Details

sample33.0ms

Algorithm

intervals

Results

7.0ms	200×	body	80	valid
6.0ms	27×	body	2560	valid
4.0ms	256×	pre	80	true
3.0ms	17×	body	1280	valid
1.0ms	9×	body	640	valid
0.0ms	2×	body	160	valid
0.0ms	1×	body	320	valid

simplify11.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.2b

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	(+ (* (* 4.0 p) p) (* x x))
0.5b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite42.0ms

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:

13.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms	(+ (* (* 4.0 p) p) (* x x))
17.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series469.0ms

Counts

4 → 12

Calls

4 calls:

294.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
40.0ms	(+ (* (* 4.0 p) p) (* x x))
80.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify90.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (83.0ms)

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

prune248.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.3b	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
0.5b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
2.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (/ 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)))

series465.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* (* 4.0 p) p) (* x x))
279.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
78.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
74.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify96.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	270	644
1	894	578
2	3144	573
3	5002	569

prune297.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.0b

localize19.0ms

Local error

Found 4 expressions with local error:

1.1b	(log (cbrt (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
1.1b	(log (cbrt (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
14.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `log-prod`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`add-exp-log` `cbrt-prod` `sqrt-prod`
4×	`expm1-log1p-u` `sqrt-div` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `rem-log-exp` `flip-+`

Counts

4 → 70

Calls

4 calls:

2.0ms	(log (cbrt (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
2.0ms	(log (cbrt (exp (sqrt (* 0.5 (+ 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)))

series1.5s

Counts

4 → 12

Calls

4 calls:

764.0ms	(log (cbrt (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
639.0ms	(log (cbrt (exp (sqrt (* 0.5 (+ 1.0 (/ x (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

82 → 82

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	167	950
1	409	864
2	1066	864
3	2635	864
4	5001	864

prune460.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.0b

localize27.0ms

Local error

Found 4 expressions with local error:

1.7b	(log (cbrt (cbrt (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
14.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

3.0ms	(log (cbrt (cbrt (exp (sqrt (* 0.5 (+ 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)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series723.0ms

Counts

4 → 12

Calls

4 calls:

558.0ms	(log (cbrt (cbrt (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
51.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify84.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	178	859
1	420	803
2	1077	803
3	2646	803
4	5001	803

prune488.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.0b

regimes753.0ms

Accuracy

85.6% (0.3b remaining)

Error of 13.2b against oracle of 13.0b and baseline of 14.8b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	56
1	39	56

end0.0ms

sample786.0ms

Algorithm

intervals

Results

201.0ms	6039×	body	80	valid
162.0ms	762×	body	2560	valid
112.0ms	673×	body	1280	valid
100.0ms	8000×	pre	80	true
43.0ms	300×	body	640	valid
15.0ms	154×	body	320	valid
5.0ms	72×	body	160	valid