Details

analyze278.0ms (6.3%)

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
37.4%	62.4%	0.1%	6
49.9%	49.9%	0.1%	7
62.4%	37.4%	0.1%	8
62.4%	37.4%	0.1%	9
71.8%	28.1%	0.1%	10
79.6%	20.3%	0.1%	11
79.6%	20.3%	0.1%	12
85%	14.8%	0.1%	13
89.3%	10.5%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample44.0ms (1%)

Algorithm

1×

intervals

Results

16.0ms	61×	body	1024	valid
10.0ms	156×	body	128	valid
5.0ms	27×	body	512	valid
2.0ms	12×	body	256	valid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	12	14
2	12	14

prune2.0ms (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

0.1b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))

Compiler

Compiled 24 to 16 computations (33.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
0.1b	(*.f64 z (sin.f64 y))
0.1b	(*.f64 x (cos.f64 y))

rewrite64.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

11×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`

Counts

3 → 47

Calls

3 calls:

8.0ms	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
4.0ms	(*.f64 x (cos.f64 y))
4.0ms	(*.f64 z (sin.f64 y))

Compiler

Compiled 689 to 163 computations (76.3% saved)

series93.0ms (2.1%)

Error

0.1b

Counts

3 → 36

Calls

3 calls:

42.0ms	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
19.0ms	(*.f64 x (cos.f64 y))
17.0ms	(*.f64 z (sin.f64 y))

Compiler

Compiled 923 to 588 computations (36.3% saved)

simplify105.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

417×	`distribute-rgt-neg-in_binary64`
386×	`sub-neg_binary64`
323×	`distribute-lft-neg-in_binary64`
264×	`*-commutative_binary64`
257×	`cancel-sign-sub-inv_binary64`

Counts

83 → 36

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	125	1020
1	321	991
2	945	967
3	1785	958
4	3565	958
5	4761	958
6	4930	958

prune43.0ms (1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	27	9	36
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	28	9	37

Error

0.1b

Counts

37 → 9

Alt Table

Status	Error	Program
	29.4b	(+.f64 (.f64 (sqrt.f64 (.f64 (cos.f64 y) x)) (sqrt.f64 (.f64 (cos.f64 y) x))) (.f64 z (sin.f64 y)))
	36.0b	(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 y) x) 3) (pow.f64 (.f64 z (sin.f64 y)) 3)) (+.f64 (.f64 (.f64 (cos.f64 y) x) (.f64 (cos.f64 y) x)) (.f64 z (.f64 (sin.f64 y) (-.f64 (.f64 z (sin.f64 y)) (*.f64 (cos.f64 y) x))))))
▶	0.6b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (sin.f64 y) (cbrt.f64 z))))
	15.1b	(+.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (.f64 z (sin.f64 y)) 3)))
	30.6b	(+.f64 (.f64 (sqrt.f64 x) (.f64 (cos.f64 y) (sqrt.f64 x))) (*.f64 z (sin.f64 y)))
	26.8b	(/.f64 (-.f64 (.f64 (.f64 (cos.f64 y) x) (.f64 (cos.f64 y) x)) (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y)))) (-.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y))))
	1.3b	(.f64 (.f64 (cbrt.f64 (+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))) (cbrt.f64 (+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y))))) (cbrt.f64 (+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))))
	31.5b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sin.f64 y) (sqrt.f64 z))))
	0.9b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 y) x)) (cbrt.f64 (.f64 (cos.f64 y) x))) (cbrt.f64 (.f64 (cos.f64 y) x))) (.f64 z (sin.f64 y)))

Compiler

Compiled 940 to 381 computations (59.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
0.5b	(cbrt.f64 z)
0.5b	(cbrt.f64 z)
0.5b	(cbrt.f64 z)

rewrite104.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

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:

6.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(cbrt.f64 z)
1.0ms	(cbrt.f64 z)
1.0ms	(cbrt.f64 z)

Compiler

Compiled 1422 to 304 computations (78.6% saved)

series71.0ms (1.6%)

Error

0.1b

Counts

4 → 12

Calls

4 calls:

19.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
15.0ms	(cbrt.f64 z)
15.0ms	(cbrt.f64 z)
14.0ms	(cbrt.f64 z)

Compiler

Compiled 671 to 429 computations (36.1% saved)

simplify93.0ms (2.1%)

