Details

analyze317.0ms (4.6%)

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)

sample74.0ms (1.1%)

Algorithm

1×

intervals

Results

26.0ms	51×	body	1024	valid
15.0ms	160×	body	128	valid
8.0ms	24×	body	512	valid
7.0ms	256×	pre	128	true
4.0ms	21×	body	256	valid

Compiler

Compiled 26 to 23 computations (11.5% saved)

simplify209.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	24	17
1	24	17

prune4.0ms (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: 0.1b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize11.0ms (0.2%)

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 (sin.f64 v))
0.1b	(*.f64 e (cos.f64 v))

rewrite23.0ms (0.3%)

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:

7.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
7.0ms	(*.f64 e (cos.f64 v))
5.0ms	(*.f64 e (sin.f64 v))

series407.0ms (5.9%)

Counts

3 → 9

Calls

3 calls:

246.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
94.0ms	(*.f64 e (cos.f64 v))
67.0ms	(*.f64 e (sin.f64 v))

simplify68.0ms (1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5072	920

prune107.0ms (1.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	6	69

Merged error: 0.0b

Counts

69 → 6

Compiler

Compiled 1177 to 469 computations (60.2% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite75.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
30×	`associate-r_binary64`
26×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`sqrt-prod_binary64`
10×	`pow1_binary64`
9×	`associate-l_binary64`
6×	`associate-/r*_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
5×	`cbrt-undiv_binary64` `unswap-sqr_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `*-commutative_binary64`
2×	`flip3-+_binary64` `associate-*r/_binary64` `div-inv_binary64` `flip-+_binary64`
1×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64`

Counts

4 → 112

Calls

4 calls:

30.0ms	(.f64 (sin.f64 v) (/.f64 e (sqrt.f64 (+.f64 (.f64 e (cos.f64 v)) 1))))
15.0ms	(/.f64 (.f64 (sin.f64 v) (/.f64 e (sqrt.f64 (+.f64 (.f64 e (cos.f64 v)) 1)))) (sqrt.f64 (+.f64 1 (*.f64 e (cos.f64 v)))))
9.0ms	(*.f64 e (cos.f64 v))
8.0ms	(*.f64 e (cos.f64 v))

series881.0ms (12.8%)

Counts

4 → 12

Calls

4 calls:

513.0ms	(.f64 (sin.f64 v) (/.f64 e (sqrt.f64 (+.f64 (.f64 e (cos.f64 v)) 1))))
223.0ms	(/.f64 (.f64 (sin.f64 v) (/.f64 e (sqrt.f64 (+.f64 (.f64 e (cos.f64 v)) 1)))) (sqrt.f64 (+.f64 1 (*.f64 e (cos.f64 v)))))
81.0ms	(*.f64 e (cos.f64 v))
65.0ms	(*.f64 e (cos.f64 v))

simplify81.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5002	2502

prune170.0ms (2.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	124	6	130

Merged error: 0b

Counts

130 → 6

Compiler

Compiled 3294 to 1535 computations (53.4% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite42.0ms (0.6%)

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:

9.0ms	(/.f64 e (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))
8.0ms	(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v))
5.0ms	(*.f64 e (cos.f64 v))

series406.0ms (5.9%)

Counts

3 → 9

Calls

3 calls:

191.0ms	(/.f64 e (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))
157.0ms	(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v))
58.0ms	(*.f64 e (cos.f64 v))

simplify110.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4933	3208
1	4933	3208

prune131.0ms (1.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	126	6	132

Merged error: 0b

Counts

132 → 6

Compiler

Compiled 2662 to 1088 computations (59.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) e)
0.1b	(*.f64 e (cos.f64 v))
0.3b	(/.f64 (sin.f64 v) (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) e))

rewrite60.0ms (0.9%)

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:

14.0ms	(/.f64 (sin.f64 v) (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) e))
13.0ms	(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) e)
9.0ms	(*.f64 e (cos.f64 v))

series432.0ms (6.3%)

Counts

3 → 9

Calls

3 calls:

269.0ms	(/.f64 (sin.f64 v) (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) e))
93.0ms	(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) e)
70.0ms	(*.f64 e (cos.f64 v))

simplify109.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4941	3122
1	4941	3122

prune148.0ms (2.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	126	6	132

Merged error: 0b

Counts

132 → 6

Compiler

Compiled 2574 to 1045 computations (59.4% saved)

regimes132.0ms (1.9%)

Compiler: Compiled 902 to 662 computations (26.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	14	17

end0.0ms (0%)

sample2.8s (41%)

Algorithm

1×

intervals

Results

998.0ms	2008×	body	1024	valid
411.0ms	4471×	body	128	valid
311.0ms	1010×	body	512	valid
205.0ms	8000×	pre	128	true
109.0ms	504×	body	256	valid
8.0ms	7×	body	2048	valid

Compiler

Compiled 318 to 235 computations (26.1% saved)

Details

analyze317.0ms (4.6%)

sample74.0ms (1.1%)

simplify209.0ms (3%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite23.0ms (0.3%)

series407.0ms (5.9%)

simplify68.0ms (1%)

prune107.0ms (1.6%)

localize28.0ms (0.4%)

rewrite75.0ms (1.1%)

series881.0ms (12.8%)

simplify81.0ms (1.2%)

prune170.0ms (2.5%)

localize10.0ms (0.1%)

rewrite42.0ms (0.6%)

series406.0ms (5.9%)

simplify110.0ms (1.6%)

prune131.0ms (1.9%)

localize9.0ms (0.1%)

rewrite60.0ms (0.9%)

series432.0ms (6.3%)

simplify109.0ms (1.6%)

prune148.0ms (2.2%)

regimes132.0ms (1.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.8s (41%)

Profiling