Details

Time bar (total: 3.4m)

sample67.0ms

Algorithm
intervals
Results
22.0ms58×body640valid
14.0ms134×body80valid
10.0ms34×body320valid
8.0ms15×body1280valid
3.0ms15×body160valid

simplify89.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
89.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.4b

localize29.0ms

Local error

Found 4 expressions with local error:

2.2b
(+ (- (/ 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))

rewrite299.0ms

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
189.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
59.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
9.0ms
(/ 1 (- x 1))
8.0ms
(/ 1 (+ x 1))

series225.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
131.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
44.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
27.0ms
(/ 1 (- x 1))
23.0ms
(/ 1 (+ x 1))

simplify2.1m

Counts
879 → 660
Calls
879 calls:
Slowest
662.0ms
(fma (/ (sqrt 1) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (sqrt 1) (cbrt (+ x 1))) (- (* (/ 2 (sqrt x)) (/ 1 (sqrt x)))))
586.0ms
(fma (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1))) (- (* (/ (cbrt 2) (sqrt x)) (/ (* (cbrt 2) (cbrt 2)) (sqrt x)))))
570.0ms
(+ (* (- (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (* (/ 2 x) (/ 2 x))) (- x 1)) (* (+ (/ 1 (+ x 1)) (/ 2 x)) 1))
551.0ms
(* (* (+ x 1) x) (- x 1))
546.0ms
(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ 1 (cbrt (+ x 1))) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))

prune3.7s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

60.8b
(fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x)))))
2.2b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (+ (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (/ 1 (- x 1))))
0.6b
(cbrt (/ 2 x))
0.6b
(cbrt (/ 2 x))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
365×*-un-lft-identity
347×times-frac
266×add-sqr-sqrt
249×add-cube-cbrt
236×associate-+l+
234×prod-diff
55×distribute-lft-out
40×div-inv
26×cbrt-prod associate-/r/
17×flip3-+ flip-+
16×add-log-exp
13×fma-def
10×distribute-lft-out--
6×sum-log frac-add difference-of-squares
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
2×cbrt-div flip3-- pow1/3 diff-log frac-sub flip--
1×+-commutative associate-+r+ sub-neg associate-+l- fma-udef
Counts
4 → 344
Calls
4 calls:
Slowest
154.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (+ (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (/ 1 (- x 1))))
1.0ms
(cbrt (/ 2 x))
1.0ms
(cbrt (/ 2 x))
0.0ms
(fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
752.0ms
(fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x)))))
251.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (+ (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (/ 1 (- x 1))))
207.0ms
(cbrt (/ 2 x))
206.0ms
(cbrt (/ 2 x))

simplify39.6s

Counts
313 → 356
Calls
313 calls:
Slowest
564.0ms
(+ (* (- (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (* (/ 2 x) (/ 2 x))) (+ (* (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x)))))) (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (/ 1 (- x 1)))))) (* (+ (/ 1 (+ x 1)) (/ 2 x)) (+ (pow (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) 3) (pow (/ 1 (- x 1)) 3))))
516.0ms
(fma (/ 1 (+ (pow x 3) (pow 1 3))) (+ (* x x) (- (* 1 1) (* x 1))) (- (* (/ 1 x) 2)))
368.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (cbrt 1) (cbrt (+ x 1))) (- (* (/ 2 x) 1)))
353.0ms
(fma (/ (sqrt 1) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (sqrt 1) (cbrt (+ x 1))) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
352.0ms
(+ (* (- (* 1 x) (* (+ x 1) 2)) (+ (* (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x)))))) (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (/ 1 (- x 1)))))) (* (* (+ x 1) x) (+ (pow (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) 3) (pow (/ 1 (- x 1)) 3))))

prune3.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 2 (pow x 7))
0.1b
(/ (/ 2 x) (* x x))
0.0b
(/ 2 (pow x 5))
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
25.0ms
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))
10.0ms
(/ (/ 2 x) (* x x))
9.0ms
(/ 2 (pow x 7))
5.0ms
(/ 2 (pow x 5))

series290.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
132.0ms
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))
65.0ms
(/ 2 (pow x 7))
49.0ms
(/ 2 (pow x 5))
43.0ms
(/ (/ 2 x) (* x x))

simplify8.1s

Counts
187 → 190
Calls
187 calls:
Slowest
246.0ms
(/ (* (* 2 2) 2) (* (* (pow x 7) (pow x 7)) (pow x 7)))
244.0ms
(/ (* (* 2 2) 2) (* (* (pow x 5) (pow x 5)) (pow x 5)))
184.0ms
(* (exp (/ (/ 2 x) (* x x))) (exp (/ 2 (pow x 5))))
177.0ms
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))
172.0ms
(/ (* (cbrt 2) (cbrt 2)) (* (cbrt (pow x 5)) (cbrt (pow x 5))))

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

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))

series190.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
70.0ms
(/ 2 (pow x 7))
55.0ms
(/ 2 (pow x 5))
38.0ms
(/ (/ (/ 2 x) x) x)
27.0ms
(/ (/ 2 x) x)

simplify19.7s

Counts
526 → 376
Calls
526 calls:
Slowest
279.0ms
(/ (* (* (/ (/ 2 x) x) (/ (/ 2 x) x)) (/ (/ 2 x) x)) (* (* x x) x))
268.0ms
(/ (/ (sqrt 2) (cbrt x)) x)
261.0ms
(/ (/ (/ (* (cbrt 2) (cbrt 2)) (sqrt x)) (* (cbrt x) (cbrt x))) (sqrt x))
250.0ms
(/ (/ (/ (* (cbrt 2) (cbrt 2)) 1) (* (cbrt x) (cbrt x))) (sqrt x))
246.0ms
(/ (* (* 2 2) 2) (* (* (pow x 7) (pow x 7)) (pow x 7)))

prune2.6s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes39.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 19.2b

bsearch144.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
861.0ms1880×body640valid
363.0ms4155×body80valid
240.0ms914×body320valid
186.0ms575×body1280valid
84.0ms477×body160valid