Details

analyze185.0ms (5.1%)

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
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)

sample22.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
1.0ms	42×	body	128	nan
0.0ms	13×	body	128	invalid

Compiler

Compiled 30 to 24 computations (20% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
2×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `associate-r_binary64`
1×	`1-exp_binary64` `+-commutative_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

prune4.0ms (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

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))

Compiler

Compiled 33 to 24 computations (27.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite41.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

9×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`
5×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
3×	`associate-l_binary64`

Counts

2 → 33

Calls

2 calls:

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

Compiler

Compiled 426 to 171 computations (59.9% saved)

series49.0ms (1.4%)

Error

0.1b

Counts

2 → 21

Calls

2 calls:

27.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))
18.0ms	(*.f64 y (sqrt.f64 z))

Compiler

Compiled 435 to 318 computations (26.9% saved)

simplify125.0ms (3.5%)

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 → 26

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	502
1	151	483
2	385	481
3	821	481
4	1486	481
5	2657	481
6	3221	481
7	4797	481
8	4972	481
9	4831	481

prune23.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	21	5	26
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	21	6	27

Error

0.0b

Counts

27 → 6

Alt Table

Status	Error	Program
	0.6b	(.f64 1/2 (+.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (sqrt.f64 z) (cbrt.f64 y)))))
	29.0b	(.f64 1/2 (+.f64 x (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) y)) (sqrt.f64 (.f64 (sqrt.f64 z) y)))))
	27.1b	(.f64 1/2 (/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 z y))) (-.f64 x (*.f64 (sqrt.f64 z) y))))
▶	0.4b	(.f64 1/2 (+.f64 x (.f64 (*.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))))
	0.6b	(.f64 1/2 (+.f64 x (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 z) y)) (cbrt.f64 (.f64 (sqrt.f64 z) y))) (cbrt.f64 (.f64 (sqrt.f64 z) y)))))
✓	0.1b	(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))

Compiler

Compiled 461 to 228 computations (50.5% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(*.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)

rewrite126.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

25×	`add-sqr-sqrt_binary64`
20×	`associate-r_binary64`
15×	`cbrt-prod_binary64`
13×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`

Counts

4 → 76

Calls

4 calls:

9.0ms	(.f64 (.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))
7.0ms	(*.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)

series102.0ms (2.9%)

Error

0.0b

Counts

4 → 18

Calls

4 calls:

43.0ms	(.f64 (.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))
19.0ms	(*.f64 y (fabs.f64 (cbrt.f64 z)))
18.0ms	(cbrt.f64 z)
16.0ms	(cbrt.f64 z)

Compiler

Compiled 805 to 619 computations (23.1% saved)

simplify109.0ms (3%)

Algorithm

1×	egg-herbie

Rules

455×	`associate-/l/_binary64`
446×	`*-commutative_binary64`
431×	`associate-/r/_binary64`
376×	`log-prod_binary64`
279×	`distribute-rgt-in_binary64`

Counts

94 → 73

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	110	1174
1	228	914
2	676	867
3	887	781
4	1532	767
5	2750	767
6	4626	767
7	5141	767

prune68.0ms (1.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	69	10	79

Error

0.0b

Counts

79 → 10

Alt Table

Status	Error	Program
	0.6b	(.f64 1/2 (+.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (sqrt.f64 z) (cbrt.f64 y)))))
	29.0b	(.f64 1/2 (+.f64 x (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) y)) (sqrt.f64 (.f64 (sqrt.f64 z) y)))))
	27.1b	(.f64 1/2 (/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 z y))) (-.f64 x (*.f64 (sqrt.f64 z) y))))
✓	0.4b	(.f64 1/2 (+.f64 x (.f64 (*.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))))
	0.6b	(.f64 1/2 (+.f64 x (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 z) y)) (cbrt.f64 (.f64 (sqrt.f64 z) y))) (cbrt.f64 (.f64 (sqrt.f64 z) y)))))
	1.8b	(.f64 1/2 (+.f64 x (.f64 (.f64 y (fabs.f64 (.f64 (cbrt.f64 (pow.f64 z 2/3)) (cbrt.f64 (cbrt.f64 z))))) (sqrt.f64 (cbrt.f64 z)))))
✓	0.1b	(.f64 1/2 (+.f64 x (.f64 y (sqrt.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)))))
▶	0.5b	(.f64 1/2 (+.f64 x (.f64 (.f64 (.f64 (cbrt.f64 z) y) (fabs.f64 (cbrt.f64 (cbrt.f64 z)))) (sqrt.f64 (cbrt.f64 (cbrt.f64 z))))))
	2.3b	(.f64 1/2 (+.f64 x (.f64 (*.f64 y (pow.f64 (pow.f64 z 1/12) 5)) (sqrt.f64 (sqrt.f64 (cbrt.f64 z))))))

