Details

analyze218.0ms (7.8%)

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
25%	74.9%	0.1%	6
34.3%	40.6%	25.1%	7
35.9%	39%	25.1%	8
42.1%	32.8%	25.1%	9
42.9%	19.5%	37.6%	10
43.3%	19.1%	37.6%	11
45%	17.5%	37.6%	12
45.1%	10.3%	44.6%	13
45.2%	10.2%	44.6%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample29.0ms (1.1%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
2.0ms	38×	body	128	nan
1.0ms	18×	body	128	invalid

Compiler

Compiled 30 to 24 computations (20% saved)

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
2×	`associate-r_binary64`
2×	`associate-l_binary64`
2×	`distribute-lft-in_binary64`
2×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	12
1	23	12
2	31	12
3	31	12
4	29	12

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

0.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.2b	(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))

Compiler

Compiled 33 to 24 computations (27.3% saved)

localize27.0ms (1%)

Local error

Found 2 expressions with local error:

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

rewrite26.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

9×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
4×	`sqrt-prod_binary64`

Counts

2 → 33

Calls

2 calls:

4.0ms	(*.f64 y (sqrt.f64 z))
2.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))

Compiler

Compiled 426 to 171 computations (59.9% saved)

series32.0ms (1.1%)

Error

0.2b

Counts

2 → 21

Calls

2 calls:

18.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))
11.0ms	(*.f64 y (sqrt.f64 z))

Compiler

Compiled 435 to 318 computations (26.9% saved)

simplify107.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

548×	`distribute-rgt-in_binary64`
546×	`unsub-neg_binary64`
457×	`distribute-lft-in_binary64`
315×	`distribute-neg-out_binary64`
291×	`sub-neg_binary64`

Counts

54 → 22

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	502
1	150	483
2	391	481
3	842	481
4	1467	481
5	2634	481
6	3198	481
7	4774	481
8	4834	481

prune13.0ms (0.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	16	6	22
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	16	7	23

Error

0.0b

Counts

23 → 7

Alt Table

Status	Error	Program
✓	0.2b	(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
	30.7b	(.f64 1/2 (/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y z))) (-.f64 x (*.f64 y (sqrt.f64 z)))))
	32.2b	(.f64 1/2 (.f64 (sqrt.f64 (+.f64 (.f64 y (sqrt.f64 z)) x)) (sqrt.f64 (+.f64 (.f64 y (sqrt.f64 z)) x))))
	1.3b	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 y (sqrt.f64 z)) x)) (cbrt.f64 (+.f64 (.f64 y (sqrt.f64 z)) x))) (cbrt.f64 (+.f64 (.f64 y (sqrt.f64 z)) x))))
▶	0.4b	(.f64 1/2 (+.f64 x (.f64 (*.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))))
	31.8b	(.f64 1/2 (+.f64 x (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 z) (sqrt.f64 y)))))
	0.7b	(.f64 1/2 (+.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (sqrt.f64 z) (cbrt.f64 y)))))

Compiler

Compiled 445 to 223 computations (49.9% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 y (fabs.f64 (cbrt.f64 z)))
0.3b	(.f64 (.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))
0.6b	(cbrt.f64 z)
0.6b	(cbrt.f64 z)

rewrite77.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

25×	`add-sqr-sqrt_binary64`
20×	`associate-r_binary64`
15×	`cbrt-prod_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`

Counts

4 → 76

Calls

4 calls:

6.0ms	(.f64 (.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))
5.0ms	(*.f64 y (fabs.f64 (cbrt.f64 z)))
1.0ms	(cbrt.f64 z)
1.0ms	(cbrt.f64 z)

Compiler

Compiled 1364 to 476 computations (65.1% saved)

series79.0ms (2.8%)

Error

0.0b

Counts

4 → 18

Calls

4 calls:

37.0ms	(.f64 (.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))
14.0ms	(*.f64 y (fabs.f64 (cbrt.f64 z)))
12.0ms	(cbrt.f64 z)
12.0ms	(cbrt.f64 z)

Compiler

Compiled 772 to 598 computations (22.5% saved)

simplify98.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

469×	`associate-/l/_binary64`
434×	`*-commutative_binary64`
346×	`associate-+l+_binary64`
284×	`associate-+r+_binary64`
265×	`sqr-pow_binary64`

Counts

94 → 76

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	106	1156
1	220	896
2	647	849
3	858	763
4	1470	749
5	3175	749
6	4881	749
7	4908	749

prune49.0ms (1.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	72	4	76
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	72	11	83

