Details

analyze303.0ms (6.8%)

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
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)

sample48.0ms (1.1%)

Algorithm

1×

intervals

Results

19.0ms	67×	body	1024	valid
10.0ms	142×	body	128	valid
6.0ms	29×	body	512	valid
3.0ms	18×	body	256	valid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify16.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

36×	`cancel-sign-sub-inv_binary64`
23×	`sub-neg_binary64` `distribute-rgt-neg-in_binary64`
19×	`unsub-neg_binary64`
17×	`neg-mul-1_binary64`
16×	`distribute-rgt-in_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	16	14
2	26	14
3	38	14
4	55	14
5	79	14
6	114	14
7	163	14
8	190	14
9	192	14
10	190	14
11	159	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 4 expressions with local error:

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

rewrite77.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

12×	`add-sqr-sqrt_binary64`
8×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64` `associate-r_binary64`
2×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
1×	`diff-log_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64` `cancel-sign-sub-inv_binary64`

Counts

4 → 55

Calls

4 calls:

4.0ms	(*.f64 z (sin.f64 y))
4.0ms	(*.f64 x (cos.f64 y))
4.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
2.0ms	(cos.f64 y)

Compiler

Compiled 792 to 191 computations (75.9% saved)

series105.0ms (2.4%)

Error

0.1b

Counts

4 → 38

Calls

4 calls:

43.0ms	(-.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))
10.0ms	(cos.f64 y)

Compiler

Compiled 980 to 640 computations (34.7% saved)

simplify100.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

582×	`times-frac_binary64`
419×	`distribute-rgt-neg-in_binary64`
389×	`cancel-sign-sub-inv_binary64`
308×	`distribute-lft-neg-in_binary64`
237×	`*-commutative_binary64`

Counts

93 → 38

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	116	1023
1	273	987
2	745	975
3	1347	975
4	2575	975
5	4268	975
6	5131	975

prune40.0ms (0.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	31	7	38
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	32	7	39

Error

0.1b

Counts

39 → 7

Alt Table

Status	Error	Program
	28.1b	(-.f64 (.f64 (sqrt.f64 x) (.f64 (cos.f64 y) (sqrt.f64 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))))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (sin.f64 y) (cbrt.f64 z))))
	33.3b	(/.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 z (sin.f64 y)) (.f64 (cos.f64 y) x)))
	31.9b	(.f64 (sqrt.f64 (-.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.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)))))
▶	0.2b	(-.f64 (.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3))) (.f64 z (sin.f64 y)))

Compiler

Compiled 794 to 298 computations (62.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3)))
0.1b	(*.f64 z (sin.f64 y))
0.3b	(cbrt.f64 (pow.f64 (cos.f64 y) 3))
0.4b	(pow.f64 (cos.f64 y) 3)

rewrite135.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

28×	`add-sqr-sqrt_binary64` `cbrt-prod_binary64`
18×	`associate-r_binary64`
17×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
10×	`unpow-prod-down_binary64` `cube-prod_binary64`
9×	`pow1_binary64` `add-exp-log_binary64`

Counts

4 → 96

Calls

4 calls:

8.0ms	(*.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3)))
4.0ms	(*.f64 z (sin.f64 y))
2.0ms	(pow.f64 (cos.f64 y) 3)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 3))

Compiler

Compiled 1451 to 704 computations (51.5% saved)

series76.0ms (1.7%)

Error

0.1b

Counts

4 → 25

Calls

4 calls:

20.0ms	(*.f64 z (sin.f64 y))
19.0ms	(*.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3)))
12.0ms	(pow.f64 (cos.f64 y) 3)
10.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 3))

Compiler

Compiled 884 to 606 computations (31.4% saved)

simplify126.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

362×	`sqr-pow_binary64`
346×	`*-commutative_binary64`
322×	`distribute-rgt-in_binary64`
321×	`log-prod_binary64`
289×	`distribute-lft-in_binary64`

