Details

Time bar (total: 5.4s)

sample34.0ms

Algorithm
intervals
Results
7.0ms197×body80valid
6.0ms24×body2560valid
4.0ms23×body1280valid
4.0ms256×pre80true
1.0ms8×body640valid
0.0ms3×body320valid
0.0ms1×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1409
2489
3509
4529
5539
6539

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize12.0ms

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)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
22×add-sqr-sqrt
21×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×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u
3×fma-def 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 → 92
Calls
4 calls:
12.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
26.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
28.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series455.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
266.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
76.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify74.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 3 (64.0ms)

IterNodesCost
0297948
1884898
22732885
35001883

prune317.0ms

Filtered
104 candidates to 82 candidates (78.8%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.4b

localize13.0ms

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)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
24×associate-*r*
22×*-un-lft-identity times-frac
20×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×expm1-log1p-u flip3-+ prod-exp flip-+ log1p-expm1-u
3×fma-def 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 → 99
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)))

series464.0ms

Counts
4 → 12
Calls
4 calls:
270.0ms
(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
58.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
78.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify47.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0407966
11757881
25001845

prune320.0ms

Filtered
111 candidates to 82 candidates (73.9%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.4b

localize16.0ms

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)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
24×*-un-lft-identity associate-*r*
22×add-cube-cbrt times-frac
15×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×pow1
6×add-log-exp
5×log-pow unswap-sqr
4×expm1-log1p-u exp-prod sqrt-div prod-exp log1p-expm1-u
3×log-prod fma-def 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 → 102
Calls
4 calls:
32.0ms
(* 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))))))
13.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series462.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
271.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
75.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
56.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify49.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04161032
11721918
25001881

prune407.0ms

Filtered
114 candidates to 87 candidates (76.3%)
Pruning

11 alts after pruning (11 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)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt log-prod log-pow
10×add-cube-cbrt *-un-lft-identity
8×pow1 exp-prod
6×add-log-exp
5×add-exp-log sqrt-prod
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×fma-def
2×flip3-+ sqrt-div rem-log-exp flip-+
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
4 → 70
Calls
4 calls:
2.0ms
(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)))

series770.0ms

Counts
4 → 12
Calls
4 calls:
365.0ms
(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
272.0ms
(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))))))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify75.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 3 (66.0ms)

IterNodesCost
0284938
1800817
22882815
35002804

prune327.0ms

Filtered
82 candidates to 70 candidates (85.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.0b

regimes407.0ms

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

sample866.0ms

Algorithm
intervals
Results
213.0ms6003×body80valid
201.0ms821×body2560valid
114.0ms613×body1280valid
110.0ms8000×pre80true
50.0ms341×body640valid
16.0ms152×body320valid
5.0ms70×body160valid