Details

sample36.0ms

Algorithm

intervals

Results

8.0ms	202×	body	80	valid
6.0ms	18×	body	1280	valid
6.0ms	24×	body	2560	valid
4.0ms	256×	pre	80	true
1.0ms	6×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	40	9
2	48	9
3	50	9
4	52	9
5	53	9
6	53	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: 11.4b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.2b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
21×	`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×	`expm1-log1p-u` `fma-def` `flip3-+` `sqrt-div` `flip-+` `log1p-expm1-u`
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 → 91

Calls

4 calls:

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

series226.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (* (* 4.0 p) p) (* x x))
54.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
78.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify155.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 3 (145.0ms)

Iter	Nodes	Cost
0	296	867
1	1081	815
2	4584	798
3	5001	795

prune315.0ms

Filtered

103 candidates to 79 candidates (76.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	88	15	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	15	104

Merged error: 11.2b

Counts

104 → 15

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.4b	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
7×	`add-exp-log`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `log-prod` `flip3-+` `sqrt-div` `flip-+` `log1p-expm1-u`
3×	`fma-def` `associate-/l*`
2×	`log-div` `associate-/r/` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `clear-num` `sum-log` `log-pow` `div-inv`

Counts

4 → 94

Calls

4 calls:

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

series379.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
79.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
185.0ms	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify76.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	296	1010
1	864	940
2	2544	926
3	5001	924

prune369.0ms

Filtered

106 candidates to 80 candidates (75.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	7	7	14
Picked	1	0	1
Done	0	0	0
Total	111	10	121

Merged error: 8.0b

Counts

121 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

2.1b	(/ x (fma (* 4.0 p) p (* x x)))
3.4b	(log (/ (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)) (fma (/ x (fma (* 4.0 p) p (* x x))) x (* 1.0 (- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

57×	`*-un-lft-identity`
36×	`times-frac`
31×	`log-prod`
29×	`add-sqr-sqrt`
27×	`add-cube-cbrt`
15×	`distribute-lft-out`
12×	`unpow-prod-down` `cube-prod`
9×	`add-exp-log`
7×	`pow1`
6×	`sqrt-prod` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `sum-cubes` `associate-/l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `rem-log-exp` `flip-+` `div-inv`
1×	`cbrt-undiv` `log-div` `frac-2neg` `clear-num` `log-pow`

Counts

4 → 107

Calls

4 calls:

3.0ms	(/ x (fma (* 4.0 p) p (* x x)))
40.0ms	(log (/ (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)) (fma (/ x (fma (* 4.0 p) p (* x x))) x (* 1.0 (- 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)))

series613.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ x (fma (* 4.0 p) p (* x x)))
440.0ms	(log (/ (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)) (fma (/ x (fma (* 4.0 p) p (* x x))) x (* 1.0 (- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify108.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	390	2287
1	1212	2170
2	3961	2117
3	5002	2082

prune584.0ms

Filtered

119 candidates to 87 candidates (73.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	118	11	129

Merged error: 8.0b

Counts

129 → 11

localize33.0ms

Local error

Found 4 expressions with local error:

13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`

Counts

4 → 68

Calls

4 calls:

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)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series234.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify92.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	106	544
1	323	524
2	963	524
3	2523	524
4	5002	524

prune706.0ms

Filtered

80 candidates to 72 candidates (90.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	80	11	91

Merged error: 8.0b

Counts

91 → 11

regimes201.0ms

Accuracy

0% (3.5b remaining)

Error of 12.5b against oracle of 9.0b and baseline of 12.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	27
1	31	27

end0.0ms

sample857.0ms

Algorithm

intervals

Results

238.0ms	6124×	body	80	valid
181.0ms	760×	body	2560	valid
114.0ms	592×	body	1280	valid
106.0ms	8000×	pre	80	true
43.0ms	291×	body	640	valid
17.0ms	158×	body	320	valid
6.0ms	75×	body	160	valid