Details

analyze26.0ms

Algorithm

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

sample64.0ms

Algorithm

intervals

Results

23.0ms	48×	body	1280	valid
11.0ms	35×	body	640	valid
10.0ms	143×	body	80	valid
5.0ms	256×	pre	80	true
4.0ms	20×	body	320	valid
1.0ms	10×	body	160	valid

simplify466.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	23	11
1	23	11

prune4.0ms

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

localize12.0ms

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

rewrite21.0ms

Algorithm

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))))
4.0ms	(*.f64 e (cos.f64 v))
7.0ms	(*.f64 e (sin.f64 v))

series59.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
7.0ms	(*.f64 e (cos.f64 v))
17.0ms	(*.f64 e (sin.f64 v))

simplify59.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4949	588
1	4949	588

prune53.0ms

Filtered

48 candidates to 68 candidates (-41.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	7	69

Merged error: 0.0b

Counts

69 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 e (cos.f64 v))
0.1b	(*.f64 e (sin.f64 v))
0.1b	(.f64 (.f64 e (cos.f64 v)) (*.f64 e (cos.f64 v)))
0.1b	(pow.f64 (*.f64 e (cos.f64 v)) 3)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

50×	`pow1_binary64`
23×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`pow-prod-down_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`cbrt-unprod_binary64` `prod-exp_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
3×	`pow-unpow_binary64` `*-commutative_binary64`
2×	`pow-pow_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `swap-sqr_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `pow2_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 92

Calls

4 calls:

5.0ms	(*.f64 e (cos.f64 v))
5.0ms	(*.f64 e (sin.f64 v))
8.0ms	(.f64 (.f64 e (cos.f64 v)) (*.f64 e (cos.f64 v)))
5.0ms	(pow.f64 (*.f64 e (cos.f64 v)) 3)

series41.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(*.f64 e (cos.f64 v))
7.0ms	(*.f64 e (sin.f64 v))
11.0ms	(.f64 (.f64 e (cos.f64 v)) (*.f64 e (cos.f64 v)))
13.0ms	(pow.f64 (*.f64 e (cos.f64 v)) 3)

simplify44.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4937	543
1	4937	543

prune61.0ms

Filtered

56 candidates to 104 candidates (-85.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	104	7	111

Merged error: 0.0b

Counts

111 → 7

localize10.0ms

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)))

rewrite23.0ms

Algorithm

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:

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

series44.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(*.f64 e (cos.f64 v))
17.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
19.0ms	(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))

simplify62.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5033	2009

prune84.0ms

Filtered

100 candidates to 126 candidates (-26.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	121	5	126
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	123	10	133

Merged error: 0.0b

Counts

133 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm

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:

5.0ms	(*.f64 e (cos.f64 v))
9.0ms	(/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e)))
11.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e))))
6.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))

series80.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(*.f64 e (cos.f64 v))
27.0ms	(/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e)))
34.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e))))
12.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))

simplify57.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4965	2410
1	4965	2410

prune68.0ms

Filtered

104 candidates to 147 candidates (-41.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	2	5	7
Picked	0	1	1
Done	0	2	2
Total	147	10	157

Merged error: 0b

Counts

157 → 10

regimes83.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	64	30
1	64	30

end0.0ms

sample1.9s

Algorithm

intervals

Results

712.0ms	1490×	body	1280	valid
369.0ms	1244×	body	640	valid
278.0ms	4326×	body	80	valid
143.0ms	8000×	pre	80	true
134.0ms	650×	body	320	valid
41.0ms	290×	body	160	valid

Details

analyze26.0ms

sample64.0ms

simplify466.0ms

prune4.0ms

localize12.0ms

rewrite21.0ms

series59.0ms

simplify59.0ms

prune53.0ms

localize18.0ms

rewrite26.0ms

series41.0ms

simplify44.0ms

prune61.0ms

localize10.0ms

rewrite23.0ms

series44.0ms

simplify62.0ms

prune84.0ms

localize12.0ms

rewrite35.0ms

series80.0ms

simplify57.0ms

prune68.0ms

regimes83.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample1.9s

Profiling