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

prune43.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	65	8	73

Error

0.1b

Counts

73 → 8

Alt Table

Status	Error	Program
	29.4b	(+.f64 (.f64 (sqrt.f64 (.f64 (cos.f64 y) x)) (sqrt.f64 (.f64 (cos.f64 y) x))) (.f64 z (sin.f64 y)))
	36.0b	(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 y) x) 3) (pow.f64 (.f64 z (sin.f64 y)) 3)) (+.f64 (.f64 (.f64 (cos.f64 y) x) (.f64 (cos.f64 y) x)) (.f64 z (.f64 (sin.f64 y) (-.f64 (.f64 z (sin.f64 y)) (*.f64 (cos.f64 y) x))))))
	15.1b	(+.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (.f64 z (sin.f64 y)) 3)))
	30.6b	(+.f64 (.f64 (sqrt.f64 x) (.f64 (cos.f64 y) (sqrt.f64 x))) (*.f64 z (sin.f64 y)))
	26.8b	(/.f64 (-.f64 (.f64 (.f64 (cos.f64 y) x) (.f64 (cos.f64 y) x)) (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y)))) (-.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y))))
	31.5b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sin.f64 y) (sqrt.f64 z))))
	0.9b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 y) x)) (cbrt.f64 (.f64 (cos.f64 y) x))) (cbrt.f64 (.f64 (cos.f64 y) x))) (.f64 z (sin.f64 y)))
▶	0.8b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (pow.f64 (cbrt.f64 (cbrt.f64 z)) 4)) (*.f64 (sin.f64 y) (cbrt.f64 z))))

Compiler

Compiled 942 to 380 computations (59.7% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 z)
0.5b	(cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
0.6b	(cbrt.f64 (cbrt.f64 z))
0.9b	(pow.f64 (cbrt.f64 (cbrt.f64 z)) 4)

rewrite88.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

22×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`unpow-prod-down_binary64`

Counts

4 → 58

Calls

4 calls:

4.0ms	(cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
4.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 z)) 4)
1.0ms	(cbrt.f64 (cbrt.f64 z))
1.0ms	(cbrt.f64 z)

Compiler

Compiled 1606 to 469 computations (70.8% saved)

series99.0ms (2.2%)

Error

0.1b

Counts

4 → 12

Calls

4 calls:

29.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 z)) 4)
23.0ms	(cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
19.0ms	(cbrt.f64 (cbrt.f64 z))
17.0ms	(cbrt.f64 z)

Compiler

Compiled 889 to 573 computations (35.5% saved)

simplify127.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

526×	`log-prod_binary64`
498×	`swap-sqr_binary64`
471×	`cube-prod_binary64`
378×	`associate-l_binary64`
357×	`distribute-rgt-neg-in_binary64`

Counts

70 → 47

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	82	718
1	155	656
2	366	641
3	1673	640
4	2801	578
5	3932	570
6	4677	570
7	4803	570

prune39.0ms (0.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	47	0	47
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	47	8	55

Error

0.1b

Counts

55 → 8

Alt Table

Status	Error	Program
	29.4b	(+.f64 (.f64 (sqrt.f64 (.f64 (cos.f64 y) x)) (sqrt.f64 (.f64 (cos.f64 y) x))) (.f64 z (sin.f64 y)))
	36.0b	(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 y) x) 3) (pow.f64 (.f64 z (sin.f64 y)) 3)) (+.f64 (.f64 (.f64 (cos.f64 y) x) (.f64 (cos.f64 y) x)) (.f64 z (.f64 (sin.f64 y) (-.f64 (.f64 z (sin.f64 y)) (*.f64 (cos.f64 y) x))))))
	15.1b	(+.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (.f64 z (sin.f64 y)) 3)))
	30.6b	(+.f64 (.f64 (sqrt.f64 x) (.f64 (cos.f64 y) (sqrt.f64 x))) (*.f64 z (sin.f64 y)))
	26.8b	(/.f64 (-.f64 (.f64 (.f64 (cos.f64 y) x) (.f64 (cos.f64 y) x)) (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y)))) (-.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y))))
	31.5b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sin.f64 y) (sqrt.f64 z))))
▶	0.9b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 y) x)) (cbrt.f64 (.f64 (cos.f64 y) x))) (cbrt.f64 (.f64 (cos.f64 y) x))) (.f64 z (sin.f64 y)))
✓	0.8b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (pow.f64 (cbrt.f64 (cbrt.f64 z)) 4)) (*.f64 (sin.f64 y) (cbrt.f64 z))))

Compiler

Compiled 976 to 412 computations (57.8% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite75.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

4 → 58

Calls

4 calls:

6.0ms	(.f64 (cbrt.f64 (.f64 (cos.f64 y) x)) (cbrt.f64 (*.f64 (cos.f64 y) x)))
2.0ms	(cbrt.f64 (*.f64 (cos.f64 y) x))
2.0ms	(cbrt.f64 (*.f64 (cos.f64 y) x))
2.0ms	(cbrt.f64 (*.f64 (cos.f64 y) x))

Compiler

Compiled 1493 to 231 computations (84.5% saved)

series217.0ms (4.9%)

Error

0.1b

Counts

4 → 33

Calls

4 calls:

