Details

sample53.0ms

Algorithm

intervals

Results

11.0ms	193×	body	80	valid
9.0ms	25×	body	2560	valid
6.0ms	21×	body	1280	valid
6.0ms	256×	pre	80	true
2.0ms	9×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	9
1	34	9
2	38	9
3	40	9
4	41	9
5	41	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: 12.3b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite35.0ms

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:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
7.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
15.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* (* 4.0 p) p) (* x x))
56.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
76.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
53.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify143.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (26.0ms)

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

prune254.0ms

Filtered

91 candidates to 67 candidates (73.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	77	14	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	14	92

Merged error: 12.0b

Counts

92 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

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

series242.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
53.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify122.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	167	517
1	465	490
2	1264	489
3	3249	489
4	5001	489

prune283.0ms

Filtered

69 candidates to 61 candidates (88.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	69	14	83

Merged error: 12.0b

Counts

83 → 14

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.9b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
40×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
26×	`sqrt-prod`
24×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`pow1`
6×	`sqrt-div` `associate-/r*` `add-log-exp`
5×	`unswap-sqr`
4×	`flip3-+` `div-exp` `prod-exp` `associate-/r/` `flip-+`
3×	`pow-flip` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 122

Calls

4 calls:

8.0ms	(/ 1 (sqrt (+ (* (* 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)))

series257.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
52.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
78.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify47.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	367	1199
1	1642	1080
2	5001	1018

prune264.0ms

Filtered

134 candidates to 79 candidates (59.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	131	3	134
Fresh	6	6	12
Picked	0	1	1
Done	0	1	1
Total	137	11	148

Merged error: 12.0b

Counts

148 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.2b	(* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2)))
4.9b	(+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))))
13.9b	(pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-exp-log` `pow-unpow`
8×	`add-log-exp`
7×	`unpow-prod-down` `associate-r`
6×	`add-cbrt-cube`
5×	`pow1`
3×	`distribute-lft-neg-in` `pow-neg` `distribute-rgt-neg-in` `associate-l` `prod-exp` `unswap-sqr` `sqr-pow`
2×	`+-commutative` `neg-sub0` `pow-to-exp` `flip3-+` `associate-*r/` `pow-exp` `sum-log` `flip-+` `pow-sub`
1×	`neg-mul-1` `pow-pow` `un-div-inv` `*-commutative` `cbrt-unprod`

Counts

4 → 76

Calls

4 calls:

9.0ms	(+ (* (* 4.0 p) p) (* x x))
22.0ms	(* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2)))
3.0ms	(+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))))
6.0ms	(pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))

series299.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* (* 4.0 p) p) (* x x))
58.0ms	(* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2)))
77.0ms	(+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))))
132.0ms	(pow (+ (* (* 4.0 p) p) (* x x)) (- 1/2))

simplify51.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	362	711
1	1483	663
2	5001	662

prune203.0ms

Filtered

88 candidates to 65 candidates (73.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	0	8	8
Picked	1	0	1
Done	1	1	2
Total	88	11	99

Merged error: 12.0b

Counts

99 → 11

regimes143.0ms

Accuracy

0% (0.5b remaining)

Error of 13.4b against oracle of 12.9b and baseline of 13.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	12
1	25	12

end0.0ms

sample856.0ms

Algorithm

intervals

Results

223.0ms	6052×	body	80	valid
181.0ms	765×	body	2560	valid
122.0ms	652×	body	1280	valid
106.0ms	8000×	pre	80	true
46.0ms	314×	body	640	valid
16.0ms	151×	body	320	valid
5.0ms	66×	body	160	valid