Details

sample36.0ms

Algorithm

intervals

Results

7.0ms	29×	body	2560	valid
7.0ms	185×	body	80	valid
5.0ms	26×	body	1280	valid
3.0ms	256×	pre	80	true
1.0ms	7×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	2×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize16.0ms

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)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

55.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
17.0ms	(+ (* (* 4.0 p) p) (* x x))
54.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

259.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
31.0ms	(+ (* (* 4.0 p) p) (* x x))
72.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
53.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify96.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	260	581
1	922	542
2	3335	537
3	5001	533

prune252.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.3b

localize20.0ms

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)))

rewrite481.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `add-log-exp`
8×	`exp-prod`
6×	`pow1`
5×	`log-pow`
4×	`add-exp-log` `expm1-log1p-u` `log-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `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 → 69

Calls

4 calls:

201.0ms	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
51.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
205.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
22.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
73.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
66.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify116.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	219	629
1	680	567
2	1814	566
3	4609	565
4	5001	565

prune303.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.3b

localize23.0ms

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)))

rewrite452.0ms

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:

200.0ms	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
204.0ms	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
22.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
157.0ms	(log (sqrt (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
53.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify90.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (5.0ms)

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

prune507.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 14.3b

localize30.0ms

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)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

31.0ms	(+ 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)))
13.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
13.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(+ 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)))
126.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify48.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	356	836
1	1267	765
2	5001	758

prune578.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 14.3b

regimes464.0ms

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

sample884.0ms

Algorithm

intervals

Results

212.0ms	6016×	body	80	valid
187.0ms	816×	body	2560	valid
114.0ms	625×	body	1280	valid
101.0ms	8000×	pre	80	true
41.0ms	295×	body	640	valid
20.0ms	172×	body	320	valid
5.0ms	76×	body	160	valid