Details

sample38.0ms

Algorithm

intervals

Results

7.0ms	185×	body	80	valid
7.0ms	29×	body	2560	valid
5.0ms	26×	body	1280	valid
4.0ms	256×	pre	80	true
1.0ms	7×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	2×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize17.0ms

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	(+ (* (* 4.0 p) p) (* x x))
0.7b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
16.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

56.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
17.0ms	(+ (* (* 4.0 p) p) (* x x))
56.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
25.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
32.0ms	(+ (* (* 4.0 p) p) (* x x))
75.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify91.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	242	529
1	853	492
2	2977	488
3	5002	487

prune216.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
0.7b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.7b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
16.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite505.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

209.0ms	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
55.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
215.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
78.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
68.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify115.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 4 (108.0ms)

Iter	Nodes	Cost
0	202	568
1	613	508
2	1609	507
3	3883	507
4	5001	506

prune264.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
0.8b	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
16.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite477.0ms

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×	`pow1/2` `sqrt-div` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `flip3-+` `rem-log-exp` `exp-sum` `flip-+` `distribute-lft-out`

Counts

4 → 74

Calls

4 calls:

213.0ms	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
214.0ms	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
171.0ms	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
52.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify94.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	153	864
1	350	792
2	912	792
3	2173	792
4	5001	792

prune474.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 14.3b

localize33.0ms

Local error

Found 4 expressions with local error:

6.6b	(+ 1.0 (/ x (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))
16.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.1b	(cbrt (+ (* (* 4.0 p) p) (* x x)))
17.1b	(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

33.0ms	(+ 1.0 (/ x (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
17.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(+ 1.0 (/ x (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
121.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
122.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify130.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	337	773
1	1188	716
2	4993	710
3	5002	710

prune592.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 14.3b

regimes461.0ms

Accuracy

0% (0.3b remaining)

Error of 13.3b against oracle of 13.1b and baseline of 13.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	23
1	23	23

end0.0ms

sample901.0ms

Algorithm

intervals

Results

219.0ms	6016×	body	80	valid
190.0ms	816×	body	2560	valid
114.0ms	625×	body	1280	valid
102.0ms	8000×	pre	80	true
41.0ms	295×	body	640	valid
18.0ms	172×	body	320	valid
6.0ms	76×	body	160	valid