Details

analyze340.0ms (3.8%)

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)

sample109.0ms (1.2%)

Algorithm

1×

intervals

Results

44.0ms	64×	body	1024	valid
18.0ms	141×	body	128	valid
16.0ms	37×	body	512	valid
9.0ms	256×	pre	128	true
4.0ms	14×	body	256	valid

Compiler

Compiled 26 to 23 computations (11.5% saved)

simplify307.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	24	17
1	24	17

prune7.0ms (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)

localize23.0ms (0.3%)

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

rewrite52.0ms (0.6%)

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:

13.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
12.0ms	(*.f64 e (sin.f64 v))
9.0ms	(*.f64 e (cos.f64 v))
6.0ms	(+.f64 1 (*.f64 e (cos.f64 v)))

series664.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

317.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
130.0ms	(*.f64 e (sin.f64 v))
114.0ms	(+.f64 1 (*.f64 e (cos.f64 v)))
102.0ms	(*.f64 e (cos.f64 v))

simplify117.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	5262	1100

prune139.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	76	6	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	76	7	83

Merged error: 0.0b

Counts

83 → 7

Compiler

Compiled 1385 to 549 computations (60.4% saved)

localize19.0ms (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))
0.1b	(.f64 e (/.f64 (sin.f64 v) (+.f64 1 (.f64 e (cos.f64 v)))))

rewrite59.0ms (0.7%)

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:

19.0ms	(.f64 e (/.f64 (sin.f64 v) (+.f64 1 (.f64 e (cos.f64 v)))))
11.0ms	(/.f64 (sin.f64 v) (+.f64 1 (*.f64 e (cos.f64 v))))
8.0ms	(*.f64 e (cos.f64 v))
6.0ms	(+.f64 1 (*.f64 e (cos.f64 v)))

series756.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

316.0ms	(.f64 e (/.f64 (sin.f64 v) (+.f64 1 (.f64 e (cos.f64 v)))))
237.0ms	(/.f64 (sin.f64 v) (+.f64 1 (*.f64 e (cos.f64 v))))
104.0ms	(+.f64 1 (*.f64 e (cos.f64 v)))
99.0ms	(*.f64 e (cos.f64 v))

simplify121.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	5180	1895

prune174.0ms (1.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	103	8	111

Merged error: 0.0b

Counts

111 → 8

Compiler

Compiled 1999 to 876 computations (56.2% saved)

localize19.0ms (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))
0.1b	(/.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)))

rewrite66.0ms (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:

16.0ms	(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
11.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
8.0ms	(*.f64 e (cos.f64 v))
6.0ms	(+.f64 1 (*.f64 e (cos.f64 v)))

series777.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

319.0ms	(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
252.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
107.0ms	(*.f64 e (cos.f64 v))
99.0ms	(+.f64 1 (*.f64 e (cos.f64 v)))

simplify181.0ms (2%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	4947	3388
1	4947	3388

prune241.0ms (2.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	135	5	140
Fresh	3	2	5
Picked	1	0	1
Done	1	1	2
Total	140	8	148

Merged error: 0.0b

Counts

148 → 8

Compiler

Compiled 2973 to 1244 computations (58.2% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e))) (+.f64 1 (*.f64 e (cos.f64 v))))
0.1b	(*.f64 e (cos.f64 v))
0.2b	(*.f64 (sin.f64 v) (sqrt.f64 e))
0.3b	(.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e)))

rewrite69.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

20.0ms	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e))) (+.f64 1 (*.f64 e (cos.f64 v))))
15.0ms	(.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e)))
11.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
8.0ms	(*.f64 e (cos.f64 v))

series865.0ms (9.6%)

Counts

4 → 12

Calls

4 calls:

430.0ms	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e))) (+.f64 1 (*.f64 e (cos.f64 v))))
183.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
138.0ms	(.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e)))
113.0ms	(*.f64 e (cos.f64 v))

simplify112.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5084	1500

prune157.0ms (1.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	98	8	106

Merged error: 0.0b

Counts

106 → 8

Compiler

Compiled 1887 to 647 computations (65.7% saved)

regimes83.0ms (0.9%)

Compiler: Compiled 334 to 224 computations (32.9% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	14	17

end0.0ms (0%)

sample3.5s (38.8%)

Algorithm

1×

intervals

Results

1.4s	1989×	body	1024	valid
580.0ms	4505×	body	128	valid
420.0ms	1003×	body	512	valid
264.0ms	8000×	pre	128	true
149.0ms	502×	body	256	valid
2.0ms	1×	body	2048	valid

Compiler

Compiled 191 to 131 computations (31.4% saved)

Details

analyze340.0ms (3.8%)

sample109.0ms (1.2%)

simplify307.0ms (3.4%)

prune7.0ms (0.1%)

localize23.0ms (0.3%)

rewrite52.0ms (0.6%)

series664.0ms (7.4%)

simplify117.0ms (1.3%)

prune139.0ms (1.6%)

localize19.0ms (0.2%)

rewrite59.0ms (0.7%)

series756.0ms (8.4%)

simplify121.0ms (1.4%)

prune174.0ms (1.9%)

localize19.0ms (0.2%)

rewrite66.0ms (0.7%)

series777.0ms (8.7%)

simplify181.0ms (2%)

prune241.0ms (2.7%)

localize24.0ms (0.3%)

rewrite69.0ms (0.8%)

series865.0ms (9.6%)

simplify112.0ms (1.2%)

prune157.0ms (1.8%)

regimes83.0ms (0.9%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.5s (38.8%)

Profiling