Details

Time bar (total: 1.5m)

sample145.0ms

Algorithm
intervals
Results
64.0ms82×body1280valid
28.0ms26×body2560valid
24.0ms46×body640valid
9.0ms28×body320valid
5.0ms60×body80valid
3.0ms14×body160valid

simplify14.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
14.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.0b

localize17.0ms

Local error

Found 3 expressions with local error:

13.8b
(sqrt (+ (* x x) 1))
2.3b
(log (+ x (sqrt (+ (* x x) 1))))
1.1b
(+ 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
19.0ms
(log (+ x (sqrt (+ (* x x) 1))))
18.0ms
(+ x (sqrt (+ (* x x) 1)))
13.0ms
(sqrt (+ (* x x) 1))

series319.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
192.0ms
(log (+ x (sqrt (+ (* x x) 1))))
79.0ms
(+ x (sqrt (+ (* x x) 1)))
48.0ms
(sqrt (+ (* x x) 1))

simplify5.8s

Counts
63 → 54
Calls
63 calls:
Slowest
437.0ms
(sqrt (+ (pow (* x x) 3) (pow 1 3)))
431.0ms
(log (+ (pow x 3) (pow (sqrt (+ (* x x) 1)) 3)))
428.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
401.0ms
(+ (pow x 3) (pow (sqrt (+ (* x x) 1)) 3))
372.0ms
(sqrt (+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1))))

prune405.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

19.5b
(+ (+ (* (* x x) (* x -1/6)) x) (* (pow x 5) 3/40))
0.3b
(* x -1/6)
0.1b
(* (* x x) (* x -1/6))
0.1b
(* (pow x 5) 3/40)

rewrite190.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
20×add-cbrt-cube
18×pow1
16×add-sqr-sqrt
12×prod-exp
11×associate-*l*
10×cbrt-unprod
9×*-un-lft-identity pow-prod-down add-cube-cbrt add-log-exp
7×associate-*r*
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
149.0ms
(+ (+ (* (* x x) (* x -1/6)) x) (* (pow x 5) 3/40))
21.0ms
(* (* x x) (* x -1/6))
13.0ms
(* (pow x 5) 3/40)
5.0ms
(* x -1/6)

series240.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
88.0ms
(+ (+ (* (* x x) (* x -1/6)) x) (* (pow x 5) 3/40))
76.0ms
(* (pow x 5) 3/40)
55.0ms
(* (* x x) (* x -1/6))
21.0ms
(* x -1/6)

simplify11.9s

Counts
96 → 94
Calls
96 calls:
Slowest
952.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* -1/6 -1/6) -1/6)))
683.0ms
(log (+ (+ (* (* x x) (* x -1/6)) x) (* (pow x 5) 3/40)))
620.0ms
(cbrt (+ (+ (* (* x x) (* x -1/6)) x) (* (pow x 5) 3/40)))
604.0ms
(sqrt (+ (+ (* (* x x) (* x -1/6)) x) (* (pow x 5) 3/40)))
555.0ms
(* (cbrt (* (pow x 5) 3/40)) (cbrt (* (pow x 5) 3/40)))

prune680.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

18.4b
(- (/ 1/16 (pow x 5)) (/ (/ (/ 1/8 x) x) x))
10.7b
(log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ (/ (/ 1/8 x) x) x))))
0.1b
(/ (/ 1/8 x) x)
0.1b
(/ (/ (/ 1/8 x) x) x)

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
510×times-frac
300×add-sqr-sqrt
248×*-un-lft-identity
231×add-cube-cbrt
56×associate-/l*
22×div-inv
19×add-exp-log
18×add-cbrt-cube difference-of-squares
9×cbrt-undiv div-exp
8×log-prod
7×distribute-lft-out--
6×associate-/r* add-log-exp
5×pow1 log-div frac-sub
4×unpow-prod-down insert-posit16 sqr-pow
3×flip3-- flip--
2×clear-num frac-2neg associate-/l/
1×sub-neg diff-log rem-log-exp log-pow
Counts
4 → 319
Calls
4 calls:
Slowest
84.0ms
(log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ (/ (/ 1/8 x) x) x))))
30.0ms
(- (/ 1/16 (pow x 5)) (/ (/ (/ 1/8 x) x) x))
23.0ms
(/ (/ (/ 1/8 x) x) x)
14.0ms
(/ (/ 1/8 x) x)

series436.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
184.0ms
(- (/ 1/16 (pow x 5)) (/ (/ (/ 1/8 x) x) x))
157.0ms
(log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ (/ (/ 1/8 x) x) x))))
48.0ms
(/ (/ 1/8 x) x)
47.0ms
(/ (/ (/ 1/8 x) x) x)

simplify49.4s

Counts
532 → 331
Calls
532 calls:
Slowest
888.0ms
(log (- (pow (/ -1/2 x) 3) (pow (- (/ 1/16 (pow x 5)) (/ (/ (/ 1/8 x) x) x)) 3)))
464.0ms
(/ (* (* (/ (/ 1/8 x) x) (/ (/ 1/8 x) x)) (/ (/ 1/8 x) x)) (* (* x x) x))
431.0ms
(exp (log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ (/ (/ 1/8 x) x) x)))))
428.0ms
(* (* (log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ (/ (/ 1/8 x) x) x)))) (log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ (/ (/ 1/8 x) x) x))))) (log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ (/ (/ 1/8 x) x) x)))))
418.0ms
(log (* (cbrt (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ (/ (/ 1/8 x) x) x)))) (cbrt (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ (/ (/ 1/8 x) x) x))))))

prune3.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

8.5b
(log (+ x (- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x))))
0.1b
(* (* x x) x)
0.1b
(/ 1/8 (* (* x x) x))

rewrite319.0ms

Algorithm
rewrite-expression-head
Rules
23×pow1
18×add-exp-log
17×add-cbrt-cube
16×*-un-lft-identity
8×add-sqr-sqrt
7×add-cube-cbrt
6×log-prod pow-plus prod-exp pow-prod-up cbrt-unprod
3×cbrt-undiv times-frac div-exp associate-*r* pow-prod-down insert-posit16 distribute-lft-out associate-/l* distribute-lft-out-- add-log-exp
2×pow2 log-div pow-sqr
1×clear-num associate-/r* frac-2neg flip3-+ rem-log-exp associate-*l* pow3 log-pow *-commutative flip-+ div-inv unswap-sqr
Counts
3 → 71
Calls
3 calls:
Slowest
270.0ms
(log (+ x (- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x))))
25.0ms
(/ 1/8 (* (* x x) x))
22.0ms
(* (* x x) x)

series224.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
126.0ms
(log (+ x (- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x))))
51.0ms
(/ 1/8 (* (* x x) x))
48.0ms
(* (* x x) x)

simplify10.8s

Counts
90 → 80
Calls
90 calls:
Slowest
762.0ms
(log (+ (pow x 3) (pow (- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x)) 3)))
603.0ms
(log (- x (- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x))))
551.0ms
(* (* (/ 1/8 (* (* x x) x)) (/ 1/8 (* (* x x) x))) (/ 1/8 (* (* x x) x)))
543.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* x x) x))
533.0ms
(log (+ (* x x) (- (* (- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x)) (- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x))) (* x (- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x))))))

prune685.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes30.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 30.8b

bsearch179.0ms

end0.0ms

sample4.8s

Algorithm
intervals
Results
2.1s2370×body1280valid
1.0s849×body2560valid
885.0ms1567×body640valid
393.0ms780×body320valid
202.0ms2022×body80valid
85.0ms412×body160valid