Details

analyze224.0ms (4.4%)

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)

sample59.0ms (1.2%)

Algorithm

1×

intervals

Results

24.0ms	64×	body	1024	valid
10.0ms	149×	body	128	valid
6.0ms	26×	body	512	valid
5.0ms	256×	pre	128	true
3.0ms	17×	body	256	valid

Compiler

Compiled 26 to 23 computations (11.5% saved)

simplify178.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 0.2b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (*.f64 e (cos.f64 v)))
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))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

7.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
6.0ms	(*.f64 e (sin.f64 v))
5.0ms	(*.f64 e (cos.f64 v))
3.0ms	(+.f64 1 (*.f64 e (cos.f64 v)))

series369.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

174.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
77.0ms	(*.f64 e (sin.f64 v))
62.0ms	(*.f64 e (cos.f64 v))
56.0ms	(+.f64 1 (*.f64 e (cos.f64 v)))

simplify79.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5284	1100

prune222.0ms (4.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Merged error: 0.0b

Counts

83 → 8

Compiler

Compiled 3664 to 2085 computations (43.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

10.0ms	(.f64 e (/.f64 (sin.f64 v) (+.f64 1 (.f64 e (cos.f64 v)))))
6.0ms	(/.f64 (sin.f64 v) (+.f64 1 (*.f64 e (cos.f64 v))))
5.0ms	(*.f64 e (cos.f64 v))
3.0ms	(+.f64 1 (*.f64 e (cos.f64 v)))

series411.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

178.0ms	(.f64 e (/.f64 (sin.f64 v) (+.f64 1 (.f64 e (cos.f64 v)))))
129.0ms	(/.f64 (sin.f64 v) (+.f64 1 (*.f64 e (cos.f64 v))))
52.0ms	(+.f64 1 (*.f64 e (cos.f64 v)))
51.0ms	(*.f64 e (cos.f64 v))

simplify82.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4958	1895
1	4958	1895

prune126.0ms (2.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	102	10	112

Merged error: 0.0b

Counts

112 → 10

Compiler

Compiled 2503 to 1240 computations (50.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (+.f64 1 (*.f64 e (cos.f64 v))) 3)
0.0b	(cbrt.f64 (pow.f64 (+.f64 1 (*.f64 e (cos.f64 v))) 3))
0.1b	(*.f64 e (cos.f64 v))
0.2b	(*.f64 e (sin.f64 v))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`cbrt-prod_binary64`
9×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-r_binary64` `associate-l_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
4×	`add-log-exp_binary64` `cube-div_binary64`
3×	`pow-unpow_binary64`
2×	`cbrt-div_binary64` `pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `sqr-pow_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip-+_binary64` `unpow3_binary64` `*-commutative_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `rem-cbrt-cube_binary64` `pow1/3_binary64` `pow-pow_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64`

Counts

4 → 84

Calls

4 calls:

5.0ms	(*.f64 e (sin.f64 v))
5.0ms	(*.f64 e (cos.f64 v))
4.0ms	(pow.f64 (+.f64 1 (*.f64 e (cos.f64 v))) 3)
4.0ms	(cbrt.f64 (pow.f64 (+.f64 1 (*.f64 e (cos.f64 v))) 3))

series250.0ms (5%)

Counts

4 → 12

Calls

4 calls:

83.0ms	(pow.f64 (+.f64 1 (*.f64 e (cos.f64 v))) 3)
57.0ms	(cbrt.f64 (pow.f64 (+.f64 1 (*.f64 e (cos.f64 v))) 3))
55.0ms	(*.f64 e (sin.f64 v))
55.0ms	(*.f64 e (cos.f64 v))

simplify63.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4951	1220
1	4951	1220

prune116.0ms (2.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	96	10	106

Merged error: 0.0b

Counts

106 → 10

Compiler

Compiled 2207 to 1130 computations (48.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite34.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 128

Calls

4 calls:

8.0ms	(/.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))
5.0ms	(*.f64 e (cos.f64 v))
3.0ms	(+.f64 1 (*.f64 e (cos.f64 v)))

series408.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

168.0ms	(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
129.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
57.0ms	(+.f64 1 (*.f64 e (cos.f64 v)))
54.0ms	(*.f64 e (cos.f64 v))

simplify87.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4961	3388
1	4961	3388

prune212.0ms (4.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	3	4	7
Picked	0	1	1
Done	1	1	2
Total	142	8	150

Merged error: 0.0b

Counts

150 → 8

Compiler

Compiled 4223 to 2117 computations (49.9% saved)

regimes39.0ms (0.8%)

Compiler: Compiled 252 to 180 computations (28.6% 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%)

sample1.9s (38.5%)

Algorithm

1×

intervals

Results

759.0ms	1989×	body	1024	valid
326.0ms	4476×	body	128	valid
231.0ms	1000×	body	512	valid
153.0ms	8000×	pre	128	true
86.0ms	532×	body	256	valid
3.0ms	3×	body	2048	valid

Compiler

Compiled 150 to 109 computations (27.3% saved)

Details

analyze224.0ms (4.4%)

sample59.0ms (1.2%)

simplify178.0ms (3.5%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

rewrite27.0ms (0.5%)

series369.0ms (7.3%)

simplify79.0ms (1.6%)

prune222.0ms (4.4%)

localize10.0ms (0.2%)

rewrite31.0ms (0.6%)

series411.0ms (8.2%)

simplify82.0ms (1.6%)

prune126.0ms (2.5%)

localize13.0ms (0.3%)

rewrite27.0ms (0.5%)

series250.0ms (5%)

simplify63.0ms (1.2%)

prune116.0ms (2.3%)

localize10.0ms (0.2%)

rewrite34.0ms (0.7%)

series408.0ms (8.1%)

simplify87.0ms (1.7%)

prune212.0ms (4.2%)

regimes39.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.9s (38.5%)

Profiling