52.0ms	(.f64 (cbrt.f64 (.f64 (cos.f64 y) x)) (cbrt.f64 (*.f64 (cos.f64 y) x)))
46.0ms	(cbrt.f64 (*.f64 (cos.f64 y) x))
46.0ms	(cbrt.f64 (*.f64 (cos.f64 y) x))
44.0ms	(cbrt.f64 (*.f64 (cos.f64 y) x))

Compiler

Compiled 2523 to 1417 computations (43.8% saved)

simplify90.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

579×	`cancel-sign-sub-inv_binary64`
517×	`associate-l_binary64`
405×	`associate-r_binary64`
313×	`exp-sum_binary64`
276×	`exp-prod_binary64`

Counts

91 → 75

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	104	1285
1	242	1176
2	644	1061
3	2072	996
4	4214	955
5	4995	955

prune62.0ms (1.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	71	4	75
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	72	11	83

Error

0.0b

Counts

83 → 11

Alt Table

Status	Error	Program
	29.4b	(+.f64 (.f64 (sqrt.f64 (.f64 (cos.f64 y) x)) (sqrt.f64 (.f64 (cos.f64 y) x))) (.f64 z (sin.f64 y)))
	0.8b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 y) x)) (cbrt.f64 (.f64 (cos.f64 y) x))) (.f64 (cbrt.f64 (/.f64 (cos.f64 y) (/.f64 -1 x))) (cbrt.f64 -1))) (.f64 z (sin.f64 y)))
	36.0b	(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 y) x) 3) (pow.f64 (.f64 z (sin.f64 y)) 3)) (+.f64 (.f64 (.f64 (cos.f64 y) x) (.f64 (cos.f64 y) x)) (.f64 z (.f64 (sin.f64 y) (-.f64 (.f64 z (sin.f64 y)) (*.f64 (cos.f64 y) x))))))
	15.1b	(+.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (.f64 z (sin.f64 y)) 3)))
	30.6b	(+.f64 (.f64 (sqrt.f64 x) (.f64 (cos.f64 y) (sqrt.f64 x))) (*.f64 z (sin.f64 y)))
	26.8b	(/.f64 (-.f64 (.f64 (.f64 (cos.f64 y) x) (.f64 (cos.f64 y) x)) (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y)))) (-.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y))))
	20.9b	(+.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 x (cos.f64 y)) 2)) (cbrt.f64 (.f64 (cos.f64 y) x))) (.f64 z (sin.f64 y)))
	0.9b	(+.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 x) (cbrt.f64 (.f64 x (cos.f64 y))))) (cbrt.f64 (.f64 (cos.f64 y) x))) (.f64 z (sin.f64 y)))
	31.5b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sin.f64 y) (sqrt.f64 z))))
	0.8b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (pow.f64 (cbrt.f64 (cbrt.f64 z)) 4)) (*.f64 (sin.f64 y) (cbrt.f64 z))))
	1.2b	(+.f64 (.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (cos.f64 y)))) 2) (cbrt.f64 (cbrt.f64 (.f64 x (cos.f64 y))))) (cbrt.f64 (.f64 (cos.f64 y) x))) (cbrt.f64 (.f64 (cos.f64 y) x))) (.f64 z (sin.f64 y)))

Compiler

Compiled 1575 to 508 computations (67.7% saved)

regimes701.0ms (15.9%)

Accuracy

Total 0.1b remaining (46.7%)

Threshold costs 0.1b (46.7%)

Compiler

Compiled 10968 to 6150 computations (43.9% 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	14
1	12	14
2	12	14

end1.0ms (0%)

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

sample1.9s (43.1%)

Algorithm

1×

intervals

Results

552.0ms	2003×	body	1024	valid
308.0ms	4489×	body	128	valid
217.0ms	1021×	body	512	valid
63.0ms	481×	body	256	valid
3.0ms	6×	body	2048	valid

Compiler

Compiled 305 to 172 computations (43.6% saved)

Details

analyze278.0ms (6.3%)

sample44.0ms (1%)

simplify8.0ms (0.2%)

prune2.0ms (0%)

localize8.0ms (0.2%)

rewrite64.0ms (1.4%)

series93.0ms (2.1%)

simplify105.0ms (2.4%)

prune43.0ms (1%)

localize13.0ms (0.3%)

rewrite104.0ms (2.4%)

series71.0ms (1.6%)

simplify93.0ms (2.1%)

prune43.0ms (1%)

localize22.0ms (0.5%)

rewrite88.0ms (2%)

series99.0ms (2.2%)

simplify127.0ms (2.9%)

prune39.0ms (0.9%)

localize15.0ms (0.3%)

rewrite75.0ms (1.7%)

series217.0ms (4.9%)

simplify90.0ms (2.1%)

prune62.0ms (1.4%)

regimes701.0ms (15.9%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.9s (43.1%)

Profiling