Details

Time bar (total: 5.3s)

sample36.0ms

Algorithm
intervals
Results
7.0ms23×body1280valid
7.0ms197×body80valid
5.0ms24×body2560valid
4.0ms256×pre80true
1.0ms8×body640valid
0.0ms3×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

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
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)))))
16.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
20×add-cube-cbrt
18×times-frac
16×sqrt-prod
8×pow1
6×add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
4×flip3-+ flip-+
3×sqrt-pow1 associate-/l*
2×pow1/2 associate-*r/ associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg div-exp pow-prod-down clear-num sum-log div-inv distribute-lft-out
Counts
4 → 81
Calls
4 calls:
13.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
28.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
25.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series487.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
295.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
75.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
62.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify76.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
0280888
1816840
22500828
35001827

prune274.0ms

Filtered
93 candidates to 71 candidates (76.3%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.4b

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)))))
3.7b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
16.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite54.0ms

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:
3.0ms
(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
34.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series483.0ms

Counts
4 → 12
Calls
4 calls:
284.0ms
(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
59.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
82.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify45.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0390900
11684818
25001784

prune287.0ms

Filtered
100 candidates to 71 candidates (71.0%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.6b
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
3.7b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
16.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite49.0ms

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:
33.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
1.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
2.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series477.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
281.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
78.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify43.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0399962
11650851
25002816

prune526.0ms

Filtered
103 candidates to 76 candidates (73.8%)
Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.4b

localize20.0ms

Local error

Found 4 expressions with local error:

1.7b
(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
3.6b
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
3.7b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
16.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite16.0ms

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:
1.0ms
(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
1.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
2.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series767.0ms

Counts
4 → 12
Calls
4 calls:
362.0ms
(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
273.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
73.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify66.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (58.0ms)

IterNodesCost
0267855
1729738
22550736
35002735

prune255.0ms

Filtered
71 candidates to 59 candidates (83.1%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.0b

regimes393.0ms

Accuracy

79.8% (1.3b remaining)

Error of 8.4b against oracle of 7.1b and baseline of 13.6b

bsearch2.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03928
13928

end0.0ms

sample817.0ms

Algorithm
intervals
Results
205.0ms6003×body80valid
175.0ms821×body2560valid
106.0ms8000×pre80true
104.0ms613×body1280valid
50.0ms341×body640valid
15.0ms152×body320valid
5.0ms70×body160valid