Error

0.0b

Counts

83 → 11

Alt Table

Status	Error	Program
	0.7b	(.f64 1/2 (+.f64 x (.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 y))) (sqrt.f64 (cbrt.f64 z)))))
	30.7b	(.f64 1/2 (/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y z))) (-.f64 x (*.f64 y (sqrt.f64 z)))))
	29.9b	(.f64 1/2 (+.f64 x (.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 z) y)) (sqrt.f64 (*.f64 (cbrt.f64 z) y))) (sqrt.f64 (cbrt.f64 z)))))
	1.3b	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 y (sqrt.f64 z)) x)) (cbrt.f64 (+.f64 (.f64 y (sqrt.f64 z)) x))) (cbrt.f64 (+.f64 (.f64 y (sqrt.f64 z)) x))))
	1.7b	(.f64 1/2 (+.f64 x (.f64 (.f64 (.f64 (cbrt.f64 z) y) (*.f64 (cbrt.f64 (pow.f64 z 1/6)) (cbrt.f64 (pow.f64 z 1/6)))) (cbrt.f64 (sqrt.f64 (cbrt.f64 z))))))
	0.7b	(.f64 1/2 (+.f64 x (.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z)))) (cbrt.f64 (fabs.f64 (cbrt.f64 z)))) (sqrt.f64 (cbrt.f64 z)))))
✓	0.2b	(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
	32.2b	(.f64 1/2 (.f64 (sqrt.f64 (+.f64 (.f64 y (sqrt.f64 z)) x)) (sqrt.f64 (+.f64 (.f64 y (sqrt.f64 z)) x))))
✓	0.4b	(.f64 1/2 (+.f64 x (.f64 (*.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))))
	31.8b	(.f64 1/2 (+.f64 x (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 z) (sqrt.f64 y)))))
▶	0.7b	(.f64 1/2 (+.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (sqrt.f64 z) (cbrt.f64 y)))))

Compiler

Compiled 1108 to 579 computations (47.7% saved)

localize56.0ms (2%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)

rewrite127.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`

Counts

4 → 73

Calls

4 calls:

5.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)

Compiler

Compiled 1354 to 438 computations (67.7% saved)

series67.0ms (2.4%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

21.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
15.0ms	(cbrt.f64 y)
12.0ms	(cbrt.f64 y)
12.0ms	(cbrt.f64 y)

Compiler

Compiled 639 to 443 computations (30.7% saved)

simplify86.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

735×	`log-prod_binary64`
577×	`distribute-rgt-in_binary64`
538×	`distribute-lft-in_binary64`
525×	`unswap-sqr_binary64`
287×	`associate-l_binary64`

Counts

85 → 64

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	54	624
1	94	576
2	292	556
3	763	542
4	1759	418
5	4280	418
6	4543	418
7	4810	418

prune37.0ms (1.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	64	11	75

Error

0.0b

Counts

75 → 11

Alt Table

Status	Error	Program
▶	0.7b	(.f64 1/2 (+.f64 x (.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 y))) (sqrt.f64 (cbrt.f64 z)))))
	30.7b	(.f64 1/2 (/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y z))) (-.f64 x (*.f64 y (sqrt.f64 z)))))
	1.0b	(.f64 1/2 (+.f64 x (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 y)) 5) (cbrt.f64 (cbrt.f64 y))) (.f64 (sqrt.f64 z) (cbrt.f64 y)))))
	1.3b	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 y (sqrt.f64 z)) x)) (cbrt.f64 (+.f64 (.f64 y (sqrt.f64 z)) x))) (cbrt.f64 (+.f64 (.f64 y (sqrt.f64 z)) x))))
	31.9b	(.f64 1/2 (+.f64 x (.f64 (.f64 (cbrt.f64 (sqrt.f64 y)) (sqrt.f64 y)) (.f64 (sqrt.f64 z) (cbrt.f64 y)))))
✓	0.4b	(.f64 1/2 (+.f64 x (.f64 (*.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))))
	0.7b	(.f64 1/2 (+.f64 x (.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z)))) (cbrt.f64 (fabs.f64 (cbrt.f64 z)))) (sqrt.f64 (cbrt.f64 z)))))
✓	0.2b	(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
	32.2b	(.f64 1/2 (.f64 (sqrt.f64 (+.f64 (.f64 y (sqrt.f64 z)) x)) (sqrt.f64 (+.f64 (.f64 y (sqrt.f64 z)) x))))
	31.8b	(.f64 1/2 (+.f64 x (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 z) (sqrt.f64 y)))))
✓	0.7b	(.f64 1/2 (+.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (sqrt.f64 z) (cbrt.f64 y)))))