Counts

121 → 77

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	140	1121
1	281	1032
2	871	1010
3	1536	1010
4	2588	1007
5	4679	1007
6	4981	1007
7	4919	1007

prune61.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	76	8	84

Error

0.0b

Counts

84 → 8

Alt Table

Status	Error	Program
	31.5b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sin.f64 y) (sqrt.f64 z))))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (sin.f64 y) (cbrt.f64 z))))
	33.3b	(/.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 z (sin.f64 y)) (.f64 (cos.f64 y) x)))
	0.4b	(-.f64 (.f64 (.f64 x (pow.f64 (cbrt.f64 (cos.f64 y)) 2)) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
▶	0.3b	(-.f64 (.f64 x (cbrt.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 9)))) (.f64 z (sin.f64 y)))
	31.9b	(.f64 (sqrt.f64 (-.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.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)))))
✓	0.2b	(-.f64 (.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3))) (.f64 z (sin.f64 y)))

Compiler

Compiled 995 to 438 computations (56% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 z (sin.f64 y))
0.3b	(cbrt.f64 (pow.f64 (cos.f64 y) 9))
0.3b	(cbrt.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 9)))
0.8b	(pow.f64 (cos.f64 y) 9)

rewrite113.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

24×	`cbrt-prod_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
9×	`unpow-prod-down_binary64`
7×	`pow1_binary64` `add-exp-log_binary64`

Counts

4 → 68

Calls

4 calls:

4.0ms	(*.f64 z (sin.f64 y))
3.0ms	(cbrt.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 9)))
2.0ms	(pow.f64 (cos.f64 y) 9)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 9))

Compiler

Compiled 1220 to 660 computations (45.9% saved)

series74.0ms (1.7%)

Error

0.0b

Counts

4 → 23

Calls

4 calls:

19.0ms	(*.f64 z (sin.f64 y))
17.0ms	(pow.f64 (cos.f64 y) 9)
12.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 9))
8.0ms	(cbrt.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 9)))

Compiler

Compiled 885 to 632 computations (28.6% saved)

simplify115.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

529×	`distribute-rgt-neg-in_binary64`
406×	`associate-l_binary64`
393×	`cancel-sign-sub-inv_binary64`
335×	`associate-r_binary64`
280×	`unswap-sqr_binary64`

Counts

91 → 38

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	126	1108
1	252	1077
2	630	1045
3	1744	1017
4	3640	1007
5	4758	1007
6	4888	1007

prune48.0ms (1.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	38	8	46

Error

0.0b

Counts

46 → 8

Alt Table

Status	Error	Program
	31.5b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sin.f64 y) (sqrt.f64 z))))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (sin.f64 y) (cbrt.f64 z))))
	33.3b	(/.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 z (sin.f64 y)) (.f64 (cos.f64 y) x)))
▶	0.4b	(-.f64 (.f64 (.f64 x (pow.f64 (cbrt.f64 (cos.f64 y)) 2)) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
✓	0.3b	(-.f64 (.f64 x (cbrt.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 9)))) (.f64 z (sin.f64 y)))
	31.9b	(.f64 (sqrt.f64 (-.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.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)))))
✓	0.2b	(-.f64 (.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3))) (.f64 z (sin.f64 y)))

Compiler

Compiled 792 to 423 computations (46.6% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 x (pow.f64 (cbrt.f64 (cos.f64 y)) 2)) (cbrt.f64 (cos.f64 y)))
0.2b	(pow.f64 (cbrt.f64 (cos.f64 y)) 2)
0.3b	(cbrt.f64 (cos.f64 y))
0.3b	(cbrt.f64 (cos.f64 y))

rewrite113.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

15×	`add-exp-log_binary64`
12×	`cbrt-prod_binary64`
11×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
7×	`pow1_binary64` `add-cbrt-cube_binary64` `prod-exp_binary64`
6×	`unpow-prod-down_binary64` `associate-r_binary64`

Counts

4 → 66

Calls

4 calls:

8.0ms	(.f64 (.f64 x (pow.f64 (cbrt.f64 (cos.f64 y)) 2)) (cbrt.f64 (cos.f64 y)))
3.0ms	(pow.f64 (cbrt.f64 (cos.f64 y)) 2)
1.0ms	(cbrt.f64 (cos.f64 y))
1.0ms	(cbrt.f64 (cos.f64 y))

Compiler

Compiled 1380 to 495 computations (64.1% saved)

series95.0ms (2.1%)

Error

0.0b

Counts

4 → 22

Calls

4 calls:

