Details

Time bar (total: 2.9m)

sample102.0ms

Algorithm
intervals
Results
26.0ms52×body640valid
18.0ms138×body80valid
18.0ms26×body1280valid
16.0ms13×body160valid
10.0ms27×body320valid

simplify91.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
90.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.3b

localize18.0ms

Local error

Found 4 expressions with local error:

2.4b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
0.0b
(/ 1 (+ x 1))
0.0b
(/ 1 (- x 1))
0.0b
(- (/ 1 (+ x 1)) (/ 2 x))

rewrite347.0ms

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
229.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
51.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
20.0ms
(/ 1 (- x 1))
12.0ms
(/ 1 (+ x 1))

series198.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
129.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
32.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
22.0ms
(/ 1 (+ x 1))
14.0ms
(/ 1 (- x 1))

simplify2.1m

Counts
879 → 660
Calls
879 calls:
Slowest
852.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (+ x 1))) (/ (cbrt 1) (sqrt (+ x 1))) (- (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))))
817.0ms
(fma (/ 1 (+ (pow x 3) (pow 1 3))) (+ (* x x) (- (* 1 1) (* x 1))) (- (* (/ 2 x) 1)))
563.0ms
(+ (* (- (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (* (/ 2 x) (/ 2 x))) (- x 1)) (* (+ (/ 1 (+ x 1)) (/ 2 x)) 1))
546.0ms
(fma (- (/ (sqrt 2) (cbrt x))) (/ (sqrt 2) (* (cbrt x) (cbrt x))) (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x)))))
529.0ms
(fma (/ 1 1) (/ 1 (+ x 1)) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))

prune3.7s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 2 (pow x 5))
0.1b
(/ (/ 2 x) (* x x))
0.0b
(/ 2 (pow x 7))
0.0b
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))

rewrite50.0ms

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
26.0ms
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))
10.0ms
(/ (/ 2 x) (* x x))
5.0ms
(/ 2 (pow x 5))
5.0ms
(/ 2 (pow x 7))

series286.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
130.0ms
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))
63.0ms
(/ 2 (pow x 7))
52.0ms
(/ 2 (pow x 5))
41.0ms
(/ (/ 2 x) (* x x))

simplify7.6s

Counts
187 → 190
Calls
187 calls:
Slowest
237.0ms
(/ (* (* 2 2) 2) (* (* (pow x 7) (pow x 7)) (pow x 7)))
237.0ms
(/ (* (* 2 2) 2) (* (* (pow x 5) (pow x 5)) (pow x 5)))
174.0ms
(* (exp (/ (/ 2 x) (* x x))) (exp (/ 2 (pow x 5))))
166.0ms
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))
163.0ms
(/ (* (cbrt 2) (cbrt 2)) (* (cbrt (pow x 5)) (cbrt (pow x 5))))

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 2 (pow x 5))
0.1b
(/ (/ 2 x) x)
0.1b
(/ (/ (/ 2 x) x) x)
0.0b
(/ 2 (pow x 7))

rewrite39.0ms

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
15.0ms
(/ (/ (/ 2 x) x) x)
7.0ms
(/ (/ 2 x) x)
5.0ms
(/ 2 (pow x 5))
5.0ms
(/ 2 (pow x 7))

series182.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
63.0ms
(/ 2 (pow x 7))
50.0ms
(/ 2 (pow x 5))
38.0ms
(/ (/ (/ 2 x) x) x)
31.0ms
(/ (/ 2 x) x)

simplify18.6s

Counts
526 → 376
Calls
526 calls:
Slowest
351.0ms
(/ (/ (* (* (/ 2 x) (/ 2 x)) (/ 2 x)) (* (* x x) x)) (* (* x x) x))
267.0ms
(/ (* (* (/ (/ 2 x) x) (/ (/ 2 x) x)) (/ (/ 2 x) x)) (* (* x x) x))
245.0ms
(/ (/ (/ (* (cbrt 2) (cbrt 2)) (sqrt x)) (* (cbrt x) (cbrt x))) (sqrt x))
234.0ms
(/ (* (* 2 2) 2) (* (* (pow x 7) (pow x 7)) (pow x 7)))
233.0ms
(/ (/ (/ (* (cbrt 2) (cbrt 2)) 1) (* (cbrt x) (cbrt x))) (sqrt x))

prune2.7s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt 2) x)
0.4b
(/ (sqrt 2) x)
0.2b
(/ (/ (sqrt 2) x) x)
0.2b
(/ 2 (pow x 5))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
195×times-frac
125×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
60×sqrt-prod
37×associate-/l*
18×add-exp-log
16×associate-/r*
15×add-cbrt-cube
12×unpow-prod-down
8×div-exp div-inv
6×cbrt-undiv
4×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp sqr-pow
1×pow-to-exp pow-exp associate-/l/
Counts
4 → 241
Calls
4 calls:
Slowest
12.0ms
(/ (/ (sqrt 2) x) x)
5.0ms
(/ 2 (pow x 5))
5.0ms
(/ (sqrt 2) x)
5.0ms
(/ (sqrt 2) x)

series197.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
56.0ms
(/ 2 (pow x 5))
51.0ms
(/ (sqrt 2) x)
45.0ms
(/ (sqrt 2) x)
45.0ms
(/ (/ (sqrt 2) x) x)

simplify6.6s

Counts
317 → 253
Calls
317 calls:
Slowest
236.0ms
(/ (* (* 2 2) 2) (* (* (pow x 5) (pow x 5)) (pow x 5)))
174.0ms
(/ (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* x x) x)) (* (* x x) x))
170.0ms
(/ (* (* (/ (sqrt 2) x) (/ (sqrt 2) x)) (/ (sqrt 2) x)) (* (* x x) x))
164.0ms
(/ (* (cbrt 2) (cbrt 2)) (* (cbrt (pow x 5)) (cbrt (pow x 5))))
153.0ms
(/ 1 (pow (* (cbrt x) (cbrt x)) 5))

prune2.1s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes70.0ms

Accuracy

99.5% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 9.9b

bsearch129.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
609.0ms4144×body80valid
560.0ms1825×body640valid
224.0ms989×body320valid
221.0ms571×body1280valid
80.0ms471×body160valid