Details

Time bar (total: 3.5m)

sample98.0ms

Algorithm
intervals
Results
40.0ms77×body640valid
16.0ms118×body80valid
14.0ms21×body1280valid
12.0ms30×body320valid
3.0ms11×body160valid

simplify105.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
104.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

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))

rewrite319.0ms

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
228.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
46.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
14.0ms
(/ 1 (+ x 1))
10.0ms
(/ 1 (- x 1))

series195.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
123.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
41.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
17.0ms
(/ 1 (- x 1))
14.0ms
(/ 1 (+ x 1))

simplify2.1m

Counts
879 → 660
Calls
879 calls:
Slowest
807.0ms
(fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x)))))
727.0ms
(fma (/ (sqrt 1) (sqrt (+ x 1))) (/ (sqrt 1) (sqrt (+ x 1))) (- (* (/ (cbrt 2) x) (/ (* (cbrt 2) (cbrt 2)) 1))))
586.0ms
(fma (/ (sqrt 1) 1) (/ (sqrt 1) (+ x 1)) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
574.0ms
(* (* (+ x 1) x) (- x 1))
564.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (+ x 1)) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))

prune3.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize54.0ms

Local error

Found 4 expressions with local error:

60.5b
(fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x)))))
2.2b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (+ (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))
1.0b
(cbrt 2)
1.0b
(cbrt 2)

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
353×*-un-lft-identity
329×times-frac
254×add-sqr-sqrt
237×add-cube-cbrt
236×associate-+l+
234×prod-diff
55×distribute-lft-out
38×div-inv
26×associate-/r/
17×flip3-+ flip-+
16×add-log-exp
13×fma-def
10×distribute-lft-out--
6×cbrt-prod sum-log frac-add difference-of-squares
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
2×flip3-- pow1/3 diff-log frac-sub flip--
1×+-commutative associate-+r+ sub-neg associate-+l- fma-udef
Counts
4 → 322
Calls
4 calls:
Slowest
158.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (+ (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))
1.0ms
(cbrt 2)
1.0ms
(cbrt 2)
0.0ms
(fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x)))))

series1.2s

Counts
4 → 8
Calls
4 calls:
Slowest
871.0ms
(fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x)))))
315.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (+ (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))
0.0ms
(cbrt 2)
0.0ms
(cbrt 2)

simplify41.6s

Counts
287 → 330
Calls
287 calls:
Slowest
553.0ms
(+ (* (- (* 1 x) (* (+ x 1) 2)) (+ (* (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x)))))) (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1)))))) (* (* (+ x 1) x) (+ (pow (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) 3) (pow (/ 1 (- x 1)) 3))))
542.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (+ (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))
504.0ms
(fma 1 (/ 1 (+ x 1)) (- (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))))
446.0ms
(* (+ (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (+ (* (/ 2 x) (/ 2 x)) (* (/ 1 (+ x 1)) (/ 2 x)))) (+ (* (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x)))))) (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))))
406.0ms
(+ (* (- (pow (/ 1 (+ x 1)) 3) (pow (/ 2 x) 3)) (- (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1)))) (* (+ (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (+ (* (/ 2 x) (/ 2 x)) (* (/ 1 (+ x 1)) (/ 2 x)))) (- (* (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x)))))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))))

prune3.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize28.0ms

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
29.0ms
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))
9.0ms
(/ (/ 2 x) (* x x))
5.0ms
(/ 2 (pow x 7))
5.0ms
(/ 2 (pow x 5))

series298.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
132.0ms
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))
69.0ms
(/ 2 (pow x 7))
57.0ms
(/ 2 (pow x 5))
40.0ms
(/ (/ 2 x) (* x x))

simplify8.1s

Counts
187 → 190
Calls
187 calls:
Slowest
245.0ms
(/ (* (* 2 2) 2) (* (* (pow x 7) (pow x 7)) (pow x 7)))
240.0ms
(/ (* (* 2 2) 2) (* (* (pow x 5) (pow x 5)) (pow x 5)))
186.0ms
(* (exp (/ (/ 2 x) (* x x))) (exp (/ 2 (pow x 5))))
176.0ms
(/ (* (cbrt 2) (cbrt 2)) (* (cbrt (pow x 5)) (cbrt (pow x 5))))
174.0ms
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

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))

rewrite34.0ms

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
11.0ms
(/ (/ (/ 2 x) x) x)
7.0ms
(/ (/ 2 x) x)
5.0ms
(/ 2 (pow x 7))
5.0ms
(/ 2 (pow x 5))

series192.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
66.0ms
(/ 2 (pow x 7))
54.0ms
(/ 2 (pow x 5))
38.0ms
(/ (/ (/ 2 x) x) x)
33.0ms
(/ (/ 2 x) x)

simplify19.8s

Counts
526 → 376
Calls
526 calls:
Slowest
435.0ms
(/ (/ (* (* 2 2) 2) (* (* x x) x)) (* (* x x) x))
270.0ms
(/ (* (* (/ (/ 2 x) x) (/ (/ 2 x) x)) (/ (/ 2 x) x)) (* (* x x) x))
256.0ms
(/ (/ (/ (* (cbrt 2) (cbrt 2)) (sqrt x)) (* (cbrt x) (cbrt x))) (sqrt x))
243.0ms
(/ (/ (/ (* (cbrt 2) (cbrt 2)) 1) (* (cbrt x) (cbrt x))) (sqrt x))
242.0ms
(/ (* (* 2 2) 2) (* (* (pow x 7) (pow x 7)) (pow x 7)))

prune2.6s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes94.0ms

Accuracy

97.9% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 19.4b

bsearch14.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
917.0ms1870×body640valid
293.0ms4138×body80valid
225.0ms568×body1280valid
210.0ms952×body320valid
82.0ms473×body160valid