Details

Time bar (total: 43.3s)

sample115.0ms

Algorithm
intervals
Results
59.0ms83×body1280valid
18.0ms39×body640valid
15.0ms28×body2560valid
8.0ms32×body320valid
4.0ms61×body80valid
2.0ms13×body160valid

simplify11.0ms

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: 53.6b

localize15.0ms

Local error

Found 3 expressions with local error:

14.4b
(sqrt (+ (* x x) 1))
3.1b
(log (+ x (sqrt (+ (* x x) 1))))
0.8b
(+ x (sqrt (+ (* x x) 1)))

rewrite57.0ms

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
34.0ms
(log (+ x (sqrt (+ (* x x) 1))))
12.0ms
(sqrt (+ (* x x) 1))
11.0ms
(+ x (sqrt (+ (* x x) 1)))

series265.0ms

Calls
3 calls:
Slowest
161.0ms
(log (+ x (sqrt (+ (* x x) 1))))
67.0ms
(+ x (sqrt (+ (* x x) 1)))
36.0ms
(sqrt (+ (* x x) 1))

simplify3.8s

Calls
25 calls:
Slowest
491.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
454.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
447.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
420.0ms
(sqrt (+ (pow (* x x) 3) (pow 1 3)))
342.0ms
(log (+ (pow x 3) (pow (sqrt (+ (* x x) 1)) 3)))

prune402.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

18.9b
(+ (+ (* (* (* 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)

rewrite456.0ms

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
331.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
80.0ms
(* (* (* x x) -1/6) x)
27.0ms
(* (* x x) -1/6)
16.0ms
(* (pow x 5) 3/40)

series258.0ms

Calls
4 calls:
Slowest
77.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
69.0ms
(* (* (* x x) -1/6) x)
62.0ms
(* (pow x 5) 3/40)
50.0ms
(* (* x x) -1/6)

simplify4.2s

Calls
55 calls:
Slowest
638.0ms
(* (* (* (* (* 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)))
341.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
340.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
259.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* -1/6 -1/6) -1/6))

prune768.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

18.4b
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
12.9b
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
0.3b
(/ 1/16 (pow x 5))
0.1b
(/ (/ 1/8 x) x)

rewrite289.0ms

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
178.0ms
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
85.0ms
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
13.0ms
(/ (/ 1/8 x) x)
9.0ms
(/ 1/16 (pow x 5))

series352.0ms

Calls
4 calls:
Slowest
156.0ms
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
99.0ms
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
62.0ms
(/ 1/16 (pow x 5))
35.0ms
(/ (/ 1/8 x) x)

simplify17.2s

Calls
199 calls:
Slowest
552.0ms
(/ (* (* (/ 1/8 x) (/ 1/8 x)) (/ 1/8 x)) (* (* x x) x))
440.0ms
(* (- (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (pow x 5))
426.0ms
(/ (exp (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x))) (exp (/ 1/16 (pow x 5))))
381.0ms
(/ (* (exp (/ -1/2 x)) (exp (/ (/ (/ 1/8 x) x) x))) (exp (/ 1/16 (pow x 5))))
349.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))

prune1.5s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

10.5b
(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
(+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))

rewrite708.0ms

Algorithm
rewrite-expression-head
Rules
24×pow1
22×*-un-lft-identity
19×add-exp-log
18×add-cbrt-cube
9×add-sqr-sqrt distribute-lft-out add-log-exp
8×add-cube-cbrt
6×log-prod pow-plus prod-exp pow-prod-up cbrt-unprod
4×insert-posit16
3×cbrt-undiv sum-log flip3-+ times-frac div-exp associate-*r* pow-prod-down flip-+ associate-/l*
2×pow2 log-div frac-add pow-sqr
1×+-commutative associate-+l+ clear-num associate-/r* frac-2neg rem-log-exp associate-*l* pow3 log-pow *-commutative div-inv unswap-sqr
Calls
4 calls:
Slowest
430.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
248.0ms
(+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))
14.0ms
(* (* x x) x)
13.0ms
(/ -1/8 (* (* x x) x))

series238.0ms

Calls
4 calls:
Slowest
95.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
55.0ms
(/ -1/8 (* (* x x) x))
45.0ms
(* (* x x) x)
43.0ms
(+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))

simplify6.9s

Calls
58 calls:
Slowest
552.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
483.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* x x) x))
455.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
452.0ms
(- (log -1/8) (+ (* 4 (pow x 2)) (+ (* 24 (pow x 4)) (* 3 (log x)))))
451.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))

prune772.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes74.0ms

Accuracy

99.5% (0.2b remaining)

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

bsearch175.0ms

end0.0ms

sample4.6s

Algorithm
intervals
Results
2.5s2433×body1280valid
810.0ms1476×body640valid
558.0ms794×body2560valid
309.0ms805×body320valid
223.0ms2109×body80valid
73.0ms383×body160valid