Details

sample192.0ms

Algorithm

intervals

Results

84.0ms	76×	body	1280	valid
45.0ms	61×	body	640	valid
21.0ms	41×	body	320	valid
11.0ms	72×	body	80	valid
2.0ms	6×	body	160	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	74	30
1	182	30
2	657	30
3	2727	30
4	5001	30

prune7.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 0.5b

Counts

2 → 1

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
2.1b	(- (cos x) (cos y))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-log-exp`
7×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`sqrt-prod` `difference-of-squares`
4×	`sub-neg`
3×	`flip3--` `sum-log` `flip--` `distribute-lft-out--`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `diff-log` `associate-r/` `associate-l/` `frac-add` `flip-+` `unswap-sqr`
1×	`+-commutative` `associate-+l+` `times-frac` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `diff-cos`

Counts

4 → 76

Calls

4 calls:

6.0ms	(+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))
10.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms	(- 3.0 (sqrt 5.0))
5.0ms	(- (cos x) (cos y))

series455.0ms

Counts

4 → 10

Calls

4 calls:

274.0ms	(+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))
109.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
71.0ms	(- (cos x) (cos y))

simplify55.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	590	866
1	2155	808
2	5001	808

prune942.0ms

Filtered

86 candidates to 61 candidates (29.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	72	14	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	14	87

Merged error: 0.2b

Counts

87 → 14

localize33.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.5b	(+ (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x)) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))
1.0b	(- 3.0 (sqrt 5.0))
2.1b	(- (cos x) (cos y))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
10×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`sqrt-prod` `difference-of-squares`
4×	`sub-neg`
3×	`flip3--` `flip--` `distribute-lft-out--`
2×	`distribute-rgt-in` `distribute-lft-in` `diff-log` `associate-r/` `associate-l/` `unswap-sqr`
1×	`+-commutative` `flip3-+` `times-frac` `pow-prod-down` `frac-add` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `diff-cos`

Counts

4 → 73

Calls

4 calls:

13.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
10.0ms	(+ (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x)) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))
4.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- (cos x) (cos y))

series443.0ms

Counts

4 → 10

Calls

4 calls:

109.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
271.0ms	(+ (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x)) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))
0.0ms	(- 3.0 (sqrt 5.0))
63.0ms	(- (cos x) (cos y))

simplify50.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	500	732
1	1775	673
2	5002	670

prune889.0ms

Filtered

83 candidates to 59 candidates (28.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	79	4	83
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	82	15	97

Merged error: 0.2b

Counts

97 → 15

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ 1.0 (+ (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x)) (* (/ (/ (+ (* 3.0 3.0) (neg 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y))))))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.5b	(+ (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x)) (* (/ (/ (+ (* 3.0 3.0) (neg 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))
2.1b	(- (cos x) (cos y))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt`
8×	`add-log-exp`
6×	`pow1` `associate-r` `associate-l`
4×	`times-frac` `associate-*r/` `sqrt-prod`
3×	`sub-neg` `flip3-+` `flip-+` `associate-/l*` `difference-of-squares`
2×	`cbrt-undiv` `distribute-rgt-in` `flip3--` `distribute-lft-in` `div-exp` `associate-*l/` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `associate-/l/` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `diff-log` `pow-prod-down` `frac-add` `clear-num` `associate-/r` `sum-log` `-commutative` `div-inv` `diff-cos`

Counts

4 → 83

Calls

4 calls:

17.0ms	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ 1.0 (+ (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x)) (* (/ (/ (+ (* 3.0 3.0) (neg 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y))))))
11.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
10.0ms	(+ (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x)) (* (/ (/ (+ (* 3.0 3.0) (neg 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))
4.0ms	(- (cos x) (cos y))

series2.6s

Counts

4 → 12

Calls

4 calls:

2.1s	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ 1.0 (+ (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x)) (* (/ (/ (+ (* 3.0 3.0) (neg 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y))))))
108.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
310.0ms	(+ (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x)) (* (/ (/ (+ (* 3.0 3.0) (neg 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))
68.0ms	(- (cos x) (cos y))

simplify95.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	865	2048
1	3745	1807
2	5001	1807

prune999.0ms

Filtered

95 candidates to 70 candidates (26.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	87	8	95
Fresh	9	5	14
Picked	1	0	1
Done	0	0	0
Total	97	13	110

Merged error: 0.1b

Counts

110 → 13

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.5b	(+ (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x)) (* (/ (/ (+ (* 3.0 3.0) (neg 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))
2.1b	(- (cos x) (cos y))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
28×	`-un-lft-identity` `associate-l*`
20×	`times-frac`
18×	`add-cube-cbrt`
11×	`add-exp-log` `add-cbrt-cube`
9×	`associate-r` `difference-of-squares`
8×	`pow1` `add-log-exp`
7×	`sqrt-prod`
5×	`distribute-lft-out--`
4×	`unswap-sqr`
3×	`sub-neg` `associate-*l/` `prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `associate-r/` `pow-prod-down` `-commutative` `flip--`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `diff-log` `div-exp` `frac-add` `sum-log` `flip-+` `div-inv` `diff-cos`

Counts

4 → 99

Calls

4 calls:

10.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
13.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
10.0ms	(+ (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x)) (* (/ (/ (+ (* 3.0 3.0) (neg 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))
4.0ms	(- (cos x) (cos y))

series595.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
107.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
307.0ms	(+ (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x)) (* (/ (/ (+ (* 3.0 3.0) (neg 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))
68.0ms	(- (cos x) (cos y))

simplify66.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	639	1043
1	2449	963
2	5001	963

prune1.2s

Filtered

111 candidates to 78 candidates (29.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	108	3	111
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	112	12	124

Merged error: 0.1b

Counts

124 → 12

regimes288.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	36
1	48	36

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.2s	2742×	body	1280	valid
1.4s	1803×	body	640	valid
393.0ms	757×	body	320	valid
388.0ms	2356×	body	80	valid
323.0ms	342×	body	160	valid

Details

sample192.0ms

simplify51.0ms

prune7.0ms

localize38.0ms

rewrite27.0ms

series455.0ms

simplify55.0ms

prune942.0ms

localize33.0ms

rewrite32.0ms

series443.0ms

simplify50.0ms

prune889.0ms

localize36.0ms

rewrite44.0ms

series2.6s

simplify95.0ms

prune999.0ms

localize36.0ms

rewrite41.0ms

series595.0ms

simplify66.0ms

prune1.2s

regimes288.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.9s

Profiling