Details

Time bar (total: 53.7s)

sample104.0ms

Algorithm
intervals
Results
44.0ms66×body1280valid
19.0ms41×body640valid
17.0ms29×body2560valid
8.0ms30×body320valid
6.0ms79×body80valid
2.0ms11×body160valid

simplify33.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
33.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 50.6b

localize13.0ms

Local error

Found 4 expressions with local error:

16.1b
(sqrt (+ (* x x) 1))
2.6b
(log (+ x (sqrt (+ (* x x) 1))))
1.0b
(+ x (sqrt (+ (* x x) 1)))
0.0b
(+ (* x x) 1)

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-log-exp
7×add-sqr-sqrt
6×pow1 add-cube-cbrt
5×add-exp-log
4×log-prod flip3-+ add-cbrt-cube flip-+ insert-posit16
3×sqrt-prod
2×+-commutative log-div sum-log sqrt-div distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp log-pow
Counts
4 → 57
Calls
4 calls:
Slowest
19.0ms
(+ x (sqrt (+ (* x x) 1)))
17.0ms
(log (+ x (sqrt (+ (* x x) 1))))
7.0ms
(sqrt (+ (* x x) 1))
6.0ms
(+ (* x x) 1)

series270.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
128.0ms
(log (+ x (sqrt (+ (* x x) 1))))
70.0ms
(+ x (sqrt (+ (* x x) 1)))
37.0ms
(+ (* x x) 1)
35.0ms
(sqrt (+ (* x x) 1))

simplify4.0s

Counts
29 → 69
Calls
29 calls:
Slowest
514.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
454.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
444.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
414.0ms
(sqrt (+ (pow (* x x) 3) (pow 1 3)))
374.0ms
(log (+ (pow x 3) (pow (sqrt (+ (* x x) 1)) 3)))

prune657.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

21.5b
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
0.2b
(* (* x x) -1/6)
0.1b
(* (* (* x x) -1/6) x)
0.0b
(* (pow x 5) 3/40)

rewrite720.0ms

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
636.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
54.0ms
(* (* (* x x) -1/6) x)
15.0ms
(* (* x x) -1/6)
13.0ms
(* (pow x 5) 3/40)

series302.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
99.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
86.0ms
(* (pow x 5) 3/40)
71.0ms
(* (* (* x x) -1/6) x)
47.0ms
(* (* x x) -1/6)

simplify4.2s

Counts
55 → 94
Calls
55 calls:
Slowest
486.0ms
(* (* (* (* (* x x) -1/6) (* (* x x) -1/6)) (* (* x x) -1/6)) (* (* x x) x))
435.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
366.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
345.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
273.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* -1/6 -1/6) -1/6))

prune843.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

9.5b
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
0.6b
(/ -1/8 (* (* x x) x))
0.1b
(* (* x x) x)
0.0b
(+ (/ -1/8 (* (* x x) x)) x)

rewrite436.0ms

Algorithm
rewrite-expression-head
Rules
24×pow1
19×*-un-lft-identity add-exp-log
18×add-cbrt-cube
9×add-sqr-sqrt
8×add-cube-cbrt
7×distribute-lft-out
6×log-prod pow-plus prod-exp pow-prod-up cbrt-unprod add-log-exp
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 clear-num associate-/r* sum-log frac-2neg rem-log-exp associate-*l* pow3 log-pow *-commutative div-inv unswap-sqr
Counts
4 → 84
Calls
4 calls:
Slowest
351.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
34.0ms
(+ (/ -1/8 (* (* x x) x)) x)
28.0ms
(/ -1/8 (* (* x x) x))
22.0ms
(* (* x x) x)

series337.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
130.0ms
(+ (/ -1/8 (* (* x x) x)) x)
105.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
53.0ms
(* (* x x) x)
49.0ms
(/ -1/8 (* (* x x) x))

simplify5.2s

Counts
51 → 96
Calls
51 calls:
Slowest
523.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* x x) x))
491.0ms
(- (+ (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)))))
444.0ms
(- x (* 1/8 (/ 1 (pow x 3))))
400.0ms
(- x (* 1/8 (/ 1 (pow x 3))))

prune869.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

16.1b
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
10.9b
(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)

rewrite276.0ms

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
185.0ms
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
63.0ms
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
14.0ms
(/ (/ (/ 1/8 x) x) x)
7.0ms
(/ (/ 1/8 x) x)

series321.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
138.0ms
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
78.0ms
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
71.0ms
(/ (/ (/ 1/8 x) x) x)
33.0ms
(/ (/ 1/8 x) x)

simplify28.4s

Counts
453 → 326
Calls
453 calls:
Slowest
435.0ms
(* (- (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (pow x 5))
398.0ms
(/ (* (exp (/ -1/2 x)) (exp (/ (/ (/ 1/8 x) x) x))) (exp (/ 1/16 (pow x 5))))
388.0ms
(/ (* (* (/ (/ 1/8 x) x) (/ (/ 1/8 x) x)) (/ (/ 1/8 x) x)) (* (* x x) x))
371.0ms
(log (sqrt (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))))
349.0ms
(/ (exp (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x))) (exp (/ 1/16 (pow x 5))))

prune2.3s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes83.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.2b

bsearch123.0ms

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.8s2366×body1280valid
751.0ms1556×body640valid
599.0ms740×body320valid
483.0ms837×body2560valid
146.0ms2111×body80valid
63.0ms390×body160valid