Compiler

Compiled 921 to 470 computations (49% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 z)
0.6b	(cbrt.f64 z)

rewrite51.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

12×	`cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

4 → 44

Calls

4 calls:

1.0ms	(cbrt.f64 z)
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 z)

Compiler

Compiled 1023 to 330 computations (67.7% saved)

series59.0ms (2.1%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

14.0ms	(cbrt.f64 z)
12.0ms	(cbrt.f64 z)
12.0ms	(cbrt.f64 y)
12.0ms	(cbrt.f64 y)

Compiler

Compiled 775 to 491 computations (36.6% saved)

simplify69.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

608×	`log-prod_binary64`
434×	`distribute-rgt-in_binary64`
426×	`distribute-lft-in_binary64`
414×	`associate-l_binary64`
378×	`unswap-sqr_binary64`

Counts

56 → 32

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	332
1	61	316
2	151	316
3	389	316
4	1198	300
5	4828	300
6	5416	300

prune25.0ms (0.9%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	32	0	32
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	32	11	43

Error

0.0b

Counts

43 → 11

Alt Table

Status	Error	Program
	0.7b	(.f64 1/2 (+.f64 x (.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 y))) (sqrt.f64 (cbrt.f64 z)))))
	30.7b	(.f64 1/2 (/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y z))) (-.f64 x (*.f64 y (sqrt.f64 z)))))
	1.0b	(.f64 1/2 (+.f64 x (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 y)) 5) (cbrt.f64 (cbrt.f64 y))) (.f64 (sqrt.f64 z) (cbrt.f64 y)))))
	1.3b	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 y (sqrt.f64 z)) x)) (cbrt.f64 (+.f64 (.f64 y (sqrt.f64 z)) x))) (cbrt.f64 (+.f64 (.f64 y (sqrt.f64 z)) x))))
	31.9b	(.f64 1/2 (+.f64 x (.f64 (.f64 (cbrt.f64 (sqrt.f64 y)) (sqrt.f64 y)) (.f64 (sqrt.f64 z) (cbrt.f64 y)))))
	0.4b	(.f64 1/2 (+.f64 x (.f64 (*.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))))
	0.7b	(.f64 1/2 (+.f64 x (.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z)))) (cbrt.f64 (fabs.f64 (cbrt.f64 z)))) (sqrt.f64 (cbrt.f64 z)))))
	0.2b	(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
	32.2b	(.f64 1/2 (.f64 (sqrt.f64 (+.f64 (.f64 y (sqrt.f64 z)) x)) (sqrt.f64 (+.f64 (.f64 y (sqrt.f64 z)) x))))
	31.8b	(.f64 1/2 (+.f64 x (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 z) (sqrt.f64 y)))))
	0.7b	(.f64 1/2 (+.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (sqrt.f64 z) (cbrt.f64 y)))))

Compiler

Compiled 611 to 296 computations (51.6% saved)

regimes513.0ms (18.5%)

Accuracy

Total 0.1b remaining (77.7%)

Threshold costs 0.1b (77.7%)

Compiler

Compiled 8142 to 4912 computations (39.7% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

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

end1.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

sample888.0ms (31.9%)

Algorithm

1×

intervals

Results

389.0ms	8000×	body	128	valid
47.0ms	1139×	body	128	nan
19.0ms	440×	body	128	invalid

Compiler

Compiled 245 to 151 computations (38.4% saved)

Details

analyze218.0ms (7.8%)

sample29.0ms (1.1%)

simplify9.0ms (0.3%)

prune3.0ms (0.1%)

localize27.0ms (1%)

rewrite26.0ms (0.9%)

series32.0ms (1.1%)

simplify107.0ms (3.8%)

prune13.0ms (0.5%)

localize12.0ms (0.4%)

rewrite77.0ms (2.8%)

series79.0ms (2.8%)

simplify98.0ms (3.5%)

prune49.0ms (1.8%)

localize56.0ms (2%)

rewrite127.0ms (4.6%)

series67.0ms (2.4%)

simplify86.0ms (3.1%)

prune37.0ms (1.3%)

localize13.0ms (0.5%)

rewrite51.0ms (1.8%)

series59.0ms (2.1%)

simplify69.0ms (2.5%)

prune25.0ms (0.9%)

regimes513.0ms (18.5%)

simplify6.0ms (0.2%)

end1.0ms (0%)

sample888.0ms (31.9%)

Profiling