Details

analyze375.0ms (7.3%)

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
12.5%	87.4%	0.1%	6
34.3%	65.5%	0.1%	7
46.8%	53%	0.1%	8
48%	51.9%	0.1%	9
63%	36.9%	0.1%	10
71.7%	28.2%	0.1%	11
72%	27.8%	0.1%	12
80.5%	19.4%	0.1%	13
85.4%	14.5%	0.1%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample41.0ms (0.8%)

Algorithm

1×

intervals

Results

13.0ms	195×	body	128	valid
12.0ms	31×	body	1024	valid
5.0ms	22×	body	512	valid
1.0ms	8×	body	256	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	14
1	20	14

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

Merged error: 0.0b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64`
7×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
5×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`sum-log_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `+-commutative_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `associate-+l+_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

3 → 43

Calls

3 calls:

8.0ms	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
5.0ms	(*.f64 z (cos.f64 y))
4.0ms	(+.f64 x (sin.f64 y))

series190.0ms (3.7%)

Counts

3 → 9

Calls

3 calls:

85.0ms	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
65.0ms	(*.f64 z (cos.f64 y))
40.0ms	(+.f64 x (sin.f64 y))

simplify77.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4969	626
1	4969	626

prune104.0ms (2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	49	3	52
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	49	4	53

Merged error: 0b

Counts

53 → 4

Compiler

Compiled 1528 to 667 computations (56.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (cos.f64 y))
0.0b	(sqrt.f64 (cos.f64 y))
0.1b	(*.f64 z (sqrt.f64 (cos.f64 y)))
0.1b	(.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y)))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
13×	`pow1_binary64` `sqrt-prod_binary64`
12×	`associate-r_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `*-commutative_binary64`

Counts

4 → 69

Calls

4 calls:

9.0ms	(.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y)))
6.0ms	(*.f64 z (sqrt.f64 (cos.f64 y)))
2.0ms	(sqrt.f64 (cos.f64 y))
2.0ms	(sqrt.f64 (cos.f64 y))

series199.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

88.0ms	(*.f64 z (sqrt.f64 (cos.f64 y)))
57.0ms	(.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y)))
29.0ms	(sqrt.f64 (cos.f64 y))
25.0ms	(sqrt.f64 (cos.f64 y))

simplify85.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4950	724
1	4950	724

prune66.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	81	4	85

Merged error: 0b

Counts

85 → 4

Compiler

Compiled 1486 to 343 computations (76.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (*.f64 z (cos.f64 y)))
0.1b	(*.f64 z (cos.f64 y))
0.1b	(*.f64 z (cos.f64 y))
0.2b	(.f64 (sqrt.f64 (.f64 z (cos.f64 y))) (sqrt.f64 (*.f64 z (cos.f64 y))))

rewrite35.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`pow1_binary64`
30×	`sqrt-pow1_binary64`
23×	`pow-prod-down_binary64`
18×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`pow1/2_binary64`
10×	`associate-r_binary64` `pow-prod-up_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
6×	`pow-sqr_binary64`
5×	`sqrt-prod_binary64`
4×	`add-log-exp_binary64` `swap-sqr_binary64`
3×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `pow2_binary64`

Counts

4 → 96

Calls

4 calls:

10.0ms	(.f64 (sqrt.f64 (.f64 z (cos.f64 y))) (sqrt.f64 (*.f64 z (cos.f64 y))))
5.0ms	(*.f64 z (cos.f64 y))
5.0ms	(*.f64 z (cos.f64 y))
3.0ms	(sqrt.f64 (*.f64 z (cos.f64 y)))

series303.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

96.0ms	(sqrt.f64 (*.f64 z (cos.f64 y)))
91.0ms	(.f64 (sqrt.f64 (.f64 z (cos.f64 y))) (sqrt.f64 (*.f64 z (cos.f64 y))))
63.0ms	(*.f64 z (cos.f64 y))
52.0ms	(*.f64 z (cos.f64 y))

simplify45.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5277	949

prune86.0ms (1.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	108	4	112

Merged error: 0b

Counts

112 → 4

Compiler

Compiled 1996 to 481 computations (75.9% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (+.f64 x (sin.f64 y)) 3)
1.2b	(+.f64 (.f64 (.f64 z (cos.f64 y)) (.f64 z (cos.f64 y))) (.f64 (+.f64 x (sin.f64 y)) (-.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))))
3.7b	(+.f64 (pow.f64 (*.f64 z (cos.f64 y)) 3) (pow.f64 (+.f64 x (sin.f64 y)) 3))
36.3b	(/.f64 (+.f64 (pow.f64 (.f64 z (cos.f64 y)) 3) (pow.f64 (+.f64 x (sin.f64 y)) 3)) (+.f64 (.f64 (.f64 z (cos.f64 y)) (.f64 z (cos.f64 y))) (.f64 (+.f64 x (sin.f64 y)) (-.f64 (+.f64 x (sin.f64 y)) (.f64 z (cos.f64 y))))))

