Details

Time bar (total: 4.8s)

sample31.0ms

Algorithm
intervals
Results
7.0ms202×body80valid
5.0ms23×body2560valid
3.0ms256×pre80true
3.0ms15×body1280valid
1.0ms11×body640valid
0.0ms4×body320valid
0.0ms1×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0279
1349
2389
3409
4419
5419

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.2b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite35.0ms

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:
5.0ms
(+ (* (* 4.0 p) p) (* x x))
7.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
15.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series212.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (* (* 4.0 p) p) (* x x))
54.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
74.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
53.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify148.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0278822
11014772
24246757
35001757

prune255.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.4b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
24×associate-*r*
22×times-frac
21×*-un-lft-identity
19×add-cube-cbrt
15×sqrt-prod
13×add-exp-log
10×pow1
9×add-cbrt-cube
6×sqrt-div add-log-exp
5×unswap-sqr
4×flip3-+ prod-exp flip-+
3×sqrt-pow1 associate-*r/ associate-*l*
2×pow1/2 div-exp pow-prod-down associate-/r/ cbrt-unprod
1×cbrt-undiv +-commutative rem-sqrt-square rec-exp 1-exp sum-log un-div-inv *-commutative div-inv
Counts
4 → 88
Calls
4 calls:
4.0ms
(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
16.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series452.0ms

Counts
4 → 12
Calls
4 calls:
271.0ms
(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
54.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
74.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
53.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify51.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0390900
11684818
25001784

prune270.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 10.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.3b
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
2.4b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
24×associate-*r*
23×*-un-lft-identity
22×times-frac
21×add-cube-cbrt
15×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×pow1
6×add-log-exp
5×log-pow unswap-sqr
4×exp-prod sqrt-div prod-exp
3×log-prod flip3-+ associate-*l* flip-+
2×div-exp associate-/r/ cbrt-unprod
1×cbrt-undiv +-commutative rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ rem-log-exp pow-prod-down sum-log un-div-inv *-commutative div-inv
Counts
4 → 91
Calls
4 calls:
14.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
3.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series467.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
284.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
76.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
53.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify52.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0399962
11650851
25002816

prune358.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 10.8b

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b
(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
2.3b
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
2.4b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
11×log-prod log-pow
10×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
8×pow1 exp-prod
6×add-log-exp
5×add-exp-log sqrt-prod
4×add-cbrt-cube
2×flip3-+ sqrt-div rem-log-exp flip-+
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
4 → 59
Calls
4 calls:
2.0ms
(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
2.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
3.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series781.0ms

Counts
4 → 12
Calls
4 calls:
364.0ms
(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
275.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
80.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
62.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify71.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (62.0ms)

IterNodesCost
0267856
1729739
22550737
35002735

prune269.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.2b

regimes362.0ms

Accuracy

76.5% (1.4b remaining)

Error of 8.9b against oracle of 7.4b and baseline of 13.6b

bsearch2.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03726
13726

end0.0ms

sample809.0ms

Algorithm
intervals
Results
204.0ms6007×body80valid
176.0ms824×body2560valid
112.0ms628×body1280valid
107.0ms8000×pre80true
42.0ms316×body640valid
15.0ms154×body320valid
5.0ms71×body160valid