Details

sample36.0ms

Algorithm

intervals

Results

7.0ms	202×	body	80	valid
7.0ms	256×	pre	80	true
7.0ms	30×	body	2560	valid
2.0ms	13×	body	1280	valid
1.0ms	9×	body	640	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid

simplify10.0ms

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: 9.8b

Counts

2 → 1

localize10.0ms

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))
0.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite31.0ms

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))
11.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
43.0ms	(+ (* (* 4.0 p) p) (* x x))
77.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify176.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (40.0ms)

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

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	80	11	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	11	92

Merged error: 9.7b

Counts

92 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.2b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite38.0ms

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

series248.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* (* 4.0 p) p) (* x x))
90.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
74.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
52.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify87.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (76.0ms)

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

prune189.0ms

Filtered

67 candidates to 52 candidates (77.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	68	10	78

Merged error: 9.7b

Counts

78 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.3b	(* (sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-prod`
30×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
21×	`pow1`
16×	`sqrt-div`
14×	`add-cube-cbrt`
11×	`swap-sqr`
10×	`sqrt-pow1` `pow1/2`
9×	`flip3-+` `flip-+`
7×	`associate-r` `associate-l` `distribute-lft-out`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
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`

Counts

4 → 104

Calls

4 calls:

12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
27.0ms	(* (sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (+ 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)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
75.0ms	(* (sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify214.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 3 (191.0ms)

Iter	Nodes	Cost
0	255	1259
1	894	1149
2	4527	1103
3	5002	1072

prune298.0ms

Filtered

116 candidates to 71 candidates (61.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	116	10	126

Merged error: 9.7b

Counts

126 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.3b	(* (sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`sqrt-prod`
19×	`*-un-lft-identity`
13×	`add-cube-cbrt`
12×	`pow1`
11×	`associate-r`
10×	`log-pow`
8×	`exp-prod`
7×	`associate-l`
6×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
4×	`log-prod` `sqrt-pow1` `pow1/2` `add-log-exp` `unswap-sqr`
3×	`flip3-+` `pow-prod-down` `flip-+` `distribute-lft-out`
2×	`rem-sqrt-square` `associate-*l/`
1×	`sqrt-unprod` `rem-log-exp` `exp-sum` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 85

Calls

4 calls:

13.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
32.0ms	(* (sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (log (exp (+ 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)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
77.0ms	(* (sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
52.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify58.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	239	1084
1	666	895
2	1842	831
3	5001	831

prune294.0ms

Filtered

97 candidates to 72 candidates (74.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	96	11	107

Merged error: 9.7b

Counts

107 → 11

regimes230.0ms

Accuracy

0% (0.3b remaining)

Error of 13.2b against oracle of 13.0b and baseline of 13.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	33
1	27	33

end0.0ms

sample832.0ms

Algorithm

intervals

Results

213.0ms	6024×	body	80	valid
183.0ms	803×	body	2560	valid
111.0ms	600×	body	1280	valid
102.0ms	8000×	pre	80	true
48.0ms	327×	body	640	valid
18.0ms	170×	body	320	valid
5.0ms	76×	body	160	valid