Details

analyze874.0ms (17.6%)

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
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
12.5%	85.8%	1.7%	9
16.4%	79.2%	4.4%	10
20.7%	72.4%	7%	11
32.6%	53.3%	14.1%	12
36%	45.5%	18.5%	13
38.3%	41.1%	20.6%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample28.0ms (0.6%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
4.0ms	93×	body	128	invalid

Compiler

Compiled 40 to 26 computations (35% saved)

simplify77.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

822×	`div-sub_binary64`
608×	`neg-mul-1_binary64`
536×	`times-frac_binary64`
461×	`unsub-neg_binary64`
417×	`distribute-frac-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	26	22
2	61	22
3	116	22
4	247	22
5	541	22
6	1124	19
7	2215	19
8	4371	19
9	4645	19
10	4898	19

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

12.0b

Counts

2 → 2

Alt Table

Status	Error	Program
	27.3b	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y 2))
▶	12.0b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))

Compiler

Compiled 84 to 52 computations (38.1% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
0.7b	(-.f64 (.f64 z z) (.f64 x x))
12.1b	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

rewrite69.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

18×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
13×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`
7×	`difference-of-squares_binary64`

Counts

3 → 65

Calls

3 calls:

8.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
5.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
3.0ms	(-.f64 (.f64 z z) (.f64 x x))

Compiler

Compiled 1446 to 385 computations (73.4% saved)

series127.0ms (2.6%)

Error

6.5b

Counts

3 → 45

Calls

3 calls:

53.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
38.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
25.0ms	(-.f64 (.f64 z z) (.f64 x x))

Compiler

Compiled 1223 to 908 computations (25.8% saved)

simplify99.0ms (2%)

Algorithm

1×	egg-herbie

Rules

341×	`div-sub_binary64`
327×	`associate-l_binary64`
304×	`associate-r_binary64`
298×	`times-frac_binary64`
235×	`distribute-rgt-in_binary64`

Counts

110 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	1865
1	323	1749
2	850	1737
3	4162	1737
4	5329	1737

prune39.0ms (0.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	79	5	84
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	81	5	86

Error

0.0b

Counts

86 → 5

Alt Table

Status	Error	Program
	12.0b	(.f64 -1/2 (-.f64 (/.f64 (.f64 (+.f64 x z) (-.f64 z x)) y) y))
▶	0.2b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)) y))
	0.6b	(.f64 -1/2 (-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z))) (cbrt.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)))) (cbrt.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)))) y))
	3.3b	(.f64 -1/2 (-.f64 (/.f64 (.f64 (/.f64 (+.f64 x z) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (-.f64 z x)) (cbrt.f64 y)) y))
	0.6b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 x z) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 z x) (cbrt.f64 y))) y))

Compiler

Compiled 1050 to 370 computations (64.8% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite106.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

43×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
19×	`associate-l_binary64`

Counts

3 → 99

Calls

3 calls:

9.0ms	(*.f64 (/.f64 (-.f64 z x) y) (+.f64 x z))
8.0ms	(-.f64 (*.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)) y)
7.0ms	(/.f64 (-.f64 z x) y)

Compiler

Compiled 1960 to 571 computations (70.9% saved)

series110.0ms (2.2%)

Error

0.0b

Counts

3 → 48

Calls

3 calls:

42.0ms	(-.f64 (*.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)) y)
36.0ms	(*.f64 (/.f64 (-.f64 z x) y) (+.f64 x z))
22.0ms	(/.f64 (-.f64 z x) y)

Compiler

Compiled 1428 to 986 computations (31% saved)

simplify114.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

552×	`associate-*l/_binary64`
527×	`times-frac_binary64`
407×	`associate-*r/_binary64`
403×	`associate-/l*_binary64`
285×	`associate-/r*_binary64`

Counts

147 → 105

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	180	2175
1	559	2080
2	1518	2068
3	4610	2068
4	4970	2068

prune51.0ms (1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	103	7	110

Error

0.0b

Counts

110 → 7

Alt Table

Status	Error	Program
	12.0b	(.f64 -1/2 (-.f64 (/.f64 (.f64 (+.f64 x z) (-.f64 z x)) y) y))
✓	0.2b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)) y))
	35.8b	(.f64 -1/2 (-.f64 (.f64 (/.f64 1 (sqrt.f64 y)) (*.f64 (+.f64 x z) (/.f64 (-.f64 z x) (sqrt.f64 y)))) y))
▶	0.6b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 x z) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 z x) (cbrt.f64 y))) y))
	34.8b	(.f64 -1/2 (-.f64 (.f64 (sqrt.f64 (/.f64 (-.f64 z x) y)) (*.f64 (+.f64 x z) (sqrt.f64 (/.f64 (-.f64 z x) y)))) y))
	0.6b	(.f64 -1/2 (-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z))) (cbrt.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)))) (cbrt.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)))) y))
	0.6b	(.f64 -1/2 (-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 z x) y)) (cbrt.f64 (/.f64 (-.f64 z x) y))) (.f64 (+.f64 x z) (cbrt.f64 (/.f64 (-.f64 z x) y)))) y))

Compiler

Compiled 1470 to 508 computations (65.4% saved)

localize16.0ms (0.3%)

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)

rewrite90.0ms (1.8%)

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 1694 to 496 computations (70.7% saved)

series61.0ms (1.2%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

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

Compiler

Compiled 799 to 499 computations (37.5% saved)

simplify99.0ms (2%)

