f64 x 1))
✓	5.6b	(/.f64 (*.f64 x (+.f64 (/.f64 x y) 1)) (+.f64 x 1))
▶	12.2b	(.f64 (/.f64 (+.f64 x (/.f64 (.f64 x x) y)) (-.f64 (*.f64 x x) 1)) (-.f64 x 1))
	29.6b	(.f64 (sqrt.f64 (.f64 (+.f64 (/.f64 x y) 1) (/.f64 x (+.f64 x 1)))) (sqrt.f64 (*.f64 (+.f64 (/.f64 x y) 1) (/.f64 x (+.f64 x 1)))))

Compiler

Compiled 974 to 512 computations (47.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 (*.f64 x x) y))
0.1b	(.f64 (/.f64 (+.f64 x (/.f64 (.f64 x x) y)) (-.f64 (*.f64 x x) 1)) (-.f64 x 1))
9.0b	(/.f64 (+.f64 x (/.f64 (.f64 x x) y)) (-.f64 (.f64 x x) 1))
9.6b	(/.f64 (*.f64 x x) y)

rewrite122.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

72×	`*-un-lft-identity_binary64`
52×	`times-frac_binary64`
50×	`add-sqr-sqrt_binary64`
32×	`add-cube-cbrt_binary64`
30×	`associate-l_binary64`

Counts

4 → 148

Calls

4 calls:

17.0ms	(.f64 (/.f64 (+.f64 x (/.f64 (.f64 x x) y)) (-.f64 (*.f64 x x) 1)) (-.f64 x 1))
8.0ms	(/.f64 (+.f64 x (/.f64 (.f64 x x) y)) (-.f64 (.f64 x x) 1))
3.0ms	(+.f64 x (/.f64 (*.f64 x x) y))
3.0ms	(/.f64 (*.f64 x x) y)

Compiler

Compiled 3583 to 1403 computations (60.8% saved)

series111.0ms (3%)

Error

0.0b

Counts

4 → 51

Calls

4 calls:

34.0ms	(.f64 (/.f64 (+.f64 x (/.f64 (.f64 x x) y)) (-.f64 (*.f64 x x) 1)) (-.f64 x 1))
28.0ms	(/.f64 (+.f64 x (/.f64 (.f64 x x) y)) (-.f64 (.f64 x x) 1))
18.0ms	(+.f64 x (/.f64 (*.f64 x x) y))
14.0ms	(/.f64 (*.f64 x x) y)

Compiler

Compiled 1839 to 1319 computations (28.3% saved)

simplify152.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

493×	`distribute-rgt-in_binary64`
416×	`distribute-lft-in_binary64`
365×	`associate-/l/_binary64`
168×	`cancel-sign-sub-inv_binary64`
149×	`associate-/l*_binary64`

Counts

199 → 165

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	237	4725
1	589	4412
2	2193	4138
3	4716	4135
4	4959	4135

prune66.0ms (1.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	165	6	171

Error

0.0b

Counts

171 → 6

Alt Table

Status	Error	Program
	41.7b	(+.f64 1 (/.f64 (+.f64 x -1) y))
✓	6.9b	(/.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (+.f64 (/.f64 x y) 1) (cbrt.f64 x))) (+.f64 x 1))
▶	24.9b	(/.f64 (/.f64 (-.f64 (/.f64 (pow.f64 x 3) (*.f64 y y)) x) (-.f64 (/.f64 x y) 1)) (+.f64 x 1))
✓	5.6b	(/.f64 (*.f64 x (+.f64 (/.f64 x y) 1)) (+.f64 x 1))
✓	12.2b	(.f64 (/.f64 (+.f64 x (/.f64 (.f64 x x) y)) (-.f64 (*.f64 x x) 1)) (-.f64 x 1))
	29.6b	(.f64 (sqrt.f64 (.f64 (+.f64 (/.f64 x y) 1) (/.f64 x (+.f64 x 1)))) (sqrt.f64 (*.f64 (+.f64 (/.f64 x y) 1) (/.f64 x (+.f64 x 1)))))

Compiler

Compiled 2663 to 1128 computations (57.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (pow.f64 x 3) (*.f64 y y)) x)
4.5b	(/.f64 (-.f64 (/.f64 (pow.f64 x 3) (*.f64 y y)) x) (-.f64 (/.f64 x y) 1))
5.2b	(/.f64 (/.f64 (-.f64 (/.f64 (pow.f64 x 3) (*.f64 y y)) x) (-.f64 (/.f64 x y) 1)) (+.f64 x 1))
17.5b	(/.f64 (pow.f64 x 3) (*.f64 y y))

rewrite441.0ms (11.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

1392×	`add-sqr-sqrt_binary64`
1349×	`times-frac_binary64`
767×	`*-un-lft-identity_binary64`
530×	`difference-of-squares_binary64`
229×	`add-cube-cbrt_binary64`