Compiler

Compiled 1036 to 552 computations (46.7% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite93.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

18×	`cbrt-prod_binary64`
9×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
4×	`pow1/3_binary64` `pow1_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`

Counts

4 → 47

Calls

4 calls:

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

Compiler

Compiled 1033 to 348 computations (66.3% saved)

series84.0ms (2.3%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt.f64 (cbrt.f64 z))
18.0ms	(cbrt.f64 z)
17.0ms	(cbrt.f64 z)
16.0ms	(cbrt.f64 z)

Compiler

Compiled 741 to 511 computations (31% saved)

simplify124.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

490×	`log-prod_binary64`
447×	`unswap-sqr_binary64`
391×	`associate-+l+_binary64`
359×	`associate-+r+_binary64`
347×	`distribute-rgt-in_binary64`

Counts

59 → 30

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	424
1	63	424
2	158	424
3	491	376
4	995	360
5	3220	360
6	4306	360
7	4727	360
8	4977	360
9	4732	360

prune38.0ms (1.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	29	1	30
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	29	11	40

Error

0.0b

Counts

40 → 11

Alt Table

Status	Error	Program
	0.6b	(.f64 1/2 (+.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (sqrt.f64 z) (cbrt.f64 y)))))
	29.0b	(.f64 1/2 (+.f64 x (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) y)) (sqrt.f64 (.f64 (sqrt.f64 z) y)))))
	27.1b	(.f64 1/2 (/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 z y))) (-.f64 x (*.f64 (sqrt.f64 z) y))))
✓	0.4b	(.f64 1/2 (+.f64 x (.f64 (*.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))))
▶	0.6b	(.f64 1/2 (+.f64 x (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 z) y)) (cbrt.f64 (.f64 (sqrt.f64 z) y))) (cbrt.f64 (.f64 (sqrt.f64 z) y)))))
	1.8b	(.f64 1/2 (+.f64 x (.f64 (.f64 y (fabs.f64 (.f64 (cbrt.f64 (pow.f64 z 2/3)) (cbrt.f64 (cbrt.f64 z))))) (sqrt.f64 (cbrt.f64 z)))))
✓	0.1b	(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
	1.2b	(.f64 1/2 (+.f64 x (.f64 (.f64 (.f64 (cbrt.f64 z) y) (fabs.f64 (cbrt.f64 (*.f64 (cbrt.f64 (pow.f64 z 2/3)) (cbrt.f64 (cbrt.f64 z)))))) (sqrt.f64 (cbrt.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)))))
✓	0.5b	(.f64 1/2 (+.f64 x (.f64 (.f64 (.f64 (cbrt.f64 z) y) (fabs.f64 (cbrt.f64 (cbrt.f64 z)))) (sqrt.f64 (cbrt.f64 (cbrt.f64 z))))))
	2.3b	(.f64 1/2 (+.f64 x (.f64 (*.f64 y (pow.f64 (pow.f64 z 1/12) 5)) (sqrt.f64 (sqrt.f64 (cbrt.f64 z))))))

Compiler

Compiled 696 to 392 computations (43.7% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (.f64 (sqrt.f64 z) y)) (cbrt.f64 (*.f64 (sqrt.f64 z) y)))
3.7b	(cbrt.f64 (*.f64 (sqrt.f64 z) y))
3.7b	(cbrt.f64 (*.f64 (sqrt.f64 z) y))
3.7b	(cbrt.f64 (*.f64 (sqrt.f64 z) y))

rewrite132.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

11×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`pow1/3_binary64`
8×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
7×	`cbrt-prod_binary64`

Counts

4 → 58

Calls

4 calls:

6.0ms	(.f64 (cbrt.f64 (.f64 (sqrt.f64 z) y)) (cbrt.f64 (*.f64 (sqrt.f64 z) y)))
3.0ms	(cbrt.f64 (*.f64 (sqrt.f64 z) y))
3.0ms	(cbrt.f64 (*.f64 (sqrt.f64 z) y))
3.0ms	(cbrt.f64 (*.f64 (sqrt.f64 z) y))

Compiler

Compiled 1439 to 337 computations (76.6% saved)

series200.0ms (5.6%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

48.0ms	(cbrt.f64 (*.f64 (sqrt.f64 z) y))
47.0ms	(cbrt.f64 (*.f64 (sqrt.f64 z) y))
46.0ms	(cbrt.f64 (*.f64 (sqrt.f64 z) y))
43.0ms	(.f64 (cbrt.f64 (.f64 (sqrt.f64 z) y)) (cbrt.f64 (*.f64 (sqrt.f64 z) y)))

