Details

sample49.0ms

Algorithm

intervals

Results

10.0ms	189×	body	80	valid
9.0ms	29×	body	2560	valid
8.0ms	256×	pre	80	true
5.0ms	21×	body	1280	valid
2.0ms	11×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	27	9
1	34	9
2	38	9
3	40	9
4	41	9
5	41	9

prune3.0ms

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: 14.0b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0b	(+ (* (* 4.0 p) p) (* x x))
0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

7.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
5.0ms	(+ (* (* 4.0 p) p) (* x x))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
31.0ms	(+ (* (* 4.0 p) p) (* x x))
72.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify146.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	278	822
1	1014	772
2	4246	757
3	5001	757

prune233.0ms

Filtered

91 candidates to 67 candidates (73.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	79	12	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	12	92

Merged error: 13.7b

Counts

92 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.4b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt`
6×	`pow1`
5×	`log-pow`
4×	`add-exp-log` `log-prod` `exp-prod` `add-cbrt-cube`
3×	`flip3-+` `sqrt-prod` `flip-+`
2×	`+-commutative` `sqrt-div` `sum-log` `distribute-lft-out`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `exp-sum`

Counts

4 → 55

Calls

4 calls:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
15.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* (* 4.0 p) p) (* x x))
73.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
73.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
52.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify82.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	231	541
1	855	487
2	2820	483
3	5001	482

prune195.0ms

Filtered

67 candidates to 54 candidates (80.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	66	13	79

Merged error: 13.7b

Counts

79 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.8b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`associate-r`
22×	`times-frac`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
14×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
5×	`unswap-sqr`
4×	`flip3-+` `sqrt-div` `prod-exp` `flip-+`
3×	`associate-l`
2×	`+-commutative` `div-exp` `sum-log` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 86

Calls

4 calls:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
14.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* (* 4.0 p) p) (* x x))
51.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
73.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify53.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	387	817
1	1913	734
2	5002	700

prune234.0ms

Filtered

98 candidates to 68 candidates (69.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	98	13	111

Merged error: 13.7b

Counts

111 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
7.9b	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `distribute-lft-out`

Counts

4 → 125

Calls

4 calls:

17.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
76.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify57.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	290	1356
1	1084	1258
2	5001	1216

prune249.0ms

Filtered

137 candidates to 75 candidates (54.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	134	3	137
Fresh	3	8	11
Picked	1	0	1
Done	0	1	1
Total	138	12	150

Merged error: 13.7b

Counts

150 → 12

regimes242.0ms

Accuracy

0% (0.3b remaining)

Error of 13.5b against oracle of 13.3b and baseline of 13.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	11
1	21	11

end0.0ms

sample1.1s

Algorithm

intervals

Results

308.0ms	5985×	body	80	valid
264.0ms	838×	body	2560	valid
158.0ms	634×	body	1280	valid
144.0ms	8000×	pre	80	true
61.0ms	302×	body	640	valid
27.0ms	167×	body	320	valid
7.0ms	74×	body	160	valid