Details

Time bar (total: 49.7s)

sample112.0ms

Algorithm
intervals
Results
46.0ms77×body1280valid
23.0ms22×body2560valid
21.0ms52×body640valid
7.0ms25×body320valid
5.0ms71×body80valid
1.0ms9×body160valid

simplify11.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
11.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.0b

localize12.0ms

Local error

Found 3 expressions with local error:

15.0b
(sqrt (+ (* x x) 1))
2.1b
(log (+ x (sqrt (+ (* x x) 1))))
0.5b
(+ x (sqrt (+ (* x x) 1)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×log-prod add-exp-log
3×flip3-+ add-cbrt-cube sqrt-prod flip-+ insert-posit16
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 rem-log-exp log-pow
Counts
3 → 45
Calls
3 calls:
Slowest
15.0ms
(+ x (sqrt (+ (* x x) 1)))
11.0ms
(log (+ x (sqrt (+ (* x x) 1))))
6.0ms
(sqrt (+ (* x x) 1))

series237.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
142.0ms
(log (+ x (sqrt (+ (* x x) 1))))
52.0ms
(+ x (sqrt (+ (* x x) 1)))
43.0ms
(sqrt (+ (* x x) 1))

simplify3.6s

Counts
25 → 54
Calls
25 calls:
Slowest
446.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
427.0ms
(sqrt (+ (pow (* x x) 3) (pow 1 3)))
356.0ms
(log (+ (pow x 3) (pow (sqrt (+ (* x x) 1)) 3)))
350.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
345.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))

prune520.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

20.6b
(+ (+ (* (* x x) (* x -1/6)) x) (* (pow x 5) 3/40))
0.3b
(* x -1/6)
0.1b
(* (* x x) (* x -1/6))
0.1b
(* (pow x 5) 3/40)

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
20×add-cbrt-cube
18×pow1
16×add-sqr-sqrt
12×prod-exp
11×associate-*l*
10×cbrt-unprod
9×*-un-lft-identity pow-prod-down add-cube-cbrt add-log-exp
7×associate-*r*
4×unpow-prod-down insert-posit16 unswap-sqr
3×sum-log *-commutative
2×sqr-pow
1×pow-to-exp +-commutative associate-+l+ flip3-+ pow-exp flip-+
Counts
4 → 82
Calls
4 calls:
Slowest
118.0ms
(+ (+ (* (* x x) (* x -1/6)) x) (* (pow x 5) 3/40))
30.0ms
(* (* x x) (* x -1/6))
9.0ms
(* x -1/6)
8.0ms
(* (pow x 5) 3/40)

series272.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
97.0ms
(* (pow x 5) 3/40)
96.0ms
(+ (+ (* (* x x) (* x -1/6)) x) (* (pow x 5) 3/40))
62.0ms
(* (* x x) (* x -1/6))
16.0ms
(* x -1/6)

simplify4.7s

Counts
54 → 94
Calls
54 calls:
Slowest
652.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* -1/6 -1/6) -1/6)))
489.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* -1/6 -1/6) -1/6)))
440.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
403.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
400.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

8.0b
(log (+ x (- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x))))
0.2b
(/ 1/8 (* (* x x) x))
0.1b
(* (* x x) x)
0.0b
(+ x (- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x)))

rewrite753.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
24×pow1
19×add-exp-log
18×add-cbrt-cube
13×add-log-exp
9×add-sqr-sqrt
8×add-cube-cbrt
6×log-prod pow-plus prod-exp pow-prod-up cbrt-unprod distribute-lft-out distribute-lft-out--
4×insert-posit16
3×cbrt-undiv associate-+r+ sum-log times-frac diff-log div-exp associate-*r* pow-prod-down associate-/l*
2×pow2 log-div flip3-+ pow-sqr flip-+
1×+-commutative clear-num associate-+r- associate-/r* sub-neg frac-2neg rem-log-exp associate-*l* pow3 log-pow *-commutative div-inv associate--r- unswap-sqr
Counts
4 → 92
Calls
4 calls:
Slowest
355.0ms
(+ x (- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x)))
341.0ms
(log (+ x (- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x))))
29.0ms
(* (* x x) x)
26.0ms
(/ 1/8 (* (* x x) x))

series346.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
153.0ms
(log (+ x (- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x))))
72.0ms
(/ 1/8 (* (* x x) x))
61.0ms
(* (* x x) x)
60.0ms
(+ x (- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x)))

simplify6.9s

Counts
58 → 104
Calls
58 calls:
Slowest
747.0ms
(log (+ (pow x 3) (pow (- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x)) 3)))
555.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* x x) x))
402.0ms
(log (- (* x x) (* (- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x)) (- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x)))))
393.0ms
(* (exp x) (/ (exp (/ 1/2 x)) (/ (exp (/ 1/8 (* (* x x) x))) (exp x))))
362.0ms
(- (log -1/8) (+ (* 4 (pow x 2)) (+ (* 24 (pow x 4)) (* 3 (log x)))))

prune872.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

16.9b
(- (/ 1/16 (pow x 5)) (/ (/ (/ 1/8 x) x) x))
12.2b
(log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ (/ (/ 1/8 x) x) x))))
0.2b
(/ 1/16 (pow x 5))
0.1b
(/ (/ 1/8 x) x)

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
132×add-sqr-sqrt
80×*-un-lft-identity
63×add-cube-cbrt
18×difference-of-squares
16×unpow-prod-down associate-/l*
15×add-exp-log
11×add-cbrt-cube
10×associate-/r*
8×log-prod sqr-pow
7×distribute-lft-out--
6×div-exp div-inv add-log-exp
5×pow1 log-div frac-sub
4×cbrt-undiv insert-posit16
3×flip3-- flip--
2×clear-num frac-2neg
1×pow-to-exp sub-neg diff-log rem-log-exp pow-exp log-pow associate-/l/
Counts
4 → 172
Calls
4 calls:
Slowest
59.0ms
(log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ (/ (/ 1/8 x) x) x))))
53.0ms
(- (/ 1/16 (pow x 5)) (/ (/ (/ 1/8 x) x) x))
7.0ms
(/ (/ 1/8 x) x)
5.0ms
(/ 1/16 (pow x 5))

series460.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
182.0ms
(- (/ 1/16 (pow x 5)) (/ (/ (/ 1/8 x) x) x))
169.0ms
(log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ (/ (/ 1/8 x) x) x))))
80.0ms
(/ 1/16 (pow x 5))
29.0ms
(/ (/ 1/8 x) x)

simplify22.5s

Counts
214 → 184
Calls
214 calls:
Slowest
567.0ms
(/ (/ (* (cbrt 1/8) (cbrt 1/8)) (* (cbrt x) (cbrt x))) (* (cbrt x) (cbrt x)))
507.0ms
(log (- (pow (/ -1/2 x) 3) (pow (- (/ 1/16 (pow x 5)) (/ (/ (/ 1/8 x) x) x)) 3)))
384.0ms
(log (* (cbrt (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ (/ (/ 1/8 x) x) x)))) (cbrt (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ (/ (/ 1/8 x) x) x))))))
380.0ms
(/ (* (* 1/16 1/16) 1/16) (* (* (pow x 5) (pow x 5)) (pow x 5)))
376.0ms
(log (sqrt (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ (/ (/ 1/8 x) x) x)))))

prune1.7s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes103.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.3b

bsearch140.0ms

end0.0ms

sample4.9s

Algorithm
intervals
Results
2.2s2333×body1280valid
1.3s1552×body640valid
583.0ms835×body2560valid
366.0ms772×body320valid
184.0ms2114×body80valid
117.0ms394×body160valid