Details

analyze224.0ms (4.1%)

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)

sample61.0ms (1.1%)

Algorithm

1×

intervals

Results

25.0ms	64×	body	1024	valid
11.0ms	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 (3.2%)

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))
4.0ms	(*.f64 e (cos.f64 v))
3.0ms	(+.f64 1 (*.f64 e (cos.f64 v)))

series357.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

172.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
67.0ms	(*.f64 e (sin.f64 v))
61.0ms	(*.f64 e (cos.f64 v))
57.0ms	(+.f64 1 (*.f64 e (cos.f64 v)))

simplify64.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5262	1100

prune82.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	7	83

Merged error: 0.0b

Counts

83 → 7

Compiler

Compiled 1408 to 564 computations (59.9% saved)

localize13.0ms (0.2%)

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))

rewrite26.0ms (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:

7.0ms	(pow.f64 (+.f64 1 (*.f64 e (cos.f64 v))) 3)
4.0ms	(*.f64 e (cos.f64 v))
4.0ms	(*.f64 e (sin.f64 v))
4.0ms	(cbrt.f64 (pow.f64 (+.f64 1 (*.f64 e (cos.f64 v))) 3))

series267.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

90.0ms	(pow.f64 (+.f64 1 (*.f64 e (cos.f64 v))) 3)
60.0ms	(*.f64 e (cos.f64 v))
59.0ms	(*.f64 e (sin.f64 v))
57.0ms	(cbrt.f64 (pow.f64 (+.f64 1 (*.f64 e (cos.f64 v))) 3))

simplify63.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4950	1220
1	4950	1220

prune91.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	96	7	103

Merged error: 0.0b

Counts

103 → 7

Compiler

Compiled 1848 to 864 computations (53.2% saved)

localize11.0ms (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)))

rewrite37.0ms (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:

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

series416.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

180.0ms	(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
132.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
53.0ms	(+.f64 1 (*.f64 e (cos.f64 v)))
51.0ms	(*.f64 e (cos.f64 v))

simplify103.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4947	3388
1	4947	3388

prune136.0ms (2.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	136	4	140
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	138	9	147

Merged error: 0.0b

Counts

147 → 9

Compiler

Compiled 2961 to 1233 computations (58.4% saved)

localize12.0ms (0.2%)

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 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e)))
0.2b	(*.f64 (sin.f64 v) (sqrt.f64 e))

rewrite39.0ms (0.7%)

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:

14.0ms	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e))) (+.f64 1 (*.f64 e (cos.f64 v))))
8.0ms	(.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e)))
6.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
4.0ms	(*.f64 e (cos.f64 v))

series427.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

213.0ms	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e))) (+.f64 1 (*.f64 e (cos.f64 v))))
92.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
68.0ms	(.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e)))
53.0ms	(*.f64 e (cos.f64 v))

simplify60.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5084	1500

prune81.0ms (1.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	98	9	107

Merged error: 0.0b

Counts

107 → 9

Compiler

Compiled 1887 to 646 computations (65.8% saved)

regimes218.0ms (4%)

Compiler: Compiled 2099 to 1456 computations (30.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	21
1	16	21

end0.0ms (0%)

sample2.5s (45.4%)

Algorithm

1×

intervals

Results

776.0ms	1989×	body	1024	valid
347.0ms	4476×	body	128	valid
245.0ms	1000×	body	512	valid
166.0ms	8000×	pre	128	true
85.0ms	532×	body	256	valid
3.0ms	3×	body	2048	valid

Compiler

Compiled 699 to 485 computations (30.6% saved)

Details

analyze224.0ms (4.1%)

sample61.0ms (1.1%)

simplify178.0ms (3.2%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

rewrite27.0ms (0.5%)

series357.0ms (6.5%)

simplify64.0ms (1.2%)

prune82.0ms (1.5%)

localize13.0ms (0.2%)

rewrite26.0ms (0.5%)

series267.0ms (4.8%)

simplify63.0ms (1.1%)

prune91.0ms (1.7%)

localize11.0ms (0.2%)

rewrite37.0ms (0.7%)

series416.0ms (7.5%)

simplify103.0ms (1.9%)

prune136.0ms (2.5%)

localize12.0ms (0.2%)

rewrite39.0ms (0.7%)

series427.0ms (7.7%)

simplify60.0ms (1.1%)

prune81.0ms (1.5%)

regimes218.0ms (4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.5s (45.4%)

Profiling