Details

analyze25.0ms (1.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
12.5%	12.5%	75%	2
12.5%	12.5%	75%	3
18.7%	6.2%	75%	4
21.8%	3.1%	75%	5
23.4%	1.6%	75%	6
23.4%	1.6%	75%	7
24.2%	0.8%	75%	8
24.2%	0.8%	75%	9
24.6%	0.4%	75%	10
24.6%	0.4%	75%	11
24.8%	0.2%	75%	12
24.8%	0.2%	75%	13
24.9%	0.1%	75%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample72.0ms (4.4%)

Algorithm

1×

intervals

Results

30.0ms	61×	body	1280	valid
12.0ms	39×	body	640	valid
9.0ms	131×	body	80	valid
5.0ms	256×	pre	80	true
4.0ms	20×	body	320	valid
1.0ms	5×	body	160	valid

Compiler

Compiled 26 to 23 computations (11.5% saved)

simplify500.0ms (30.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	25	17
1	25	17

prune6.0ms (0.3%)

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: 0.2b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize12.0ms (0.7%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
0.1b	(*.f64 e (cos.f64 v))
0.2b	(*.f64 e (sin.f64 v))

rewrite28.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
12×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
3×	`associate-/r*_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `times-frac_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip-+_binary64`

Counts

3 → 59

Calls

3 calls:

14.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
7.0ms	(*.f64 e (sin.f64 v))
4.0ms	(*.f64 e (cos.f64 v))

series47.0ms (2.8%)

Counts

3 → 9

Calls

3 calls:

22.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
17.0ms	(*.f64 e (sin.f64 v))
7.0ms	(*.f64 e (cos.f64 v))

simplify94.0ms (5.7%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4951	924
1	4951	924

prune66.0ms (4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	60	8	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	8	69

Merged error: 0.0b

Counts

69 → 8

Compiler

Compiled 1204 to 490 computations (59.3% saved)

localize11.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 1 (*.f64 e (cos.f64 v))))
0.0b	(.f64 (.f64 e (sin.f64 v)) (/.f64 1 (+.f64 1 (*.f64 e (cos.f64 v)))))
0.1b	(*.f64 e (cos.f64 v))
0.2b	(*.f64 e (sin.f64 v))

rewrite31.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log_binary64`
27×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
22×	`add-cbrt-cube_binary64`
21×	`associate-r_binary64`
18×	`times-frac_binary64`
14×	`pow1_binary64` `prod-exp_binary64`
8×	`cbrt-unprod_binary64`
7×	`associate-l_binary64`
6×	`div-exp_binary64`
5×	`pow-prod-down_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64`
3×	`associate-/r_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `associate-/l_binary64` `*-commutative_binary64`
2×	`flip3-+_binary64` `unswap-sqr_binary64` `div-inv_binary64` `flip-+_binary64`
1×	`associate-*r/_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `pow-flip_binary64`

Counts

4 → 109

Calls

4 calls:

12.0ms	(.f64 (.f64 e (sin.f64 v)) (/.f64 1 (+.f64 1 (*.f64 e (cos.f64 v)))))
5.0ms	(/.f64 1 (+.f64 1 (*.f64 e (cos.f64 v))))
5.0ms	(*.f64 e (sin.f64 v))
5.0ms	(*.f64 e (cos.f64 v))

series48.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

21.0ms	(.f64 (.f64 e (sin.f64 v)) (/.f64 1 (+.f64 1 (*.f64 e (cos.f64 v)))))
12.0ms	(/.f64 1 (+.f64 1 (*.f64 e (cos.f64 v))))
8.0ms	(*.f64 e (sin.f64 v))
7.0ms	(*.f64 e (cos.f64 v))

simplify115.0ms (7%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4928	1866
1	4928	1866

prune78.0ms (4.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	121	8	129

Merged error: 0.0b

Counts

129 → 8

Compiler

Compiled 2323 to 1064 computations (54.2% saved)

localize10.0ms (0.6%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 e (cos.f64 v))
0.1b	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
0.2b	(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))

rewrite26.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
57×	`add-sqr-sqrt_binary64`
55×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`
12×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/l*_binary64` `div-inv_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
2×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

3 → 117

Calls

3 calls:

10.0ms	(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
6.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
4.0ms	(*.f64 e (cos.f64 v))

series43.0ms (2.6%)

Counts

3 → 9

Calls

3 calls:

20.0ms	(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
16.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
7.0ms	(*.f64 e (cos.f64 v))

simplify110.0ms (6.7%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5035	3222

prune84.0ms (5.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	4	2	6
Picked	0	1	1
Done	0	1	1
Total	127	7	134

Merged error: 0.0b

Counts

134 → 7

Compiler

Compiled 2714 to 1115 computations (58.9% saved)

localize12.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 e (cos.f64 v))
0.2b	(*.f64 (sin.f64 v) (sqrt.f64 e))
0.3b	(/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e)))
0.3b	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e))))

rewrite36.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
47×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
28×	`sqrt-prod_binary64`
22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-r_binary64` `associate-/l*_binary64` `div-inv_binary64`
8×	`associate-/r*_binary64` `pow1_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`associate-l_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
3×	`unswap-sqr_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `associate-/r/_binary64` `flip-+_binary64`

Counts

4 → 135

Calls

4 calls:

11.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e))))
9.0ms	(/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e)))
6.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
4.0ms	(*.f64 e (cos.f64 v))

series84.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

34.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e))))
31.0ms	(/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e)))
12.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
7.0ms	(*.f64 e (cos.f64 v))

simplify102.0ms (6.2%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4967	3898
1	4967	3898

Details

analyze25.0ms (1.5%)

sample72.0ms (4.4%)

simplify500.0ms (30.3%)

prune6.0ms (0.3%)

localize12.0ms (0.7%)

rewrite28.0ms (1.7%)

series47.0ms (2.8%)

simplify94.0ms (5.7%)

prune66.0ms (4%)

localize11.0ms (0.7%)

rewrite31.0ms (1.9%)

series48.0ms (2.9%)

simplify115.0ms (7%)

prune78.0ms (4.7%)

localize10.0ms (0.6%)

rewrite26.0ms (1.6%)

series43.0ms (2.6%)

simplify110.0ms (6.7%)

prune84.0ms (5.1%)

localize12.0ms (0.7%)

rewrite36.0ms (2.2%)

series84.0ms (5.1%)

simplify102.0ms (6.2%)

prune9.0ms (0.5%)

Profiling