Details

sample15.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	9
1	36	9
2	68	9
3	117	9
4	174	9
5	195	9
6	197	9
7	197	9

prune2.0ms

Filtered

1 candidates to 0 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: 29.6b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
2.8b	(- (* x x) (* (* y 4.0) y))
29.1b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 55

Calls

3 calls:

4.0ms	(+ (* x x) (* (* y 4.0) y))
3.0ms	(- (* x x) (* (* y 4.0) y))
8.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series140.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(+ (* x x) (* (* y 4.0) y))
40.0ms	(- (* x x) (* (* y 4.0) y))
63.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify38.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	234	680
1	1007	622
2	5001	620

prune138.0ms

Filtered

64 candidates to 49 candidates (76.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	59	5	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	5	65

Merged error: 0.3b

Counts

65 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (exp (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))))
0.0b	(+ (* x x) (* (* y 4.0) y))
2.8b	(- (* x x) (* (* y 4.0) y))
29.1b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
16×	`log-pow`
15×	`exp-prod`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`associate-/r/`
3×	`log-prod` `flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`flip3--` `div-sub` `flip--` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `log-div` `frac-2neg` `exp-diff` `diff-log` `div-exp` `rem-log-exp` `clear-num` `sum-log`

Counts

4 → 83

Calls

4 calls:

8.0ms	(log (exp (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))))
4.0ms	(+ (* x x) (* (* y 4.0) y))
3.0ms	(- (* x x) (* (* y 4.0) y))
9.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series203.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(log (exp (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))))
36.0ms	(+ (* x x) (* (* y 4.0) y))
39.0ms	(- (* x x) (* (* y 4.0) y))
70.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify41.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	287	1034
1	1088	945
2	5002	942

prune215.0ms

Filtered

95 candidates to 73 candidates (76.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	96	4	100

Merged error: 0.3b

Counts

100 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
0.0b	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
19.9b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
21.6b	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`add-cube-cbrt` `associate-/r/` `add-log-exp`
7×	`times-frac`
6×	`associate-/r*`
5×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+`
4×	`pow1` `prod-exp` `cbrt-unprod` `div-inv`
3×	`distribute-rgt-out--`
2×	`frac-2neg` `clear-num` `associate-/l*` `difference-of-squares`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `sum-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div`

Counts

4 → 79

Calls

4 calls:

4.0ms	(+ (* x x) (* (* y 4.0) y))
14.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
6.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
8.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

series210.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* x x) (* (* y 4.0) y))
72.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
48.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
55.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

simplify58.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	396	987
1	1942	882
2	5001	881

prune178.0ms

Filtered

91 candidates to 68 candidates (74.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	91	4	95

Merged error: 0.3b

Counts

95 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* x x) (* (* y 4.0) y))
27.3b	(sqrt (+ (* x x) (* (* y 4.0) y)))
27.3b	(sqrt (+ (* x x) (* (* y 4.0) y)))
27.6b	(/ (- (* x x) (* (* y 4.0) y)) (sqrt (+ (* x x) (* (* y 4.0) y))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

4.0ms	(- (* x x) (* (* y 4.0) y))
4.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
4.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
10.0ms	(/ (- (* x x) (* (* y 4.0) y)) (sqrt (+ (* x x) (* (* y 4.0) y))))

series244.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* x x) (* (* y 4.0) y))
53.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
50.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
101.0ms	(/ (- (* x x) (* (* y 4.0) y)) (sqrt (+ (* x x) (* (* y 4.0) y))))

simplify173.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	274	1117
1	1020	1045
2	4854	1032
3	5002	1032

prune268.0ms

Filtered

98 candidates to 74 candidates (75.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	98	4	102

Merged error: 0.3b

Counts

102 → 4

regimes124.0ms

Accuracy

60.4% (12.2b remaining)

Error of 12.6b against oracle of 0.4b and baseline of 31.2b

bsearch102.0ms

Steps

Iters	Range		Point
4	1.5549168953101855e+143	2.483185623213712e+143	1.617000239523037e+143
6	1.6552168713535222e-160	7.56737574009597e-160	3.017383604922435e-160
9	-1.7961890248789646e-153	-4.991866581371744e-162	-1.8002238488316346e-154
7	-8.221844882759494e+75	-6.577909208550379e+73	-8.024730975973789e+75

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	30
1	32	30

end0.0ms

sample365.0ms

Algorithm

intervals

Results

229.0ms

8000×

body

valid