Details

Time bar (total: 3.2m)

sample68.0ms

Algorithm
intervals
Results
20.0ms59×body640valid
11.0ms25×body1280valid
11.0ms30×body320valid
11.0ms129×body80valid
2.0ms13×body160valid

simplify107.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
107.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.6b

localize39.0ms

Local error

Found 4 expressions with local error:

3.2b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
0.0b
(- (/ 1 (+ x 1)) (/ 2 x))
0.0b
(/ 1 (+ x 1))
0.0b
(/ 1 (- x 1))

rewrite378.0ms

Algorithm
rewrite-expression-head
Rules
743×*-un-lft-identity
715×times-frac
544×add-sqr-sqrt
494×add-cube-cbrt
468×prod-diff
236×associate-+l+
99×distribute-lft-out
72×div-inv
58×associate-/r/
29×flip3-+ flip-+
22×distribute-lft-out--
20×difference-of-squares
18×fma-neg
13×fma-def
12×add-exp-log
11×associate-/r* add-log-exp
8×add-cbrt-cube
6×pow1 associate-/l*
4×expm1-log1p-u difference-of-sqr-1 div-exp insert-posit16 log1p-expm1-u
3×flip3-- frac-add flip--
2×cbrt-undiv rec-exp clear-num sum-log sub-neg frac-2neg diff-log 1-exp frac-sub pow-flip inv-pow
1×+-commutative associate-+l-
Counts
4 → 648
Calls
4 calls:
Slowest
267.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
64.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
9.0ms
(/ 1 (- x 1))
9.0ms
(/ 1 (+ x 1))

series184.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
111.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
38.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
21.0ms
(/ 1 (- x 1))
14.0ms
(/ 1 (+ x 1))

simplify2.2m

Counts
927 → 660
Calls
927 calls:
Slowest
797.0ms
(+ (fma (- (/ (cbrt 2) x)) (/ (* (cbrt 2) (cbrt 2)) 1) (* (/ (cbrt 2) x) (/ (* (cbrt 2) (cbrt 2)) 1))) (/ 1 (- x 1)))
686.0ms
(fma (/ (sqrt 1) 1) (/ (sqrt 1) (+ x 1)) (- (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))))
607.0ms
(fma (* (cbrt (/ 1 (+ x 1))) (cbrt (/ 1 (+ x 1)))) (cbrt (/ 1 (+ x 1))) (- (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x))))))
556.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (+ x 1)) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
554.0ms
(* (* (+ x 1) x) (- x 1))

prune3.7s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 2 x) (* x x))
0.1b
(/ 2 (pow x 5))
0.0b
(/ 2 (pow x 7))
0.0b
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
95×times-frac
60×*-un-lft-identity
58×add-sqr-sqrt add-cube-cbrt
26×add-exp-log
24×unpow-prod-down
20×add-cbrt-cube
19×associate-/l*
17×fma-def
15×associate-/r*
12×div-exp
8×cbrt-undiv sqr-pow
7×div-inv
6×add-log-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×clear-num frac-2neg
2×pow-to-exp pow-exp prod-exp cbrt-unprod
1×+-commutative sum-log flip3-+ frac-add flip-+ distribute-lft-out associate-/l/
Counts
4 → 178
Calls
4 calls:
Slowest
28.0ms
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))
11.0ms
(/ (/ 2 x) (* x x))
5.0ms
(/ 2 (pow x 5))
5.0ms
(/ 2 (pow x 7))

series301.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
137.0ms
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))
68.0ms
(/ 2 (pow x 7))
51.0ms
(/ 2 (pow x 5))
44.0ms
(/ (/ 2 x) (* x x))

simplify12.9s

Counts
233 → 190
Calls
233 calls:
Slowest
402.0ms
(/ 2 (* (cbrt (pow x 5)) (cbrt (pow x 5))))
266.0ms
(* (* (/ (/ 2 x) (* x x)) (/ (/ 2 x) (* x x))) (/ (/ 2 x) (* x x)))
243.0ms
(/ (* (* 2 2) 2) (* (* (pow x 5) (pow x 5)) (pow x 5)))
241.0ms
(/ (* (* 2 2) 2) (* (* (pow x 7) (pow x 7)) (pow x 7)))
220.0ms
(* (* (/ 2 (pow x 5)) (/ 2 (pow x 5))) (/ 2 (pow x 5)))