rewrite78.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
8×	`add-log-exp_binary64`
7×	`distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-+r+_binary64`
5×	`flip3-+_binary64` `pow1_binary64` `sum-cubes_binary64` `associate-/l*_binary64` `flip-+_binary64`
4×	`unpow-prod-down_binary64` `cube-prod_binary64`
3×	`pow-unpow_binary64` `associate-/r*_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `associate-/r/_binary64` `cube-div_binary64` `cancel-sign-sub-inv_binary64` `+-commutative_binary64` `associate--l+_binary64` `sum-log_binary64`
1×	`pow-to-exp_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sqr-pow_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 96

Calls

4 calls:

29.0ms	(/.f64 (+.f64 (pow.f64 (.f64 z (cos.f64 y)) 3) (pow.f64 (+.f64 x (sin.f64 y)) 3)) (+.f64 (.f64 (.f64 z (cos.f64 y)) (.f64 z (cos.f64 y))) (.f64 (+.f64 x (sin.f64 y)) (-.f64 (+.f64 x (sin.f64 y)) (.f64 z (cos.f64 y))))))
14.0ms	(+.f64 (pow.f64 (*.f64 z (cos.f64 y)) 3) (pow.f64 (+.f64 x (sin.f64 y)) 3))
13.0ms	(+.f64 (.f64 (.f64 z (cos.f64 y)) (.f64 z (cos.f64 y))) (.f64 (+.f64 x (sin.f64 y)) (-.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))))
6.0ms	(pow.f64 (+.f64 x (sin.f64 y)) 3)

series1.4s (27.2%)

Counts

4 → 12

Calls

4 calls:

621.0ms	(/.f64 (+.f64 (pow.f64 (.f64 z (cos.f64 y)) 3) (pow.f64 (+.f64 x (sin.f64 y)) 3)) (+.f64 (.f64 (.f64 z (cos.f64 y)) (.f64 z (cos.f64 y))) (.f64 (+.f64 x (sin.f64 y)) (-.f64 (+.f64 x (sin.f64 y)) (.f64 z (cos.f64 y))))))
413.0ms	(+.f64 (pow.f64 (*.f64 z (cos.f64 y)) 3) (pow.f64 (+.f64 x (sin.f64 y)) 3))
292.0ms	(+.f64 (.f64 (.f64 z (cos.f64 y)) (.f64 z (cos.f64 y))) (.f64 (+.f64 x (sin.f64 y)) (-.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))))
62.0ms	(pow.f64 (+.f64 x (sin.f64 y)) 3)

simplify77.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5379	4949

prune185.0ms (3.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	108	4	112

Merged error: 0b

Counts

112 → 4

Compiler

Compiled 5496 to 1485 computations (73% saved)

regimes209.0ms (4.1%)

Compiler: Compiled 332 to 214 computations (35.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	14
1	12	14

end0.0ms (0%)

sample1.4s (28.4%)

Algorithm

1×

intervals

Results

506.0ms	1281×	body	1024	valid
392.0ms	5697×	body	128	valid
147.0ms	644×	body	512	valid
55.0ms	371×	body	256	valid
6.0ms	7×	body	2048	valid

Compiler

Compiled 96 to 65 computations (32.3% saved)

Details

analyze375.0ms (7.3%)

sample41.0ms (0.8%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite20.0ms (0.4%)

series190.0ms (3.7%)

simplify77.0ms (1.5%)

prune104.0ms (2%)

localize12.0ms (0.2%)

rewrite24.0ms (0.5%)

series199.0ms (3.9%)

simplify85.0ms (1.7%)

prune66.0ms (1.3%)

localize11.0ms (0.2%)

rewrite35.0ms (0.7%)

series303.0ms (5.9%)

simplify45.0ms (0.9%)

prune86.0ms (1.7%)

localize20.0ms (0.4%)

rewrite78.0ms (1.5%)

series1.4s (27.2%)

simplify77.0ms (1.5%)

prune185.0ms (3.6%)

regimes209.0ms (4.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.4s (28.4%)

Profiling