Details

Time bar (total: 8.9s)

sample65.0ms

Algorithm
intervals
Results
15.0ms256×pre80true
12.0ms31×body2560valid
11.0ms192×body80valid
5.0ms18×body1280valid
2.0ms4×body5120valid
1.0ms7×body640valid
0.0ms2×body320valid
0.0ms2×body160valid

simplify5.0ms

Counts
1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize17.0ms

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))))
0.5b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite168.0ms

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:
21.0ms
(+ (* (* 4.0 p) p) (* x x))
51.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
69.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
25.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series311.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(+ (* (* 4.0 p) p) (* x x))
87.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
98.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
70.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify91.0ms

Counts
91 → 91

prune443.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.5b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.5b
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite362.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
23×add-sqr-sqrt
22×add-cube-cbrt
18×times-frac
15×sqrt-prod
6×pow1 add-exp-log associate-/r* add-cbrt-cube add-log-exp
5×log-pow
4×log-prod exp-prod sqrt-div
3×flip3-+ flip-+ associate-/l*
2×associate-/r/ distribute-lft-out
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp exp-sum clear-num sum-log div-inv
Counts
4 → 85
Calls
4 calls:
34.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
72.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
222.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
30.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series349.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
105.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
94.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
61.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify128.0ms

Counts
97 → 97

prune530.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.1b

localize23.0ms

Local error

Found 4 expressions with local error:

3.8b
(cbrt (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod
23×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
8×sqrt-div
7×pow1
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×associate-/r/
1×cbrt-div pow1/3 div-inv
Counts
4 → 78
Calls
4 calls:
25.0ms
(cbrt (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
33.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
31.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
27.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series475.0ms

Counts
4 → 12
Calls
4 calls:
247.0ms
(cbrt (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
84.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
72.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
72.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify70.0ms

Counts
90 → 90

prune559.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.1b

localize52.0ms

Local error

Found 4 expressions with local error:

0.5b
(log (exp (/ (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)) (+ (* 1.0 (- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (/ (* x x) (+ (* (* 4.0 p) p) (* x x)))))))
2.5b
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
14.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity
36×log-pow
35×exp-prod
30×times-frac
24×add-sqr-sqrt
22×add-cube-cbrt
15×distribute-lft-out
12×unpow-prod-down cube-prod
9×add-exp-log add-cbrt-cube
7×pow1
6×sqrt-prod associate-/r/
4×flip3-+ sqrt-div flip-+ add-log-exp
3×log-prod associate-/r* sum-cubes
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ div-exp frac-add div-inv
1×flip3-- frac-2neg rem-log-exp prod-exp clear-num flip-- cbrt-unprod associate-/l*
Counts
4 → 100
Calls
4 calls:
1.3s
(log (exp (/ (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)) (+ (* 1.0 (- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (/ (* x x) (+ (* (* 4.0 p) p) (* x x)))))))
36.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
25.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
40.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series558.0ms

Counts
4 → 12
Calls
4 calls:
361.0ms
(log (exp (/ (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)) (+ (* 1.0 (- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (/ (* x x) (+ (* (* 4.0 p) p) (* x x)))))))
72.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
63.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
62.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify58.0ms

Counts
112 → 112

prune550.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.1b

regimes211.0ms

Accuracy

0% (0.2b remaining)

Error of 13.0b against oracle of 12.7b and baseline of 13.0b

bsearch0.0ms

simplify75.0ms

end0.0ms

sample2.2s

Algorithm
intervals
Results
670.0ms594×body1280valid
462.0ms6070×body80valid
440.0ms739×body2560valid
162.0ms8000×pre80true
80.0ms311×body640valid
29.0ms156×body320valid
29.0ms58×body5120valid
9.0ms72×body160valid