Details

sample39.0ms

Algorithm

intervals

Results

11.0ms	34×	body	2560	valid
7.0ms	191×	body	80	valid
4.0ms	256×	pre	80	true
2.0ms	13×	body	1280	valid
1.0ms	9×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	5×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 14.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 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)))))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

12.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 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)))

series475.0ms

Counts

4 → 12

Calls

4 calls:

282.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
53.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
81.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify79.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	297	948
1	884	898
2	2732	885
3	5001	883

prune287.0ms

Filtered

104 candidates to 82 candidates (78.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	92	12	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	12	105

Merged error: 13.7b

Counts

105 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
1.2b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

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

series264.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
78.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
77.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify79.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	286	956
1	875	889
2	2480	876
3	5002	874

prune320.0ms

Filtered

108 candidates to 82 candidates (75.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	105	15	120

Merged error: 13.7b

Counts

120 → 15

localize23.0ms

Local error

Found 4 expressions with local error:

1.2b	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
1.2b	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `log-prod` `sqrt-prod` `log-pow`
12×	`add-cube-cbrt` `sqrt-pow1`
10×	`pow1`
8×	`exp-prod`
6×	`add-exp-log`
4×	`expm1-log1p-u` `pow1/2` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `flip3-+` `rem-log-exp` `exp-sum` `flip-+` `distribute-lft-out`

Counts

4 → 82

Calls

4 calls:

14.0ms	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
14.0ms	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
6.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series479.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
179.0ms	(log (sqrt (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)))

simplify92.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	163	930
1	392	856
2	1050	856
3	2648	856
4	5001	856

prune442.0ms

Filtered

94 candidates to 80 candidates (85.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	90	4	94
Fresh	3	10	13
Picked	1	0	1
Done	0	1	1
Total	94	15	109

Merged error: 13.7b

Counts

109 → 15

localize21.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
1.2b	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `sqrt-prod`
8×	`pow1`
7×	`log-prod` `sqrt-pow1` `log-pow`
6×	`add-log-exp`
5×	`add-exp-log`
4×	`expm1-log1p-u` `exp-prod` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `pow1/2` `flip-+`
2×	`rem-sqrt-square` `distribute-lft-out`
1×	`+-commutative` `rem-log-exp` `exp-sum` `sum-log`

Counts

4 → 75

Calls

4 calls:

12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
18.0ms	(log (sqrt (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)))

series553.0ms

Counts

4 → 12

Calls

4 calls:

267.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
175.0ms	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
53.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify119.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	225	759
1	594	701
2	1621	700
3	4440	691
4	5001	691

prune315.0ms

Filtered

87 candidates to 76 candidates (87.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	78	9	87
Fresh	7	6	13
Picked	1	0	1
Done	1	0	1
Total	87	15	102

Merged error: 13.7b

Counts

102 → 15

regimes388.0ms

Accuracy

0% (0.3b remaining)

Error of 13.1b against oracle of 12.9b and baseline of 13.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	24
1	32	24

end0.0ms

sample870.0ms

Algorithm

intervals

Results

230.0ms	6046×	body	80	valid
185.0ms	817×	body	2560	valid
113.0ms	602×	body	1280	valid
109.0ms	8000×	pre	80	true
46.0ms	310×	body	640	valid
17.0ms	153×	body	320	valid
5.0ms	72×	body	160	valid