Details

Time bar (total: 5.8s)

sample51.0ms

Algorithm
intervals
Results
14.0ms195×body80valid
10.0ms26×body2560valid
5.0ms256×pre80true
4.0ms14×body640valid
3.0ms9×body1280valid
1.0ms6×body320valid
1.0ms5×body160valid
0.0ms1×body5120valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0279
1349
2389
3409
4419
5419

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0b
(+ (* (* 4.0 p) p) (* x x))
1.3b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
20×add-cube-cbrt
18×times-frac
15×sqrt-prod
8×add-log-exp
6×add-exp-log associate-/r* add-cbrt-cube
5×pow1
4×flip3-+ sqrt-div flip-+
3×associate-/l*
2×+-commutative sum-log associate-/r/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv distribute-lft-out
Counts
4 → 79
Calls
4 calls:
12.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
6.0ms
(+ (* (* 4.0 p) p) (* x x))
24.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series227.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
33.0ms
(+ (* (* 4.0 p) p) (* x x))
77.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify147.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0278822
11014772
24246757
35001757

prune270.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
1.3b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.2b
(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
12.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
9×add-sqr-sqrt
8×add-cube-cbrt log-prod
7×pow1
6×add-log-exp
5×add-exp-log
4×log-div exp-prod flip3-+ exp-sum add-cbrt-cube flip-+
3×sqrt-prod distribute-lft-out
2×exp-diff sqrt-div log-pow
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log rem-exp-log
Counts
4 → 60
Calls
4 calls:
25.0ms
(exp (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
27.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
24.0ms
(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series406.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(exp (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
82.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
183.0ms
(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify114.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (43.0ms)

IterNodesCost
0230707
1588645
21449625
33630619
45001619

prune260.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.8b

localize21.0ms

Local error

Found 4 expressions with local error:

3.3b
(log (sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
3.3b
(log (sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
14×log-prod *-un-lft-identity sqrt-prod
12×add-sqr-sqrt
10×pow1 add-cube-cbrt
8×sqrt-div
6×add-exp-log log-pow
4×log-div sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
2×rem-sqrt-square rem-log-exp distribute-lft-out
Counts
4 → 70
Calls
4 calls:
28.0ms
(log (sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
24.0ms
(log (sqrt (+ 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)))

series705.0ms

Counts
4 → 12
Calls
4 calls:
294.0ms
(log (sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
294.0ms
(log (sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
61.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify99.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0198906
1469840
21217840
32945840
45002840

prune415.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 8.8b

localize33.0ms

Local error

Found 4 expressions with local error:

12.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
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)))
13.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series426.0ms

Counts
4 → 12
Calls
4 calls:
249.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
61.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
54.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
61.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify85.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
098500
1283484
2827484
32050484
45001484

prune529.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 8.8b

regimes317.0ms

Accuracy

58.8% (1.4b remaining)

Error of 11.2b against oracle of 9.8b and baseline of 13.2b

bsearch2.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04339
14339

end0.0ms

sample1.4s

Algorithm
intervals
Results
443.0ms6027×body80valid
294.0ms764×body2560valid
196.0ms614×body1280valid
144.0ms8000×pre80true
84.0ms329×body640valid
26.0ms139×body320valid
24.0ms51×body5120valid
10.0ms76×body160valid