Details

Time bar (total: 44.2s)

sample95.0ms

Algorithm
intervals
Results
52.0ms96×body1280valid
17.0ms48×body640valid
10.0ms22×body2560valid
5.0ms21×body320valid
3.0ms61×body80valid
1.0ms8×body160valid

simplify12.0ms

Calls
1 calls:
Slowest
12.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.7b

localize15.0ms

Local error

Found 3 expressions with local error:

16.2b
(sqrt (+ (* x x) 1))
1.8b
(log (+ x (sqrt (+ (* x x) 1))))
0.1b
(+ x (sqrt (+ (* x x) 1)))

rewrite76.0ms

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
Calls
3 calls:
Slowest
31.0ms
(sqrt (+ (* x x) 1))
23.0ms
(log (+ x (sqrt (+ (* x x) 1))))
21.0ms
(+ x (sqrt (+ (* x x) 1)))

series249.0ms

Calls
3 calls:
Slowest
162.0ms
(log (+ x (sqrt (+ (* x x) 1))))
52.0ms
(+ x (sqrt (+ (* x x) 1)))
35.0ms
(sqrt (+ (* x x) 1))

simplify3.9s

Calls
25 calls:
Slowest
507.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
459.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
406.0ms
(sqrt (+ (pow (* x x) 3) (pow 1 3)))
385.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
384.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))

prune474.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

20.7b
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
0.4b
(* (* x x) -1/6)
0.1b
(* (pow x 5) 3/40)
0.1b
(* (* (* x x) -1/6) x)

rewrite417.0ms

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-+
Calls
4 calls:
Slowest
320.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
53.0ms
(* (* (* x x) -1/6) x)
27.0ms
(* (* x x) -1/6)
15.0ms
(* (pow x 5) 3/40)

series263.0ms

Calls
4 calls:
Slowest
92.0ms
(* (pow x 5) 3/40)
73.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
65.0ms
(* (* (* x x) -1/6) x)
33.0ms
(* (* x x) -1/6)

simplify5.2s

Calls
55 calls:
Slowest
770.0ms
(* (* (* (* (* x x) -1/6) (* (* x x) -1/6)) (* (* x x) -1/6)) (* (* x x) x))
680.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
477.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
383.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
319.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* -1/6 -1/6) -1/6))

prune797.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

22.1b
(- (+ (/ -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))))
0.2b
(/ 1/16 (pow x 5))
0.1b
(/ (/ 1/8 x) x)

rewrite271.0ms

Algorithm
rewrite-expression-head
Rules
108×times-frac
85×*-un-lft-identity
83×add-sqr-sqrt
63×add-cube-cbrt
16×associate-/l*
15×add-exp-log
14×unpow-prod-down
11×add-cbrt-cube
10×log-prod associate-/r*
9×add-log-exp
8×difference-of-squares
6×div-exp frac-sub div-inv distribute-lft-out-- sqr-pow
5×pow1 log-div
4×cbrt-undiv insert-posit16 distribute-lft-out
2×clear-num frac-2neg flip3-+ flip3-- diff-log frac-add flip-+ flip--
1×pow-to-exp sum-log sub-neg rem-log-exp pow-exp associate--l+ log-pow associate-/l/
Calls
4 calls:
Slowest
189.0ms
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
67.0ms
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
7.0ms
(/ (/ 1/8 x) x)
5.0ms
(/ 1/16 (pow x 5))

series342.0ms

Calls
4 calls:
Slowest
130.0ms
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
92.0ms
(/ 1/16 (pow x 5))
81.0ms
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
37.0ms
(/ (/ 1/8 x) x)

simplify17.7s

Calls
199 calls:
Slowest
478.0ms
(* (- (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (pow x 5))
473.0ms
(/ (* (exp (/ -1/2 x)) (exp (/ (/ (/ 1/8 x) x) x))) (exp (/ 1/16 (pow x 5))))
404.0ms
(/ (exp (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x))) (exp (/ 1/16 (pow x 5))))
383.0ms
(log (* (cbrt (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))) (cbrt (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))))
362.0ms
(- (+ (* 6 (pow x 4)) (log -1/16)) (+ (* 2 (pow x 2)) (* 5 (log x))))

prune1.7s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

11.9b
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
0.2b
(/ -1/8 (* (* x x) x))
0.1b
(* (* x x) x)
0.0b
(+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
24×pow1
19×add-exp-log
18×add-cbrt-cube
13×add-log-exp
12×distribute-lft-out
9×add-sqr-sqrt
8×add-cube-cbrt
6×log-prod sum-log pow-plus prod-exp pow-prod-up cbrt-unprod
4×insert-posit16
3×cbrt-undiv times-frac div-exp associate-*r* pow-prod-down associate-/l*
2×pow2 log-div flip3-+ pow-sqr flip-+
1×+-commutative associate-+r+ clear-num associate-/r* frac-2neg rem-log-exp associate-*l* pow3 log-pow *-commutative div-inv unswap-sqr
Calls
4 calls:
Slowest
576.0ms
(+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x)))
425.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
14.0ms
(* (* x x) x)
14.0ms
(/ -1/8 (* (* x x) x))

series345.0ms

Calls
4 calls:
Slowest
149.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
78.0ms
(+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x)))
59.0ms
(* (* x x) x)
58.0ms
(/ -1/8 (* (* x x) x))

simplify5.4s

Calls
56 calls:
Slowest
495.0ms
(- (+ (log -2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ -1 x)) (* 3/32 (/ 1 (pow x 4)))))
479.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
470.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* x x) x))
464.0ms
(- (log -1/8) (+ (* 4 (pow x 2)) (+ (* 24 (pow x 4)) (* 3 (log x)))))
394.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* x x) x))

prune840.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes246.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.2b

bsearch158.0ms

end0.0ms

sample4.6s

Algorithm
intervals
Results
2.1s2336×body1280valid
1.2s1558×body640valid
529.0ms769×body2560valid
263.0ms2122×body80valid
255.0ms800×body320valid
82.0ms415×body160valid