Details

Time bar (total: 46.6s)

sample16.0ms

Algorithm
intervals
Results
10.0ms256×body80valid

simplify10.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
10.0ms
(/ x (+ (* x x) 1))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.7b

localize9.0ms

Local error

Found 1 expressions with local error:

18.7b
(/ x (+ (* x x) 1))

rewrite16.0ms

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
15.0ms
(/ x (+ (* x x) 1))

series64.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
64.0ms
(/ x (+ (* x x) 1))

simplify2.0s

Counts
30 → 33
Calls
30 calls:
Slowest
381.0ms
(+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1)))
378.0ms
(/ (* (* x x) x) (* (* (+ (* x x) 1) (+ (* x x) 1)) (+ (* x x) 1)))
282.0ms
(- (+ x (pow x 5)) (pow x 3))
251.0ms
(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
245.0ms
(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))

prune269.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 2 expressions with local error:

18.7b
(/ (+ (* x x) 1) x)
0.1b
(/ 1 (/ (+ (* x x) 1) x))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
52×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-/r*
15×add-exp-log
9×add-cbrt-cube
8×div-exp
6×div-inv associate-/l*
4×cbrt-undiv
3×pow1
2×rec-exp clear-num frac-2neg 1-exp insert-posit16 add-log-exp associate-/l/
1×flip3-+ associate-/r/ flip-+ pow-flip inv-pow
Counts
2 → 107
Calls
2 calls:
Slowest
29.0ms
(/ (+ (* x x) 1) x)
12.0ms
(/ 1 (/ (+ (* x x) 1) x))

series152.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
86.0ms
(/ (+ (* x x) 1) x)
65.0ms
(/ 1 (/ (+ (* x x) 1) x))

simplify7.3s

Counts
132 → 113
Calls
132 calls:
Slowest
865.0ms
(/ (* (* (+ (* x x) 1) (+ (* x x) 1)) (+ (* x x) 1)) (* (* x x) x))
607.0ms
(/ (* (* 1 1) 1) (/ (* (* (+ (* x x) 1) (+ (* x x) 1)) (+ (* x x) 1)) (* (* x x) x)))
371.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (+ (* x x) 1)) (cbrt (+ (* x x) 1))) (* (cbrt x) (cbrt x))))
320.0ms
(/ (sqrt 1) (/ (* (cbrt (+ (* x x) 1)) (cbrt (+ (* x x) 1))) (* (cbrt x) (cbrt x))))
283.0ms
(/ (* (* 1 1) 1) (* (* (/ (+ (* x x) 1) x) (/ (+ (* x x) 1) x)) (/ (+ (* x x) 1) x)))

prune789.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ 1 (+ x (/ 1 x)))
0.0b
(+ x (/ 1 x))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
15×times-frac
12×add-sqr-sqrt add-cube-cbrt
10×distribute-lft-out
6×add-exp-log div-inv
5×associate-/r*
4×add-cbrt-cube add-log-exp
3×pow1 associate-/l*
2×flip3-+ div-exp associate-/r/ flip-+ insert-posit16
1×cbrt-undiv +-commutative rec-exp clear-num sum-log frac-2neg 1-exp pow-flip inv-pow
Counts
2 → 56
Calls
2 calls:
Slowest
22.0ms
(/ 1 (+ x (/ 1 x)))
12.0ms
(+ x (/ 1 x))

series70.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
39.0ms
(+ x (/ 1 x))
31.0ms
(/ 1 (+ x (/ 1 x)))

simplify2.1s

Counts
52 → 62
Calls
52 calls:
Slowest
513.0ms
(/ (* (* 1 1) 1) (* (* (+ x (/ 1 x)) (+ x (/ 1 x))) (+ x (/ 1 x))))
259.0ms
(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
242.0ms
(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
186.0ms
(- (+ x (pow x 5)) (pow x 3))
185.0ms
(+ (* x x) (- (* (/ 1 x) (/ 1 x)) (* x (/ 1 x))))

prune367.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

28.4b
(* (/ x (+ (pow (* x x) 3) (pow 1 3))) (+ 1 (- (* (* x x) (* x x)) (* x x))))
16.0b
(- (* (* x x) (* x x)) (* x x))
0.7b
(/ x (+ (pow (* x x) 3) (pow 1 3)))
0.1b
(* (* x x) (* x x))

rewrite355.0ms

Algorithm
rewrite-expression-head
Rules
117×pow1
49×*-un-lft-identity
37×times-frac
36×pow-prod-up
31×add-sqr-sqrt
26×add-cube-cbrt
25×associate-*l*
24×pow-prod-down
23×add-cbrt-cube add-exp-log
22×pow-sqr
18×pow-plus
15×distribute-lft-out
13×pow2
10×prod-exp cbrt-unprod
7×cube-mult sum-cubes
6×associate-/r* add-log-exp
5×associate-*r*
4×flip3-+ associate-/r/ flip-+ insert-posit16
3×associate-/l* unswap-sqr
2×frac-times cbrt-undiv div-exp associate-*r/ *-commutative div-inv
1×distribute-rgt-in clear-num sub-neg frac-2neg distribute-lft-in flip3-- diff-log swap-sqr associate-*l/ flip-- difference-of-squares
Counts
4 → 171
Calls
4 calls:
Slowest
262.0ms
(* (/ x (+ (pow (* x x) 3) (pow 1 3))) (+ 1 (- (* (* x x) (* x x)) (* x x))))
42.0ms
(- (* (* x x) (* x x)) (* x x))
32.0ms
(* (* x x) (* x x))
13.0ms
(/ x (+ (pow (* x x) 3) (pow 1 3)))

series603.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
261.0ms
(/ x (+ (pow (* x x) 3) (pow 1 3)))
150.0ms
(* (/ x (+ (pow (* x x) 3) (pow 1 3))) (+ 1 (- (* (* x x) (* x x)) (* x x))))
131.0ms
(- (* (* x x) (* x x)) (* x x))
61.0ms
(* (* x x) (* x x))

simplify30.1s

Counts
174 → 183
Calls
174 calls:
Slowest
959.0ms
(/ x (+ (pow (pow (* x x) 3) 3) (pow (pow 1 3) 3)))
773.0ms
(* (/ (* (* x x) x) (* (* (+ (pow (* x x) 3) (pow 1 3)) (+ (pow (* x x) 3) (pow 1 3))) (+ (pow (* x x) 3) (pow 1 3)))) (* (* (+ 1 (- (* (* x x) (* x x)) (* x x))) (+ 1 (- (* (* x x) (* x x)) (* x x)))) (+ 1 (- (* (* x x) (* x x)) (* x x)))))
741.0ms
(/ (sqrt x) (+ (pow (* x x) 3) (pow 1 3)))
588.0ms
(* x (- (* 1 1) (* (- (* (* x x) (* x x)) (* x x)) (- (* (* x x) (* x x)) (* x x)))))
532.0ms
(/ (* (cbrt x) (cbrt x)) (+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1))))

prune1.7s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes26.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample610.0ms

Algorithm
intervals
Results
492.0ms8000×body80valid