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

prune33.0ms (0.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	64	7	71

Error

0.0b

Counts

71 → 7

Alt Table

Status	Error	Program
	12.0b	(.f64 -1/2 (-.f64 (/.f64 (.f64 (+.f64 x z) (-.f64 z x)) y) y))
✓	0.2b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)) y))
	35.8b	(.f64 -1/2 (-.f64 (.f64 (/.f64 1 (sqrt.f64 y)) (*.f64 (+.f64 x z) (/.f64 (-.f64 z x) (sqrt.f64 y)))) y))
✓	0.6b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 x z) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 z x) (cbrt.f64 y))) y))
	34.8b	(.f64 -1/2 (-.f64 (.f64 (sqrt.f64 (/.f64 (-.f64 z x) y)) (*.f64 (+.f64 x z) (sqrt.f64 (/.f64 (-.f64 z x) y)))) y))
▶	0.6b	(.f64 -1/2 (-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z))) (cbrt.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)))) (cbrt.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)))) y))
	0.9b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 x z) (.f64 (cbrt.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (pow.f64 (cbrt.f64 (cbrt.f64 y)) 4))) (/.f64 (-.f64 z x) (cbrt.f64 y))) y))

Compiler

Compiled 983 to 426 computations (56.7% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z))) (cbrt.f64 (*.f64 (/.f64 (-.f64 z x) y) (+.f64 x z))))
8.6b	(cbrt.f64 (*.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)))
8.6b	(cbrt.f64 (*.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)))
8.6b	(cbrt.f64 (*.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)))

rewrite144.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

75×	`cbrt-div_binary64`
55×	`frac-times_binary64`
35×	`associate-*r/_binary64`
30×	`flip-+_binary64`
30×	`flip3-+_binary64`

Counts

4 → 108

Calls

4 calls:

9.0ms	(.f64 (cbrt.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z))) (cbrt.f64 (*.f64 (/.f64 (-.f64 z x) y) (+.f64 x z))))
7.0ms	(cbrt.f64 (*.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)))
6.0ms	(cbrt.f64 (*.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)))
6.0ms	(cbrt.f64 (*.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)))

Compiler

Compiled 5004 to 883 computations (82.4% saved)

series375.0ms (7.6%)

Error

0.0b

Counts

4 → 55

Calls

4 calls:

86.0ms	(cbrt.f64 (*.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)))
81.0ms	(cbrt.f64 (*.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)))
78.0ms	(cbrt.f64 (*.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)))
78.0ms	(.f64 (cbrt.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z))) (cbrt.f64 (*.f64 (/.f64 (-.f64 z x) y) (+.f64 x z))))

Compiler

Compiled 7669 to 4645 computations (39.4% saved)

simplify169.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

273×	`distribute-rgt-in_binary64`
253×	`distribute-lft-in_binary64`
248×	`times-frac_binary64`
235×	`associate-/l*_binary64`
192×	`associate-/r*_binary64`

Counts

163 → 137

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	267	5379
1	617	5201
2	1628	4965
3	4942	4965
4	4964	4965

prune109.0ms (2.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	136	8	144

Error

0.0b

Counts

144 → 8

Alt Table

Status	Error	Program
	12.0b	(.f64 -1/2 (-.f64 (/.f64 (.f64 (+.f64 x z) (-.f64 z x)) y) y))
	0.2b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)) y))
	35.8b	(.f64 -1/2 (-.f64 (.f64 (/.f64 1 (sqrt.f64 y)) (*.f64 (+.f64 x z) (/.f64 (-.f64 z x) (sqrt.f64 y)))) y))
	0.6b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 x z) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 z x) (cbrt.f64 y))) y))
	34.8b	(.f64 -1/2 (-.f64 (.f64 (sqrt.f64 (/.f64 (-.f64 z x) y)) (*.f64 (+.f64 x z) (sqrt.f64 (/.f64 (-.f64 z x) y)))) y))
	0.6b	(.f64 -1/2 (-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z))) (cbrt.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)))) (cbrt.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)))) y))
	0.5b	(.f64 -1/2 (-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 z x) y)) (.f64 (cbrt.f64 (.f64 (+.f64 x z) (/.f64 (-.f64 z x) y))) (cbrt.f64 (+.f64 x z)))) (cbrt.f64 (.f64 (/.f64 (-.f64 z x) y) (+.f64 x z)))) y))
	0.9b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 x z) (.f64 (cbrt.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (pow.f64 (cbrt.f64 (cbrt.f64 y)) 4))) (/.f64 (-.f64 z x) (cbrt.f64 y))) y))

Compiler

Compiled 5093 to 1483 computations (70.9% saved)

regimes703.0ms (14.2%)

Accuracy

Total 0.1b remaining (70.2%)

Threshold costs 0.1b (70.2%)

Compiler

Compiled 16438 to 8635 computations (47.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	17	19
2	25	19
3	29	19
4	31	19
5	31	19

end0.0ms (0%)

Compiler: Compiled 16 to 10 computations (37.5% saved)

sample1.4s (28.8%)

Algorithm

1×

intervals

Results

669.0ms	8000×	body	128	valid
288.0ms	2894×	body	128	invalid

Compiler

Compiled 248 to 133 computations (46.4% saved)

Details

analyze874.0ms (17.6%)

sample28.0ms (0.6%)

simplify77.0ms (1.6%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

rewrite69.0ms (1.4%)

series127.0ms (2.6%)

simplify99.0ms (2%)

prune39.0ms (0.8%)

localize9.0ms (0.2%)

rewrite106.0ms (2.1%)

series110.0ms (2.2%)

simplify114.0ms (2.3%)

prune51.0ms (1%)

localize16.0ms (0.3%)

rewrite90.0ms (1.8%)

series61.0ms (1.2%)

simplify99.0ms (2%)

prune33.0ms (0.7%)

localize13.0ms (0.3%)

rewrite144.0ms (2.9%)

series375.0ms (7.6%)

simplify169.0ms (3.4%)

prune109.0ms (2.2%)

regimes703.0ms (14.2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (28.8%)

Profiling