Details

Time bar (total: 5.1s)

sample33.0ms

Algorithm
intervals
Results
7.0ms197×body80valid
5.0ms22×body2560valid
4.0ms256×pre80true
3.0ms19×body1280valid
1.0ms10×body640valid
1.0ms6×body320valid
0.0ms2×body160valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0279
1349
2389
3409
4419
5419

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.6b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
17.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1
6×*-un-lft-identity
5×add-sqr-sqrt add-log-exp
4×add-cube-cbrt sqrt-div sqrt-prod
3×add-exp-log sqrt-pow1 flip3-+ add-cbrt-cube flip-+
2×pow1/2 associate-*r/
1×+-commutative rem-sqrt-square pow-prod-down sum-log distribute-lft-out
Counts
3 → 40
Calls
3 calls:
26.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
26.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
11.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series391.0ms

Counts
3 → 9
Calls
3 calls:
261.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
74.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
56.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify113.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0206431
1565404
21561403
34083403
45001403

prune161.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.5b
(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
0.6b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
17.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 *-un-lft-identity
8×add-sqr-sqrt
7×add-cube-cbrt
6×add-log-exp
5×sqrt-prod log-pow
4×add-exp-log exp-prod sqrt-div add-cbrt-cube
3×log-prod sqrt-pow1 flip3-+ flip-+
2×pow1/2 associate-*r/
1×+-commutative rem-sqrt-square rem-log-exp pow-prod-down sum-log distribute-lft-out
Counts
4 → 56
Calls
4 calls:
26.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
1.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
26.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series688.0ms

Counts
4 → 12
Calls
4 calls:
284.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
270.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
77.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify119.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
0234637
1607590
21618589
34163589
45001589

prune259.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.6b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
17.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt sqrt-prod
4×add-exp-log flip3-+ sqrt-div add-cbrt-cube flip-+
2×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log distribute-lft-out
Counts
4 → 54
Calls
4 calls:
29.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
26.0ms
(+ 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)))

series269.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
76.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
60.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
55.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify102.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0167534
1465496
21264494
33249494
45001494

prune429.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.7b

localize29.0ms

Local error

Found 4 expressions with local error:

7.1b
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
17.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×*-un-lft-identity sqrt-prod
7×pow1 add-cube-cbrt
6×sqrt-div add-log-exp
4×add-exp-log flip3-+ add-cbrt-cube flip-+
3×rem-sqrt-square sqrt-pow1 pow1/2
1×+-commutative sum-log distribute-lft-out
Counts
4 → 57
Calls
4 calls:
27.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (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)))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series250.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
54.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify136.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0170654
1531615
21677588
34730588
45001588

prune445.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.7b

regimes567.0ms

Accuracy

85.1% (0.3b remaining)

Error of 12.9b against oracle of 12.7b and baseline of 14.4b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05279
15279

end0.0ms

sample806.0ms

Algorithm
intervals
Results
210.0ms6057×body80valid
175.0ms808×body2560valid
104.0ms8000×pre80true
101.0ms578×body1280valid
42.0ms312×body640valid
16.0ms161×body320valid
5.0ms84×body160valid