Compiler

Compiled 1575 to 1032 computations (34.5% saved)

simplify124.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

422×	`*-commutative_binary64`
375×	`exp-prod_binary64`
354×	`log-prod_binary64`
340×	`unswap-sqr_binary64`
318×	`exp-sum_binary64`

Counts

82 → 66

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	90	1041
1	189	988
2	433	902
3	1326	878
4	2954	755
5	4137	749
6	4106	740
7	4946	740

prune73.0ms (2%)

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	64	13	77

Error

0.0b

Counts

77 → 13

Alt Table

Status	Error	Program
	0.6b	(.f64 1/2 (+.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (sqrt.f64 z) (cbrt.f64 y)))))
	29.0b	(.f64 1/2 (+.f64 x (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) y)) (sqrt.f64 (.f64 (sqrt.f64 z) y)))))
	27.1b	(.f64 1/2 (/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 z y))) (-.f64 x (*.f64 (sqrt.f64 z) y))))
	0.4b	(.f64 1/2 (+.f64 x (.f64 (*.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))))
	0.6b	(.f64 1/2 (+.f64 x (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 z) y)) (cbrt.f64 (.f64 (sqrt.f64 z) y))) (cbrt.f64 (.f64 (sqrt.f64 z) y)))))
	30.6b	(.f64 1/2 (+.f64 x (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 z) y)) (cbrt.f64 (.f64 (sqrt.f64 z) y))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (pow.f64 y 2/3))) (cbrt.f64 (cbrt.f64 (.f64 y (sqrt.f64 z))))))))
	1.8b	(.f64 1/2 (+.f64 x (.f64 (.f64 y (fabs.f64 (.f64 (cbrt.f64 (pow.f64 z 2/3)) (cbrt.f64 (cbrt.f64 z))))) (sqrt.f64 (cbrt.f64 z)))))
	0.1b	(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
	1.2b	(.f64 1/2 (+.f64 x (.f64 (.f64 (.f64 (cbrt.f64 z) y) (fabs.f64 (cbrt.f64 (*.f64 (cbrt.f64 (pow.f64 z 2/3)) (cbrt.f64 (cbrt.f64 z)))))) (sqrt.f64 (cbrt.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)))))
	0.5b	(.f64 1/2 (+.f64 x (.f64 (.f64 (.f64 (cbrt.f64 z) y) (fabs.f64 (cbrt.f64 (cbrt.f64 z)))) (sqrt.f64 (cbrt.f64 (cbrt.f64 z))))))
	0.6b	(.f64 1/2 (+.f64 x (.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (.f64 (cbrt.f64 y) (cbrt.f64 (.f64 y (sqrt.f64 z))))) (cbrt.f64 (.f64 (sqrt.f64 z) y)))))
	2.3b	(.f64 1/2 (+.f64 x (.f64 (*.f64 y (pow.f64 (pow.f64 z 1/12) 5)) (sqrt.f64 (sqrt.f64 (cbrt.f64 z))))))

Compiler

Compiled 1175 to 475 computations (59.6% saved)

regimes873.0ms (24.4%)

Accuracy

Total 0.1b remaining (72.2%)

Threshold costs 0.1b (72.2%)

Compiler

Compiled 13469 to 8062 computations (40.1% saved)

simplify3.0ms (0.1%)

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)

sample937.0ms (26.1%)

Algorithm

1×

intervals

Results

308.0ms	8000×	body	128	valid
42.0ms	1107×	body	128	nan
14.0ms	380×	body	128	invalid

Compiler

Compiled 308 to 199 computations (35.4% saved)

Details

analyze185.0ms (5.1%)

sample22.0ms (0.6%)

simplify9.0ms (0.2%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

rewrite41.0ms (1.1%)

series49.0ms (1.4%)

simplify125.0ms (3.5%)

prune23.0ms (0.6%)

localize10.0ms (0.3%)

rewrite126.0ms (3.5%)

series102.0ms (2.9%)

simplify109.0ms (3%)

prune68.0ms (1.9%)

localize13.0ms (0.4%)

rewrite93.0ms (2.6%)

series84.0ms (2.3%)

simplify124.0ms (3.4%)

prune38.0ms (1.1%)

localize11.0ms (0.3%)

rewrite132.0ms (3.7%)

series200.0ms (5.6%)

simplify124.0ms (3.5%)

prune73.0ms (2%)

regimes873.0ms (24.4%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample937.0ms (26.1%)

Profiling