Details

sample38.0ms

Algorithm

intervals

Results

8.0ms	256×	pre	80	true
7.0ms	200×	body	80	valid
6.0ms	27×	body	2560	valid
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 (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: 11.2b

localize12.0ms

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)))

rewrite72.0ms

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:

29.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
6.0ms	(+ (* (* 4.0 p) p) (* x x))
25.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
11.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series469.0ms

Counts

4 → 12

Calls

4 calls:

291.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
41.0ms	(+ (* (* 4.0 p) p) (* x x))
79.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
57.0ms	(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

prune213.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.0b

localize16.0ms

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)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt`
6×	`pow1`
5×	`log-pow`
4×	`add-exp-log` `exp-prod` `sqrt-prod` `add-cbrt-cube`
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 → 54

Calls

4 calls:

6.0ms	(+ (* (* 4.0 p) p) (* x x))
1.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
29.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* (* 4.0 p) p) (* x x))
291.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
83.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify87.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	252	589
1	827	524
2	2807	520
3	5002	519

prune257.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.0b

localize27.0ms

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)))

rewrite24.0ms

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×	`sqrt-div` `log-pow` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `rem-log-exp` `flip-+`

Counts

4 → 62

Calls

4 calls:

1.0ms	(log (cbrt (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
1.0ms	(log (cbrt (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series1.5s

Counts

4 → 12

Calls

4 calls:

780.0ms	(log (cbrt (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
604.0ms	(log (cbrt (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
62.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify91.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	157	876
1	365	792
2	923	792
3	2155	792
4	5002	792

prune404.0ms

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)))

rewrite35.0ms

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×	`add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
2×	`log-pow`
1×	`pow1/3` `rem-log-exp`

Counts

4 → 64

Calls

4 calls:

2.0ms	(log (cbrt (cbrt (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series761.0ms

Counts

4 → 12

Calls

4 calls:

594.0ms	(log (cbrt (cbrt (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify85.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	168	798
1	376	745
2	934	745
3	2166	745
4	5001	745

prune477.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.0b

regimes806.0ms

Accuracy

85.5% (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

sample810.0ms

Algorithm

intervals

Results

208.0ms	6039×	body	80	valid
165.0ms	762×	body	2560	valid
118.0ms	673×	body	1280	valid
103.0ms	8000×	pre	80	true
40.0ms	300×	body	640	valid
15.0ms	154×	body	320	valid
5.0ms	72×	body	160	valid