Counts

4 → 691

Calls

4 calls:

31.0ms	(/.f64 (/.f64 (-.f64 (/.f64 (pow.f64 x 3) (*.f64 y y)) x) (-.f64 (/.f64 x y) 1)) (+.f64 x 1))
15.0ms	(/.f64 (-.f64 (/.f64 (pow.f64 x 3) (*.f64 y y)) x) (-.f64 (/.f64 x y) 1))
12.0ms	(-.f64 (/.f64 (pow.f64 x 3) (*.f64 y y)) x)
5.0ms	(/.f64 (pow.f64 x 3) (*.f64 y y))

Compiler

Compiled 14666 to 8284 computations (43.5% saved)

series108.0ms (2.9%)

Error

0.0b

Counts

4 → 48

Calls

4 calls:

33.0ms	(/.f64 (/.f64 (-.f64 (/.f64 (pow.f64 x 3) (*.f64 y y)) x) (-.f64 (/.f64 x y) 1)) (+.f64 x 1))
25.0ms	(/.f64 (-.f64 (/.f64 (pow.f64 x 3) (*.f64 y y)) x) (-.f64 (/.f64 x y) 1))
22.0ms	(-.f64 (/.f64 (pow.f64 x 3) (*.f64 y y)) x)
15.0ms	(/.f64 (pow.f64 x 3) (*.f64 y y))

Compiler

Compiled 1589 to 1129 computations (28.9% saved)

simplify696.0ms (18.6%)

Algorithm

1×	egg-herbie

Rules

574×	`div-sub_binary64`
544×	`associate-/l/_binary64`
332×	`associate-/r*_binary64`
192×	`associate-/l*_binary64`
152×	`times-frac_binary64`

Counts

739 → 708

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	577	34712
1	1374	34386
2	4292	33577
3	4957	33577

prune201.0ms (5.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	707	1	708
Fresh	0	2	2
Picked	1	0	1
Done	0	3	3
Total	708	6	714

Error

Counts

714 → 6

Alt Table

Status	Error	Program
	41.7b	(+.f64 1 (/.f64 (+.f64 x -1) y))
	6.9b	(/.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (+.f64 (/.f64 x y) 1) (cbrt.f64 x))) (+.f64 x 1))
	5.6b	(/.f64 (*.f64 x (+.f64 (/.f64 x y) 1)) (+.f64 x 1))
	12.2b	(.f64 (/.f64 (+.f64 x (/.f64 (.f64 x x) y)) (-.f64 (*.f64 x x) 1)) (-.f64 x 1))
	20.4b	(/.f64 (/.f64 (-.f64 (/.f64 1 (/.f64 y (/.f64 (pow.f64 x 3) y))) x) (-.f64 (/.f64 x y) 1)) (+.f64 x 1))
	29.6b	(.f64 (sqrt.f64 (.f64 (+.f64 (/.f64 x y) 1) (/.f64 x (+.f64 x 1)))) (sqrt.f64 (*.f64 (+.f64 (/.f64 x y) 1) (/.f64 x (+.f64 x 1)))))

Compiler

Compiled 9834 to 5280 computations (46.3% saved)

regimes302.0ms (8.1%)

Accuracy

Total 0.1b remaining (78.6%)

Threshold costs 0.1b (78.6%)

Compiler

Compiled 5549 to 3739 computations (32.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	13	16
2	12	16

end0.0ms (0%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

sample631.0ms (16.8%)

Algorithm

1×

intervals

Results

321.0ms	8000×	body	128	valid
11.0ms	285×	body	128	invalid

Compiler

Compiled 140 to 94 computations (32.9% saved)

Details

analyze280.0ms (7.5%)

sample19.0ms (0.5%)

simplify101.0ms (2.7%)

prune1.0ms (0%)

localize6.0ms (0.2%)

rewrite58.0ms (1.6%)

series52.0ms (1.4%)

simplify108.0ms (2.9%)

prune33.0ms (0.9%)

localize11.0ms (0.3%)

rewrite47.0ms (1.2%)

series86.0ms (2.3%)

simplify67.0ms (1.8%)

prune25.0ms (0.7%)

localize10.0ms (0.3%)

rewrite122.0ms (3.3%)

series111.0ms (3%)

simplify152.0ms (4.1%)

prune66.0ms (1.8%)

localize11.0ms (0.3%)

rewrite441.0ms (11.8%)

series108.0ms (2.9%)

simplify696.0ms (18.6%)

prune201.0ms (5.3%)

regimes302.0ms (8.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample631.0ms (16.8%)

Profiling