Details

analyze493.0ms (14.1%)

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
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
15.6%	84.3%	0.1%	7
29.6%	70.2%	0.1%	8
36.7%	60.1%	3.3%	9
43.3%	49.5%	7.2%	10
52.1%	39.2%	8.7%	11
57.6%	31.1%	11.3%	12
60.6%	25.6%	13.8%	13
65.2%	20.4%	14.4%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample18.0ms (0.5%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
1.0ms	23×	body	128	invalid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify25.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

52×	`cancel-sign-sub-inv_binary64`
45×	`distribute-rgt-in_binary64`
45×	`sub-neg_binary64`
43×	`associate--r+_binary64`
28×	`unsub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	16	13
2	26	13
3	42	13
4	87	12
5	122	10
6	168	10
7	291	10
8	345	10
9	353	10
10	344	10
11	301	10

prune3.0ms (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 → 2

Alt Table

Status	Error	Program
	0.0b	(+.f64 y (*.f64 x (-.f64 z y)))
▶	0.0b	(+.f64 (.f64 (-.f64 1 x) y) (.f64 x z))

Compiler

Compiled 54 to 34 computations (37% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite30.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
6×	`associate-l_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 34

Calls

2 calls:

5.0ms	(+.f64 (.f64 (-.f64 1 x) y) (.f64 x z))
5.0ms	(*.f64 (-.f64 1 x) y)

Compiler

Compiled 541 to 298 computations (44.9% saved)

series47.0ms (1.3%)

Error

0.0b

Counts

2 → 27

Calls

2 calls:

27.0ms	(+.f64 (.f64 (-.f64 1 x) y) (.f64 x z))
11.0ms	(*.f64 (-.f64 1 x) y)

Compiler

Compiled 535 to 315 computations (41.1% saved)

simplify72.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

532×	`associate-+l+_binary64`
366×	`neg-mul-1_binary64`
350×	`associate-+r+_binary64`
327×	`associate-l_binary64`
256×	`associate-r_binary64`

Counts

61 → 47

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	81	702
1	218	648
2	606	615
3	1619	612
4	4606	612
5	5146	612

prune16.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	46	1	47
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	46	3	49

Error

0.0b

Counts

49 → 3

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 y (*.f64 x (-.f64 z y)))
✓	0.0b	(+.f64 (.f64 (-.f64 1 x) y) (.f64 x z))
	1.3b	(.f64 (.f64 (cbrt.f64 (+.f64 y (.f64 x (-.f64 z y)))) (cbrt.f64 (+.f64 y (.f64 x (-.f64 z y))))) (cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y)))))

Compiler

Compiled 483 to 172 computations (64.4% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite33.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

12×	`cancel-sign-sub-inv_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
8×	`distribute-lft-in_binary64`
8×	`associate-+r+_binary64`

Counts

2 → 49

Calls

2 calls:

5.0ms	(*.f64 x (-.f64 z y))
3.0ms	(+.f64 y (*.f64 x (-.f64 z y)))

Compiler

Compiled 658 to 182 computations (72.3% saved)

series350.0ms (10%)

Error

0.0b

Counts

2 → 33

Calls

2 calls:

322.0ms	(+.f64 y (*.f64 x (-.f64 z y)))
24.0ms	(*.f64 x (-.f64 z y))

Compiler

Compiled 613 to 356 computations (41.9% saved)

simplify79.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

492×	`neg-mul-1_binary64`
382×	`distribute-rgt-in_binary64`
370×	`distribute-lft-in_binary64`
268×	`distribute-rgt-neg-out_binary64`
262×	`exp-prod_binary64`

Counts

82 → 54

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	99	785
1	242	764
2	756	764
3	2262	764
4	4309	764
5	5277	764

prune15.0ms (0.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	54	3	57

Error

0.0b

Counts

57 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 y (*.f64 x (-.f64 z y)))
✓	0.0b	(+.f64 (.f64 (-.f64 1 x) y) (.f64 x z))
▶	1.3b	(.f64 (.f64 (cbrt.f64 (+.f64 y (.f64 x (-.f64 z y)))) (cbrt.f64 (+.f64 y (.f64 x (-.f64 z y))))) (cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y)))))

Compiler

Compiled 352 to 120 computations (65.9% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y))))
0.5b	(cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y))))
0.5b	(cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y))))
0.6b	(.f64 (cbrt.f64 (+.f64 y (.f64 x (-.f64 z y)))) (cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y)))))

rewrite53.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
18×	`cbrt-div_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`

Counts

4 → 87

Calls

4 calls:

11.0ms	(.f64 (cbrt.f64 (+.f64 y (.f64 x (-.f64 z y)))) (cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y)))))
2.0ms	(cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y))))
2.0ms	(cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y))))
2.0ms	(cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y))))

Compiler

Compiled 3222 to 329 computations (89.8% saved)

series518.0ms (14.9%)

Error

0.0b

Counts

4 → 77

Calls

4 calls:

191.0ms	(.f64 (cbrt.f64 (+.f64 y (.f64 x (-.f64 z y)))) (cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y)))))
108.0ms	(cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y))))
80.0ms	(cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y))))
76.0ms	(cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y))))

Compiler

Compiled 12729 to 7957 computations (37.5% saved)

simplify156.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

346×	`times-frac_binary64`
329×	`associate-r_binary64`
255×	`associate-/l*_binary64`
230×	`associate-/r*_binary64`
227×	`associate-l_binary64`

