Details

Time bar (total: 42.6s)

sample123.0ms

Algorithm
intervals
Results
63.0ms76×body1280valid
21.0ms45×body640valid
14.0ms23×body2560valid
6.0ms21×body320valid
6.0ms73×body80valid
4.0ms18×body160valid

simplify19.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
19.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.0b

localize37.0ms

Local error

Found 3 expressions with local error:

14.4b
(sqrt (+ (* x x) 1))
4.4b
(log (+ x (sqrt (+ (* x x) 1))))
0.7b
(+ x (sqrt (+ (* x x) 1)))

rewrite51.0ms

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
24.0ms
(+ x (sqrt (+ (* x x) 1)))
19.0ms
(log (+ x (sqrt (+ (* x x) 1))))
7.0ms
(sqrt (+ (* x x) 1))

series251.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
147.0ms
(log (+ x (sqrt (+ (* x x) 1))))
53.0ms
(sqrt (+ (* x x) 1))
51.0ms
(+ x (sqrt (+ (* x x) 1)))

simplify4.0s

Counts
25 → 54
Calls
25 calls:
Slowest
514.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
499.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
459.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
397.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
397.0ms
(sqrt (+ (pow (* x x) 3) (pow 1 3)))

prune510.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

17.7b
(+ (+ (* (* (* 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)

rewrite388.0ms

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
313.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
44.0ms
(* (* (* x x) -1/6) x)
15.0ms
(* (pow x 5) 3/40)
14.0ms
(* (* x x) -1/6)

series281.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
101.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
74.0ms
(* (pow x 5) 3/40)
64.0ms
(* (* (* x x) -1/6) x)
40.0ms
(* (* x x) -1/6)

simplify4.2s

Counts
55 → 94
Calls
55 calls:
Slowest
593.0ms
(* (* (* (* (* x x) -1/6) (* (* x x) -1/6)) (* (* x x) -1/6)) (* (* x x) x))
360.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
355.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
303.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
280.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* -1/6 -1/6) -1/6))

prune738.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

12.2b
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
0.1b
(* (* x x) x)
0.1b
(/ -1/8 (* (* 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
Counts
4 → 89
Calls
4 calls:
Slowest
419.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
259.0ms
(+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))
14.0ms
(* (* x x) x)
14.0ms
(/ -1/8 (* (* x x) x))

series293.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
137.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
62.0ms
(* (* x x) x)
55.0ms
(/ -1/8 (* (* x x) x))
39.0ms
(+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))

simplify7.2s

Counts
58 → 101
Calls
58 calls:
Slowest
719.0ms
(* (+ (* (/ -1/8 (* (* x x) x)) (/ -1/8 (* (* x x) x))) (- (* x x) (* (/ -1/8 (* (* x x) x)) x))) x)
549.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
468.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* x x) x))
446.0ms
(- (+ (log -2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ -1 x)) (* 3/32 (/ 1 (pow x 4)))))
443.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))

prune798.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

19.5b
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
14.3b
(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)

rewrite246.0ms

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/
Counts
4 → 167
Calls
4 calls:
Slowest
157.0ms
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
73.0ms
(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))

series303.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
139.0ms
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
66.0ms
(/ 1/16 (pow x 5))
61.0ms
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
38.0ms
(/ (/ 1/8 x) x)

simplify16.7s

Counts
199 → 179
Calls
199 calls:
Slowest
433.0ms
(* (- (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (pow x 5))
411.0ms
(/ (exp (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x))) (exp (/ 1/16 (pow x 5))))
407.0ms
(/ (* (exp (/ -1/2 x)) (exp (/ (/ (/ 1/8 x) x) x))) (exp (/ 1/16 (pow x 5))))
373.0ms
(- (+ (* 6 (pow x 4)) (log -1/16)) (+ (* 2 (pow x 2)) (* 5 (log x))))
353.0ms
(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))))))

prune1.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes60.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 30.3b

bsearch118.0ms

end0.0ms

sample4.1s

Algorithm
intervals
Results
2.2s2333×body1280valid
805.0ms1643×body640valid
469.0ms762×body2560valid
254.0ms762×body320valid
170.0ms2064×body80valid
95.0ms436×body160valid