Details

Time bar (total: 58.9s)

sample136.0ms

Algorithm
intervals
Results
64.0ms71×body1280valid
30.0ms57×body640valid
12.0ms21×body2560valid
11.0ms34×body320valid
5.0ms65×body80valid
1.0ms8×body160valid

simplify21.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
21.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.0b

localize25.0ms

Local error

Found 3 expressions with local error:

14.2b
(sqrt (+ (* x x) 1))
2.6b
(log (+ x (sqrt (+ (* x x) 1))))
0.4b
(+ x (sqrt (+ (* x x) 1)))

rewrite54.0ms

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
20.0ms
(log (+ x (sqrt (+ (* x x) 1))))
19.0ms
(+ x (sqrt (+ (* x x) 1)))
13.0ms
(sqrt (+ (* x x) 1))

series261.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
150.0ms
(log (+ x (sqrt (+ (* x x) 1))))
63.0ms
(+ x (sqrt (+ (* x x) 1)))
48.0ms
(sqrt (+ (* x x) 1))

simplify4.4s

Counts
25 → 54
Calls
25 calls:
Slowest
549.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
513.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
461.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
426.0ms
(log (+ (pow x 3) (pow (sqrt (+ (* x x) 1)) 3)))
383.0ms
(log (* (cbrt (+ x (sqrt (+ (* x x) 1)))) (cbrt (+ x (sqrt (+ (* x x) 1))))))

prune503.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

18.3b
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
0.2b
(* (* x x) -1/6)
0.1b
(* (* (* x x) -1/6) x)
0.1b
(* (pow x 5) 3/40)

rewrite387.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
20×add-cbrt-cube
18×pow1
15×add-sqr-sqrt
12×prod-exp
10×cbrt-unprod
9×*-un-lft-identity associate-*r* associate-*l* pow-prod-down add-cube-cbrt add-log-exp
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
291.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
59.0ms
(* (* (* x x) -1/6) x)
27.0ms
(* (* x x) -1/6)
8.0ms
(* (pow x 5) 3/40)

series298.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
94.0ms
(* (pow x 5) 3/40)
81.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
68.0ms
(* (* (* x x) -1/6) x)
54.0ms
(* (* x x) -1/6)

simplify4.4s

Counts
55 → 94
Calls
55 calls:
Slowest
642.0ms
(* (* (* (* (* x x) -1/6) (* (* x x) -1/6)) (* (* x x) -1/6)) (* (* x x) x))
369.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
351.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
333.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
266.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* -1/6 -1/6) -1/6))

prune800.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize74.0ms

Local error

Found 4 expressions with local error:

18.3b
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
18.3b
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
18.3b
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
11.0b
(cbrt (+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
19×add-log-exp
9×sum-log
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16
3×cbrt-prod +-commutative associate-+l+
2×cbrt-div
1×pow1/3
Counts
4 → 56
Calls
4 calls:
Slowest
295.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
289.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
250.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
182.0ms
(cbrt (+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40)))

series420.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
207.0ms
(cbrt (+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40)))
83.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
69.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
61.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))

simplify6.6s

Counts
26 → 68
Calls
26 calls:
Slowest
519.0ms
(cbrt (sqrt (+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))))
400.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
396.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
394.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
387.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))

prune679.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

20.5b
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
13.4b
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
0.1b
(/ (/ 1/8 x) x)
0.1b
(/ (/ (/ 1/8 x) x) x)

rewrite302.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
253×*-un-lft-identity
251×add-sqr-sqrt
231×add-cube-cbrt
56×associate-/l*
22×div-inv
19×add-exp-log
18×add-cbrt-cube
10×log-prod
9×cbrt-undiv div-exp add-log-exp
8×difference-of-squares
6×associate-/r* frac-sub distribute-lft-out--
5×pow1 log-div
4×insert-posit16 distribute-lft-out
2×clear-num unpow-prod-down frac-2neg flip3-+ flip3-- diff-log frac-add flip-+ flip-- sqr-pow associate-/l/
1×sum-log sub-neg rem-log-exp associate--l+ log-pow
Counts
4 → 314
Calls
4 calls:
Slowest
187.0ms
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
69.0ms
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
19.0ms
(/ (/ (/ 1/8 x) x) x)
13.0ms
(/ (/ 1/8 x) x)

series321.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
134.0ms
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
77.0ms
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
62.0ms
(/ (/ (/ 1/8 x) x) x)
48.0ms
(/ (/ 1/8 x) x)

simplify30.2s

Counts
453 → 326
Calls
453 calls:
Slowest
652.0ms
(log (+ (sqrt (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x))) (/ (sqrt 1/16) (sqrt (pow x 5)))))
480.0ms
(* (- (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (pow x 5))
402.0ms
(- (sqrt (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x))) (/ (sqrt 1/16) (pow x (/ 5 2))))
402.0ms
(/ (* (exp (/ -1/2 x)) (exp (/ (/ (/ 1/8 x) x) x))) (exp (/ 1/16 (pow x 5))))
374.0ms
(/ (/ (/ (* (cbrt 1/8) (cbrt 1/8)) 1) (sqrt x)) (* (cbrt x) (cbrt x)))

prune2.8s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes174.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.0b

bsearch157.0ms

end0.0ms

sample4.7s

Algorithm
intervals
Results
2.5s2364×body1280valid
978.0ms1562×body640valid
588.0ms758×body2560valid
261.0ms805×body320valid
220.0ms2126×body80valid
81.0ms385×body160valid