Details

Time bar (total: 22.8s)

sample109.0ms

Algorithm
intervals
Results
29.0ms17×body1280valid
27.0ms202×body80valid
12.0ms16×body2560valid
12.0ms256×pre80true
7.0ms13×body640valid
1.0ms5×body160valid
1.0ms1×body5120valid
1.0ms2×body320valid

simplify133.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
132.0ms
(sqrt (* 0.5 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.1b

localize40.0ms

Local error

Found 4 expressions with local error:

14.7b
(sqrt (+ (* x x) (* p (* 4 p))))
1.1b
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
0.0b
(/ x (sqrt (+ (* x x) (* p (* 4 p)))))
0.0b
(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube sqrt-div add-exp-log add-log-exp
4×flip3-+ flip-+ insert-posit16
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg div-exp div-inv
Counts
4 → 86
Calls
4 calls:
Slowest
24.0ms
(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))
23.0ms
(/ x (sqrt (+ (* x x) (* p (* 4 p)))))
12.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
6.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series550.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
274.0ms
(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))
128.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
83.0ms
(/ x (sqrt (+ (* x x) (* p (* 4 p)))))
65.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify4.3s

Counts
75 → 98
Calls
75 calls:
Slowest
503.0ms
(sqrt (+ (pow (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 3) (pow 0.5 3)))
423.0ms
(* (exp (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))) (exp 0.5))
419.0ms
(sqrt (- (* (* x x) (* x x)) (* (* p (* 4 p)) (* p (* 4 p)))))
405.0ms
(sqrt (- (* (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))) (* 0.5 0.5)))
295.0ms
(sqrt (+ (* (* x x) (* x x)) (- (* (* p (* 4 p)) (* p (* 4 p))) (* (* x x) (* p (* 4 p))))))

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.8b

localize53.0ms

Local error

Found 4 expressions with local error:

14.7b
(sqrt (+ (* x x) (* p (* 4 p))))
14.7b
(sqrt (+ (* x x) (* p (* 4 p))))
1.1b
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
1.1b
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×flip3-+ add-cbrt-cube sqrt-div add-exp-log flip-+ insert-posit16
2×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2
Counts
4 → 56
Calls
4 calls:
Slowest
29.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
11.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
6.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
6.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series322.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
99.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
88.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
76.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
58.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify2.6s

Counts
28 → 68
Calls
28 calls:
Slowest
851.0ms
(sqrt (- (* (* x x) (* x x)) (* (* p (* 4 p)) (* p (* 4 p)))))
359.0ms
(* (exp (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))) (exp 0.5))
347.0ms
(* (exp (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))) (exp 0.5))
316.0ms
(sqrt (- (* (* x x) (* x x)) (* (* p (* 4 p)) (* p (* 4 p)))))
237.0ms
(sqrt (+ (pow (* x x) 3) (pow (* p (* 4 p)) 3)))

prune991.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.8b

localize64.0ms

Local error

Found 4 expressions with local error:

14.7b
(sqrt (+ (* x x) (* p (* 4 p))))
14.7b
(sqrt (+ (* x x) (* p (* 4 p))))
1.1b
(log (exp (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)))
1.1b
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
7×pow1
6×sqrt-prod add-log-exp
4×log-prod add-cbrt-cube sqrt-div add-exp-log log-pow insert-posit16
3×exp-prod flip3-+ flip-+
2×rem-sqrt-square sqrt-pow1 pow1/2
1×+-commutative sum-log rem-log-exp exp-sum
Counts
4 → 61
Calls
4 calls:
Slowest
51.0ms
(log (exp (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)))
12.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
9.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
6.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series316.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
105.0ms
(log (exp (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)))
88.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
62.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
61.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify2.6s

Counts
35 → 73
Calls
35 calls:
Slowest
327.0ms
(sqrt (- (* (* x x) (* x x)) (* (* p (* 4 p)) (* p (* 4 p)))))
324.0ms
(sqrt (- (* (* x x) (* x x)) (* (* p (* 4 p)) (* p (* 4 p)))))
323.0ms
(* (exp (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))) (exp 0.5))
264.0ms
(log (exp (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))))
231.0ms
(log (* (cbrt (exp (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))) (cbrt (exp (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)))))

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.8b

localize118.0ms

Local error

Found 4 expressions with local error:

14.7b
(sqrt (+ (* x x) (* p (* 4 p))))
14.7b
(sqrt (+ (* x x) (* p (* 4 p))))
14.7b
(sqrt (+ (* x x) (* p (* 4 p))))
14.7b
(sqrt (+ (* x x) (* p (* 4 p))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 *-un-lft-identity sqrt-div add-cube-cbrt
4×rem-sqrt-square sqrt-pow1 flip3-+ add-cbrt-cube pow1/2 add-exp-log flip-+ insert-posit16 add-log-exp
Counts
4 → 64
Calls
4 calls:
Slowest
6.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
6.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
6.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
6.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series220.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
60.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
59.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
55.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
46.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify2.7s

Counts
40 → 76
Calls
40 calls:
Slowest
395.0ms
(sqrt (- (* (* x x) (* x x)) (* (* p (* 4 p)) (* p (* 4 p)))))
366.0ms
(sqrt (- (* (* x x) (* x x)) (* (* p (* 4 p)) (* p (* 4 p)))))
331.0ms
(sqrt (- (* (* x x) (* x x)) (* (* p (* 4 p)) (* p (* 4 p)))))
319.0ms
(sqrt (- (* (* x x) (* x x)) (* (* p (* 4 p)) (* p (* 4 p)))))
236.0ms
(sqrt (+ (pow (* x x) 3) (pow (* p (* 4 p)) 3)))

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.8b

regimes209.0ms

Accuracy

0% (0.7b remaining)

Error of 13.7b against oracle of 13.0b and baseline of 13.7b

bsearch18.0ms

end0.0ms

sample3.4s

Algorithm
intervals
Results
911.0ms6005×body80valid
812.0ms8000×pre80true
701.0ms773×body2560valid
416.0ms607×body1280valid
174.0ms317×body640valid
87.0ms156×body320valid
52.0ms59×body5120valid
19.0ms83×body160valid