Details

Time bar (total: 20.8s)

sample96.0ms

Algorithm
intervals
Results
26.0ms195×body80valid
20.0ms26×body1280valid
14.0ms18×body2560valid
12.0ms256×pre80true
4.0ms9×body640valid
1.0ms3×body160valid
1.0ms4×body320valid
1.0ms1×body5120valid

simplify103.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
103.0ms
(sqrt (* 0.5 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize32.0ms

Local error

Found 4 expressions with local error:

14.3b
(sqrt (+ (* x x) (* p (* 4 p))))
0.5b
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
0.0b
(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))
0.0b
(+ (* x x) (* p (* 4 p)))

rewrite55.0ms

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
18.0ms
(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))
16.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
11.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
10.0ms
(+ (* x x) (* p (* 4 p)))

series540.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
294.0ms
(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))
121.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
63.0ms
(+ (* x x) (* p (* 4 p)))
61.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify2.6s

Counts
28 → 68
Calls
28 calls:
Slowest
493.0ms
(sqrt (+ (pow (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 3) (pow 0.5 3)))
426.0ms
(* (exp (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))) (exp 0.5))
395.0ms
(sqrt (- (* (* x x) (* x x)) (* (* p (* 4 p)) (* p (* 4 p)))))
352.0ms
(sqrt (- (* (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))) (* 0.5 0.5)))
225.0ms
(sqrt (+ (pow (* x x) 3) (pow (* p (* 4 p)) 3)))

prune721.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.2b

localize42.0ms

Local error

Found 4 expressions with local error:

14.3b
(sqrt (+ (* x x) (* p (* 4 p))))
0.5b
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
0.3b
(log (exp (sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))))
0.0b
(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt sqrt-prod
7×pow1 log-pow
6×exp-prod add-log-exp
4×add-cbrt-cube sqrt-div add-exp-log insert-posit16
3×log-prod flip3-+ flip-+
2×rem-sqrt-square sqrt-pow1 pow1/2
1×+-commutative sum-log rem-log-exp
Counts
4 → 63
Calls
4 calls:
Slowest
52.0ms
(log (exp (sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))))
28.0ms
(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))
22.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
12.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series650.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
274.0ms
(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))
245.0ms
(log (exp (sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))))
83.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
49.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify3.0s

Counts
37 → 75
Calls
37 calls:
Slowest
478.0ms
(sqrt (+ (pow (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 3) (pow 0.5 3)))
340.0ms
(sqrt (- (* (* x x) (* x x)) (* (* p (* 4 p)) (* p (* 4 p)))))
330.0ms
(sqrt (- (* (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))) (* 0.5 0.5)))
309.0ms
(* (exp (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))) (exp 0.5))
237.0ms
(sqrt (+ (pow (* x x) 3) (pow (* p (* 4 p)) 3)))

prune931.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.2b

localize92.0ms

Local error

Found 4 expressions with local error:

14.3b
(sqrt (+ (* x x) (* p (* p 4))))
14.3b
(sqrt (+ (* x x) (* p (* 4 p))))
14.3b
(sqrt (+ (* x x) (* p (* 4 p))))
14.3b
(sqrt (+ (* x x) (* p (* 4 p))))

rewrite37.0ms

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
11.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
10.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
9.0ms
(sqrt (+ (* x x) (* p (* p 4))))
6.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series533.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
362.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
74.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
49.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
47.0ms
(sqrt (+ (* x x) (* p (* p 4))))

simplify2.8s

Counts
40 → 76
Calls
40 calls:
Slowest
413.0ms
(sqrt (- (* (* x x) (* x x)) (* (* p (* p 4)) (* p (* p 4)))))
375.0ms
(sqrt (- (* (* x x) (* x x)) (* (* p (* 4 p)) (* p (* 4 p)))))
327.0ms
(sqrt (- (* (* x x) (* x x)) (* (* p (* 4 p)) (* p (* 4 p)))))
295.0ms
(sqrt (- (* (* x x) (* x x)) (* (* p (* 4 p)) (* p (* 4 p)))))
256.0ms
(sqrt (+ (pow (* x x) 3) (pow (* p (* 4 p)) 3)))

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.2b

localize95.0ms

Local error

Found 4 expressions with local error:

14.3b
(sqrt (+ (* x x) (* p (* p 4))))
14.3b
(sqrt (+ (* x x) (* p (* 4 p))))
14.3b
(sqrt (+ (* x x) (* p (* 4 p))))
14.3b
(sqrt (+ (* x x) (* p (* 4 p))))

rewrite38.0ms

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
11.0ms
(sqrt (+ (* x x) (* p (* p 4))))
10.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
9.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
6.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series230.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
69.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
62.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
55.0ms
(sqrt (+ (* x x) (* p (* p 4))))
44.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify2.6s

Counts
40 → 76
Calls
40 calls:
Slowest
383.0ms
(sqrt (- (* (* x x) (* x x)) (* (* p (* 4 p)) (* p (* 4 p)))))
350.0ms
(sqrt (- (* (* x x) (* x x)) (* (* p (* 4 p)) (* p (* 4 p)))))
309.0ms
(sqrt (- (* (* x x) (* x x)) (* (* p (* 4 p)) (* p (* 4 p)))))
303.0ms
(sqrt (- (* (* x x) (* x x)) (* (* p (* p 4)) (* p (* p 4)))))
248.0ms
(sqrt (+ (pow (* x x) 3) (pow (* p (* 4 p)) 3)))

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.2b

regimes266.0ms

Accuracy

0% (1.2b remaining)

Error of 14.1b against oracle of 12.9b and baseline of 14.1b

bsearch15.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
715.0ms733×body2560valid
685.0ms6049×body80valid
358.0ms625×body1280valid
286.0ms8000×pre80true
126.0ms289×body640valid
42.0ms159×body320valid
39.0ms59×body5120valid
17.0ms86×body160valid