Details

Time bar (total: 48.9s)

sample27.0ms

Algorithm
intervals
Results
18.0ms256×body80valid

simplify16.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
15.0ms
(/ x (+ (* x x) 1))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize17.0ms

Local error

Found 1 expressions with local error:

15.9b
(/ x (+ (* x x) 1))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
3×associate-/r* add-cbrt-cube add-exp-log associate-/l*
2×associate-/r/
1×pow1 cbrt-undiv clear-num frac-2neg flip3-+ div-exp flip-+ insert-posit16 div-inv add-log-exp
Counts
1 → 30
Calls
1 calls:
Slowest
20.0ms
(/ x (+ (* x x) 1))

series78.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
78.0ms
(/ x (+ (* x x) 1))

simplify1.7s

Counts
30 → 33
Calls
30 calls:
Slowest
333.0ms
(/ (* (* x x) x) (* (* (+ (* x x) 1) (+ (* x x) 1)) (+ (* x x) 1)))
320.0ms
(+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1)))
232.0ms
(- (+ x (pow x 5)) (pow x 3))
228.0ms
(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
184.0ms
(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))

prune209.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

15.9b
(sqrt (+ (* x x) 1))
15.9b
(sqrt (+ (* x x) 1))
0.0b
(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
0.0b
(/ x (sqrt (+ (* x x) 1)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
164×add-sqr-sqrt
162×*-un-lft-identity add-cube-cbrt
156×sqrt-prod
27×associate-/l*
22×sqrt-div
18×associate-/r/
12×associate-/r*
11×flip3-+ add-cbrt-cube add-exp-log flip-+
9×div-inv
6×pow1
4×cbrt-undiv div-exp insert-posit16 add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
1×associate-/l/
Counts
4 → 266
Calls
4 calls:
Slowest
53.0ms
(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
10.0ms
(/ x (sqrt (+ (* x x) 1)))
7.0ms
(sqrt (+ (* x x) 1))
7.0ms
(sqrt (+ (* x x) 1))

series231.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
85.0ms
(/ x (sqrt (+ (* x x) 1)))
53.0ms
(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
48.0ms
(sqrt (+ (* x x) 1))
44.0ms
(sqrt (+ (* x x) 1))

simplify25.4s

Counts
396 → 278
Calls
396 calls:
Slowest
512.0ms
(/ (/ (* (* x x) x) (* (* (sqrt (+ (* x x) 1)) (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))) (* (* (sqrt (+ (* x x) 1)) (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1))))
463.0ms
(/ (/ x (sqrt (+ (pow (* x x) 3) (pow 1 3)))) (sqrt (sqrt (+ (* x x) 1))))
461.0ms
(/ (/ x (sqrt (+ (pow (* x x) 3) (pow 1 3)))) (sqrt (sqrt (+ (* x x) 1))))
457.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
447.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))

prune2.4s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

21.3b
(- (+ (/ 1 x) (/ 1 (pow x 5))) (/ 1 (* (* x x) x)))
0.2b
(/ 1 (* (* x x) x))
0.1b
(* (* x x) x)
0.0b
(/ 1 (pow x 5))

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
43×pow1
39×add-exp-log
38×*-un-lft-identity
26×add-sqr-sqrt
24×times-frac
23×add-cube-cbrt
20×add-cbrt-cube
15×div-inv
13×pow-flip
12×unpow-prod-down pow-plus div-exp prod-exp pow-prod-up
10×distribute-lft-out--
9×add-log-exp
8×associate-/r* distribute-lft-out
6×rec-exp 1-exp pow-prod-down cbrt-unprod associate-/l*
4×pow2 cbrt-undiv pow-sqr insert-posit16 sqr-pow
3×pow-to-exp associate-*r* pow-exp frac-sub
2×clear-num frac-2neg diff-log pow3 inv-pow
1×sum-log sub-neg flip3-+ flip3-- associate-*l* frac-add associate--l+ *-commutative flip-+ flip-- difference-of-squares unswap-sqr
Counts
4 → 155
Calls
4 calls:
Slowest
139.0ms
(- (+ (/ 1 x) (/ 1 (pow x 5))) (/ 1 (* (* x x) x)))
33.0ms
(/ 1 (* (* x x) x))
15.0ms
(* (* x x) x)
6.0ms
(/ 1 (pow x 5))

series216.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
72.0ms
(/ 1 (pow x 5))
57.0ms
(* (* x x) x)
48.0ms
(/ 1 (* (* x x) x))
39.0ms
(- (+ (/ 1 x) (/ 1 (pow x 5))) (/ 1 (* (* x x) x)))

simplify15.9s

Counts
135 → 167
Calls
135 calls:
Slowest
1.0s
(/ (* (* 1 1) 1) (* (* (* (* x x) x) (* (* x x) x)) (* (* x x) x)))
1.0s
(/ (* (* 1 1) 1) (* (* (* (* x x) x) (* (* x x) x)) (* (* x x) x)))
548.0ms
(- (* (- (* (/ 1 x) (/ 1 x)) (* (/ 1 (pow x 5)) (/ 1 (pow x 5)))) (* (* x x) x)) (* (- (/ 1 x) (/ 1 (pow x 5))) 1))
523.0ms
(/ (* (cbrt 1) (cbrt 1)) (pow (* (cbrt x) (cbrt x)) 5))
492.0ms
(* (+ (* (/ 1 x) (/ 1 x)) (- (* (/ 1 (pow x 5)) (/ 1 (pow x 5))) (* (/ 1 x) (/ 1 (pow x 5))))) (* (* x x) x))

prune1.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes62.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.0b

bsearch128.0ms

end0.0ms

sample588.0ms

Algorithm
intervals
Results
472.0ms8000×body80valid