Details

Time bar (total: 39.7s)

sample132.0ms

Algorithm
intervals
Results
49.0ms69×body1280valid
44.0ms59×body640valid
15.0ms21×body2560valid
7.0ms21×body320valid
5.0ms66×body80valid
4.0ms20×body160valid

simplify11.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
11.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.8b

localize19.0ms

Local error

Found 3 expressions with local error:

16.1b
(sqrt (+ (* x x) 1))
4.1b
(log (+ x (sqrt (+ (* x x) 1))))
1.8b
(+ x (sqrt (+ (* x x) 1)))

rewrite60.0ms

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
23.0ms
(+ x (sqrt (+ (* x x) 1)))
22.0ms
(log (+ x (sqrt (+ (* x x) 1))))
14.0ms
(sqrt (+ (* x x) 1))

series241.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
131.0ms
(log (+ x (sqrt (+ (* x x) 1))))
65.0ms
(+ x (sqrt (+ (* x x) 1)))
45.0ms
(sqrt (+ (* x x) 1))

simplify4.2s

Counts
25 → 54
Calls
25 calls:
Slowest
583.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
527.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
489.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
391.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
361.0ms
(log (+ (pow x 3) (pow (sqrt (+ (* x x) 1)) 3)))

prune481.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

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)

rewrite377.0ms

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
289.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
53.0ms
(* (* (* x x) -1/6) x)
24.0ms
(* (* x x) -1/6)
9.0ms
(* (pow x 5) 3/40)

series247.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
78.0ms
(* (pow x 5) 3/40)
70.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
63.0ms
(* (* (* x x) -1/6) x)
35.0ms
(* (* x x) -1/6)

simplify4.4s

Counts
55 → 94
Calls
55 calls:
Slowest
674.0ms
(* (* (* (* (* x x) -1/6) (* (* x x) -1/6)) (* (* x x) -1/6)) (* (* x x) x))
359.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
347.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
306.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
263.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* -1/6 -1/6) -1/6))

prune661.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

17.7b
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
12.2b
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
0.2b
(/ (/ 1/8 x) x)
0.1b
(/ 1/16 (pow x 5))

rewrite292.0ms

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
194.0ms
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
83.0ms
(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))

series319.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
135.0ms
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
75.0ms
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
67.0ms
(/ 1/16 (pow x 5))
42.0ms
(/ (/ 1/8 x) x)

simplify16.3s

Counts
199 → 179
Calls
199 calls:
Slowest
435.0ms
(* (- (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (pow x 5))
416.0ms
(/ (exp (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x))) (exp (/ 1/16 (pow x 5))))
397.0ms
(/ (* (exp (/ -1/2 x)) (exp (/ (/ (/ 1/8 x) x) x))) (exp (/ 1/16 (pow x 5))))
384.0ms
(- (sqrt (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x))) (/ (sqrt 1/16) (pow (sqrt x) 5)))
377.0ms
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

10.2b
(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)))

rewrite859.0ms

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
Counts
4 → 89
Calls
4 calls:
Slowest
510.0ms
(+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x)))
318.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
15.0ms
(* (* x x) x)
14.0ms
(/ -1/8 (* (* x x) x))

series229.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
93.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
51.0ms
(+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x)))
44.0ms
(/ -1/8 (* (* x x) x))
41.0ms
(* (* x x) x)

simplify4.7s

Counts
56 → 101
Calls
56 calls:
Slowest
481.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
422.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* x x) x))
390.0ms
(- (+ (log -2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ -1 x)) (* 3/32 (/ 1 (pow x 4)))))
342.0ms
(- (log -1/8) (+ (* 4 (pow x 2)) (+ (* 24 (pow x 4)) (* 3 (log x)))))
276.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* x x) x))

prune616.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes106.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.4b

bsearch113.0ms

end0.0ms

sample3.9s

Algorithm
intervals
Results
2.1s2324×body1280valid
707.0ms1561×body640valid
565.0ms817×body2560valid
198.0ms741×body320valid
145.0ms2122×body80valid
68.0ms435×body160valid