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 2 x) x)
0.1b
(/ (/ (/ 2 x) x) x)
0.1b
(/ 2 (pow x 5))
0.0b
(/ 2 (pow x 7))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
510×times-frac
262×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
62×associate-/l*
28×add-exp-log
24×unpow-prod-down div-inv
22×add-cbrt-cube
20×associate-/r*
15×div-exp
11×cbrt-undiv
8×sqr-pow
4×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
2×pow-to-exp pow-exp associate-/l/
Counts
4 → 364
Calls
4 calls:
Slowest
12.0ms
(/ (/ (/ 2 x) x) x)
8.0ms
(/ (/ 2 x) x)
5.0ms
(/ 2 (pow x 7))
5.0ms
(/ 2 (pow x 5))

series180.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
61.0ms
(/ 2 (pow x 7))
50.0ms
(/ 2 (pow x 5))
38.0ms
(/ (/ (/ 2 x) x) x)
31.0ms
(/ (/ 2 x) x)

simplify22.1s

Counts
590 → 376
Calls
590 calls:
Slowest
458.0ms
(* (* (/ 2 (pow x 7)) (/ 2 (pow x 7))) (/ 2 (pow x 7)))
298.0ms
(/ (* (* (/ (/ 2 x) x) (/ (/ 2 x) x)) (/ (/ 2 x) x)) (* (* x x) x))
271.0ms
(/ (/ (/ (* (cbrt 2) (cbrt 2)) (sqrt x)) (* (cbrt x) (cbrt x))) (sqrt x))
255.0ms
(* (* (/ (/ 2 x) x) (/ (/ 2 x) x)) (/ (/ 2 x) x))
250.0ms
(/ (/ (/ (* (cbrt 2) (cbrt 2)) 1) (* (cbrt x) (cbrt x))) (sqrt x))

prune2.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 2 (* (* x x) x))
0.1b
(* (* x x) x)
0.1b
(/ 2 (pow x 5))
0.0b
(/ 2 (pow x 7))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
40×add-sqr-sqrt
39×*-un-lft-identity add-cube-cbrt
28×add-exp-log
24×unpow-prod-down
23×pow1
22×add-cbrt-cube
15×associate-/r*
9×div-exp associate-/l*
8×sqr-pow
6×pow-plus prod-exp pow-prod-up cbrt-unprod
5×cbrt-undiv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*r* pow-prod-down div-inv
2×pow2 pow-to-exp pow-exp pow-sqr
1×associate-*l* pow3 *-commutative unswap-sqr
Counts
4 → 153
Calls
4 calls:
Slowest
15.0ms
(* (* x x) x)
15.0ms
(/ 2 (* (* x x) x))
6.0ms
(/ 2 (pow x 5))
5.0ms
(/ 2 (pow x 7))

series191.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
65.0ms
(/ 2 (pow x 7))
53.0ms
(/ 2 (pow x 5))
40.0ms
(/ 2 (* (* x x) x))
33.0ms
(* (* x x) x)

simplify10.0s

Counts
212 → 165
Calls
212 calls:
Slowest
338.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* x x) x))
288.0ms
(* (* (/ 2 (* (* x x) x)) (/ 2 (* (* x x) x))) (/ 2 (* (* x x) x)))
280.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* x x) x))
278.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* x x) x))
233.0ms
(/ (* (* 2 2) 2) (* (* (pow x 7) (pow x 7)) (pow x 7)))

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes40.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 32.4b

bsearch125.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
547.0ms1805×body640valid
350.0ms440×body160valid
299.0ms4202×body80valid
254.0ms959×body320valid
246.0ms597×body1280valid