Details

analyze759.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
50%	50%	0.1%	4
74.9%	25%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
74.9%	25%	0.1%	9
74.9%	25%	0.1%	10
74.9%	25%	0.1%	11
74.9%	25%	0.1%	12
74.9%	25%	0.1%	13
74.9%	25%	0.1%	14

sample205.0ms

Algorithm

intervals

Results

106.0ms	83×	body	1280	valid
55.0ms	63×	body	640	valid
16.0ms	28×	body	320	valid
12.0ms	67×	body	80	valid
6.0ms	15×	body	160	valid

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4925	77
1	4925	77

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 0.4b

Counts

2 → 2

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
0.4b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
1.0b	(-.f64 3 (sqrt.f64 5))
2.1b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-cube-cbrt_binary64`
8×	`add-log-exp_binary64`
6×	`pow1_binary64` `associate-r_binary64` `associate-r/_binary64` `associate-l*_binary64`
5×	`difference-of-squares_binary64` `sqrt-prod_binary64`
4×	`sub-neg_binary64` `associate-/r/_binary64` `times-frac_binary64`
3×	`flip3-+_binary64` `flip3--_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-exp_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `diff-cos_binary64` `-commutative_binary64`

Counts

4 → 84

Calls

4 calls:

13.0ms	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
12.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
4.0ms	(-.f64 3 (sqrt.f64 5))
7.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

series1.5s

Counts

4 → 10

Calls

4 calls:

1.4s	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
63.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
0.0ms	(-.f64 3 (sqrt.f64 5))
43.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

simplify100.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4930	3915
1	4930	3915

prune291.0ms

Filtered

71 candidates to 94 candidates (-32.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	83	11	94
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	85	11	96

Merged error: 0.0b

Counts

96 → 11

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)))
0.3b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (/.f64 4 (+.f64 3 (sqrt.f64 5))) 2) (cos.f64 y)))))
0.4b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
2.1b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`associate-*r/_binary64`
12×	`associate-r_binary64`
11×	`pow1_binary64`
10×	`add-cube-cbrt_binary64`
8×	`flip3--_binary64` `flip--_binary64`
7×	`associate-l_binary64`
6×	`add-log-exp_binary64`
5×	`sub-neg_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `times-frac_binary64`
4×	`pow-prod-down_binary64` `associate-/r/_binary64` `sqrt-prod_binary64` `frac-times_binary64` `associate-*l/_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`associate-/r*_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `diff-cos_binary64`

Counts

4 → 101

Calls

4 calls:

19.0ms	(.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)))
13.0ms	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (/.f64 4 (+.f64 3 (sqrt.f64 5))) 2) (cos.f64 y)))))
14.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
5.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

series1.6s

Counts

4 → 12

Calls

4 calls:

107.0ms	(.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)))
1.4s	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (/.f64 4 (+.f64 3 (sqrt.f64 5))) 2) (cos.f64 y)))))
61.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
41.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

simplify118.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4963	5120
1	4963	5120

prune327.0ms

Filtered

83 candidates to 113 candidates (-36.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	108	5	113
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	112	12	124

Merged error: 0.0b

Counts

124 → 12

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 -2 (.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))))) (+.f64 -3 (.f64 (+.f64 (.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2)) (.f64 (cos.f64 y) (/.f64 2 (+.f64 3 (sqrt.f64 5))))) -3)))
0.4b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
0.5b	(+.f64 (.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2)) (.f64 (cos.f64 y) (/.f64 2 (+.f64 3 (sqrt.f64 5)))))
2.1b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
16×	`times-frac_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64` `associate-r_binary64` `associate-l_binary64`
5×	`associate-/r*_binary64`
4×	`associate-*r/_binary64` `distribute-rgt-out_binary64` `distribute-rgt1-in_binary64` `sqrt-prod_binary64`
3×	`sub-neg_binary64` `flip3--_binary64` `difference-of-squares_binary64` `associate-/l*_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `distribute-lft-out--_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-sub_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `diff-cos_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 95

Calls

4 calls:

7.0ms	(/.f64 (-.f64 -2 (.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))))) (+.f64 -3 (.f64 (+.f64 (.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2)) (.f64 (cos.f64 y) (/.f64 2 (+.f64 3 (sqrt.f64 5))))) -3)))
14.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
12.0ms	(+.f64 (.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2)) (.f64 (cos.f64 y) (/.f64 2 (+.f64 3 (sqrt.f64 5)))))
5.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

series1.5s

Counts

4 → 12

Calls

4 calls:

1.3s	(/.f64 (-.f64 -2 (.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))))) (+.f64 -3 (.f64 (+.f64 (.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2)) (.f64 (cos.f64 y) (/.f64 2 (+.f64 3 (sqrt.f64 5))))) -3)))
65.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
117.0ms	(+.f64 (.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2)) (.f64 (cos.f64 y) (/.f64 2 (+.f64 3 (sqrt.f64 5)))))
43.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

simplify149.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4938	6344
1	4938	6344

prune349.0ms

Filtered

85 candidates to 107 candidates (-25.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	3	7	10
Picked	1	0	1
Done	0	1	1
Total	109	10	119