Counts

164 → 131

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	390	6880
1	1211	6486
2	4596	6179
3	4997	6179

prune74.0ms (2.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	130	4	134

Error

0.0b

Counts

134 → 4

Alt Table

Status	Error	Program
▶	34.3b	(.f64 (pow.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 y (.f64 x (-.f64 z y))))) 4) 1) (cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y)))))
✓	0.0b	(+.f64 y (*.f64 x (-.f64 z y)))
✓	0.0b	(+.f64 (.f64 (-.f64 1 x) y) (.f64 x z))
✓	1.3b	(.f64 (.f64 (cbrt.f64 (+.f64 y (.f64 x (-.f64 z y)))) (cbrt.f64 (+.f64 y (.f64 x (-.f64 z y))))) (cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y)))))

Compiler

Compiled 5261 to 1741 computations (66.9% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (pow.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 y (.f64 x (-.f64 z y))))) 4) 1) (cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y)))))
0.4b	(pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y))))) 4)
0.5b	(cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y))))
0.5b	(cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y))))

rewrite102.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

47×	`unpow-prod-down_binary64`
41×	`add-sqr-sqrt_binary64`
24×	`cbrt-prod_binary64`
17×	`associate-l_binary64`
17×	`*-un-lft-identity_binary64`

Counts

4 → 107

Calls

4 calls:

13.0ms	(.f64 (pow.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 y (.f64 x (-.f64 z y))))) 4) 1) (cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y)))))
4.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y))))) 4)
2.0ms	(cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y))))
2.0ms	(cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y))))

Compiler

Compiled 3565 to 956 computations (73.2% saved)

series376.0ms (10.8%)

Error

0.0b

Counts

4 → 74

Calls

4 calls:

140.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y))))) 4)
88.0ms	(cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y))))
82.0ms	(cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y))))
23.0ms	(.f64 (pow.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 y (.f64 x (-.f64 z y))))) 4) 1) (cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y)))))

Compiler

Compiled 7762 to 5303 computations (31.7% saved)

simplify175.0ms (5%)

Algorithm

1×	egg-herbie

Rules

970×	`times-frac_binary64`
248×	`associate-r_binary64`
215×	`associate-l_binary64`
199×	`*-commutative_binary64`
194×	`sqr-pow_binary64`

Counts

181 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	344	5717
1	926	4822
2	2928	4685
3	4821	4607
4	4928	4607

prune72.0ms (2.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	154	4	158

Error

0.0b

Counts

158 → 4

Alt Table

Status	Error	Program
	34.3b	(.f64 (pow.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 y (.f64 x (-.f64 z y))))) 4) 1) (cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y)))))
	0.0b	(+.f64 y (*.f64 x (-.f64 z y)))
	0.0b	(+.f64 (.f64 (-.f64 1 x) y) (.f64 x z))
	1.3b	(.f64 (.f64 (cbrt.f64 (+.f64 y (.f64 x (-.f64 z y)))) (cbrt.f64 (+.f64 y (.f64 x (-.f64 z y))))) (cbrt.f64 (+.f64 y (*.f64 x (-.f64 z y)))))

Compiler

Compiled 3697 to 1511 computations (59.1% saved)

regimes129.0ms (3.7%)

Accuracy

Total 0.0b remaining (69.5%)

Threshold costs 0.0b (69.5%)

Compiler

Compiled 2264 to 1234 computations (45.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	16	13
2	20	13
3	22	13
4	23	13
5	22	13

end0.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

sample614.0ms (17.6%)

Algorithm

1×

intervals

Results

281.0ms	8000×	body	128	valid
24.0ms	632×	body	128	invalid

Compiler

Compiled 104 to 56 computations (46.2% saved)

Iter	Nodes	Cost
0	9	13
1	16	13
2	26	13
3	42	13
4	87	12
5	122	10
6	168	10
7	291	10
8	345	10
9	353	10
10	344	10
11	301	10

Iter	Nodes	Cost
0	9	13
1	16	13
2	26	13
3	42	13
4	87	12
5	122	10
6	168	10
7	291	10
8	345	10
9	353	10
10	344	10
11	301	10

Details

analyze493.0ms (14.1%)

sample18.0ms (0.5%)

simplify25.0ms (0.7%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

rewrite30.0ms (0.9%)

series47.0ms (1.3%)

simplify72.0ms (2.1%)

prune16.0ms (0.5%)

localize4.0ms (0.1%)

rewrite33.0ms (0.9%)

series350.0ms (10%)

simplify79.0ms (2.3%)

prune15.0ms (0.4%)

localize9.0ms (0.3%)

rewrite53.0ms (1.5%)

series518.0ms (14.9%)

simplify156.0ms (4.5%)

prune74.0ms (2.1%)

localize14.0ms (0.4%)

rewrite102.0ms (2.9%)

series376.0ms (10.8%)

simplify175.0ms (5%)

prune72.0ms (2.1%)

regimes129.0ms (3.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample614.0ms (17.6%)

Profiling

Iter	Nodes	Cost
0	9	13
1	16	13
2	26	13
3	42	13
4	87	12
5	122	10
6	168	10
7	291	10
8	345	10
9	353	10
10	344	10
11	301	10