20.0ms	(cbrt.f64 (cos.f64 y))
19.0ms	(.f64 (.f64 x (pow.f64 (cbrt.f64 (cos.f64 y)) 2)) (cbrt.f64 (cos.f64 y)))
18.0ms	(cbrt.f64 (cos.f64 y))
17.0ms	(pow.f64 (cbrt.f64 (cos.f64 y)) 2)

Compiler

Compiled 970 to 650 computations (33% saved)

simplify94.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

668×	`distribute-rgt-in_binary64`
622×	`distribute-lft-in_binary64`
355×	`*-commutative_binary64`
261×	`sqr-pow_binary64`
232×	`log-prod_binary64`

Counts

88 → 59

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	100	850
1	240	764
2	724	753
3	1268	745
4	2141	723
5	4801	723
6	4823	723

prune54.0ms (1.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	59	8	67

Error

0.0b

Counts

67 → 8

Alt Table

Status	Error	Program
	31.5b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sin.f64 y) (sqrt.f64 z))))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (sin.f64 y) (cbrt.f64 z))))
	33.3b	(/.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 z (sin.f64 y)) (.f64 (cos.f64 y) x)))
	0.3b	(-.f64 (.f64 x (cbrt.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 9)))) (.f64 z (sin.f64 y)))
	0.5b	(-.f64 (.f64 (.f64 x (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) 8)) (cbrt.f64 (cbrt.f64 (cos.f64 y)))) (*.f64 z (sin.f64 y)))
	31.9b	(.f64 (sqrt.f64 (-.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.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)))))
	0.2b	(-.f64 (.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3))) (.f64 z (sin.f64 y)))

Compiler

Compiled 871 to 367 computations (57.9% saved)

regimes995.0ms (22.3%)

Accuracy

Total 0.1b remaining (48.5%)

Threshold costs 0.1b (48.5%)

Compiler

Compiled 10240 to 6608 computations (35.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
4×	`sub-neg_binary64` `+-commutative_binary64`
3×	`neg-mul-1_binary64` `neg-sub0_binary64`
2×	`cancel-sign-sub-inv_binary64` `distribute-rgt-neg-in_binary64`
1×	`1-exp_binary64` `*-rgt-identity_binary64` `distribute-lft-neg-out_binary64` `distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	21	14
2	30	14
3	36	14
4	40	14
5	41	14
6	40	14

end1.0ms (0%)

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

sample1.6s (36.4%)

Algorithm

1×

intervals

Results

555.0ms	1959×	body	1024	valid
320.0ms	4538×	body	128	valid
197.0ms	973×	body	512	valid
74.0ms	527×	body	256	valid
2.0ms	3×	body	2048	valid

Compiler

Compiled 206 to 110 computations (46.6% saved)

Iter	Nodes	Cost
0	9	14
1	16	14
2	26	14
3	38	14
4	55	14
5	79	14
6	114	14
7	163	14
8	190	14
9	192	14
10	190	14
11	159	14

Iter	Nodes	Cost
0	9	14
1	16	14
2	26	14
3	38	14
4	55	14
5	79	14
6	114	14
7	163	14
8	190	14
9	192	14
10	190	14
11	159	14

Details

analyze303.0ms (6.8%)

sample48.0ms (1.1%)

simplify16.0ms (0.4%)

prune2.0ms (0%)

localize8.0ms (0.2%)

rewrite77.0ms (1.7%)

series105.0ms (2.4%)

simplify100.0ms (2.2%)

prune40.0ms (0.9%)

localize11.0ms (0.2%)

rewrite135.0ms (3%)

series76.0ms (1.7%)

simplify126.0ms (2.8%)

prune61.0ms (1.4%)

localize12.0ms (0.3%)

rewrite113.0ms (2.5%)

series74.0ms (1.7%)

simplify115.0ms (2.6%)

prune48.0ms (1.1%)

localize15.0ms (0.3%)

rewrite113.0ms (2.5%)

series95.0ms (2.1%)

simplify94.0ms (2.1%)

prune54.0ms (1.2%)

regimes995.0ms (22.3%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.6s (36.4%)

Profiling

Iter	Nodes	Cost
0	9	14
1	16	14
2	26	14
3	38	14
4	55	14
5	79	14
6	114	14
7	163	14
8	190	14
9	192	14
10	190	14
11	159	14