Merged error: 0.0b

Counts

119 → 10

localize52.0ms

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (sqrt.f64 2) (sin.f64 x))
0.4b	(*.f64 (sqrt.f64 2) (sin.f64 x))
2.1b	(-.f64 (+.f64 (.f64 1/16 (.f64 (.f64 (cos.f64 x) (sqrt.f64 2)) (+.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (sin.f64 y) 2)))) (.f64 (sin.f64 y) (-.f64 (.f64 (.f64 (cos.f64 y) 257/256) (.f64 (sqrt.f64 2) (sin.f64 x))) (.f64 257/256 (.f64 (cos.f64 x) (.f64 (sqrt.f64 2) (sin.f64 x))))))) (.f64 (.f64 (*.f64 (cos.f64 y) (sqrt.f64 2)) 1/16) (+.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (sin.f64 y) 2))))
2.2b	(-.f64 (.f64 (.f64 (cos.f64 y) 257/256) (.f64 (sqrt.f64 2) (sin.f64 x))) (.f64 257/256 (.f64 (cos.f64 x) (.f64 (sqrt.f64 2) (sin.f64 x)))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

36×	`associate-*r/_binary64`
18×	`add-sqr-sqrt_binary64`
12×	`flip3-+_binary64` `associate-l_binary64` `flip-+_binary64` `frac-sub_binary64`
11×	`add-log-exp_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`pow1_binary64` `frac-add_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
6×	`flip3--_binary64` `associate-r_binary64` `flip--_binary64`
4×	`unswap-sqr_binary64`
3×	`diff-log_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `associate--r+_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

4 → 82

Calls

4 calls:

6.0ms	(*.f64 (sqrt.f64 2) (sin.f64 x))
6.0ms	(*.f64 (sqrt.f64 2) (sin.f64 x))
27.0ms	(-.f64 (+.f64 (.f64 1/16 (.f64 (.f64 (cos.f64 x) (sqrt.f64 2)) (+.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (sin.f64 y) 2)))) (.f64 (sin.f64 y) (-.f64 (.f64 (.f64 (cos.f64 y) 257/256) (.f64 (sqrt.f64 2) (sin.f64 x))) (.f64 257/256 (.f64 (cos.f64 x) (.f64 (sqrt.f64 2) (sin.f64 x))))))) (.f64 (.f64 (*.f64 (cos.f64 y) (sqrt.f64 2)) 1/16) (+.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (sin.f64 y) 2))))
10.0ms	(-.f64 (.f64 (.f64 (cos.f64 y) 257/256) (.f64 (sqrt.f64 2) (sin.f64 x))) (.f64 257/256 (.f64 (cos.f64 x) (.f64 (sqrt.f64 2) (sin.f64 x)))))

series824.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(*.f64 (sqrt.f64 2) (sin.f64 x))
25.0ms	(*.f64 (sqrt.f64 2) (sin.f64 x))
634.0ms	(-.f64 (+.f64 (.f64 1/16 (.f64 (.f64 (cos.f64 x) (sqrt.f64 2)) (+.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (sin.f64 y) 2)))) (.f64 (sin.f64 y) (-.f64 (.f64 (.f64 (cos.f64 y) 257/256) (.f64 (sqrt.f64 2) (sin.f64 x))) (.f64 257/256 (.f64 (cos.f64 x) (.f64 (sqrt.f64 2) (sin.f64 x))))))) (.f64 (.f64 (*.f64 (cos.f64 y) (sqrt.f64 2)) 1/16) (+.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (sin.f64 y) 2))))
142.0ms	(-.f64 (.f64 (.f64 (cos.f64 y) 257/256) (.f64 (sqrt.f64 2) (sin.f64 x))) (.f64 257/256 (.f64 (cos.f64 x) (.f64 (sqrt.f64 2) (sin.f64 x)))))

simplify142.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4967	7199
1	4967	7199

prune492.0ms

Filtered

71 candidates to 94 candidates (-32.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	94	10	104

Merged error: 0.0b

Counts

104 → 10

regimes118.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify7.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	275	140
1	275	140

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.6s	2728×	body	1280	valid
1.5s	1824×	body	640	valid
453.0ms	777×	body	320	valid
446.0ms	2317×	body	80	valid
140.0ms	354×	body	160	valid

Details

analyze759.0ms

sample205.0ms

simplify61.0ms

prune8.0ms

localize32.0ms

rewrite39.0ms

series1.5s

simplify100.0ms

prune291.0ms

localize34.0ms

rewrite54.0ms

series1.6s

simplify118.0ms

prune327.0ms

localize34.0ms

rewrite41.0ms

series1.5s

simplify149.0ms

prune349.0ms

localize52.0ms

rewrite52.0ms

series824.0ms

simplify142.0ms

prune492.0ms

regimes118.0ms

bsearch0.0ms

simplify7.0ms

end0.0ms

sample6.3s

Profiling