Details

Time bar (total: 50.8s)

sample65.0ms

Algorithm
intervals
Results
31.0ms137×body80valid
14.0ms54×body1280valid
10.0ms35×body640valid
3.0ms20×body320valid
1.0ms10×body160valid

simplify48.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
48.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize30.0ms

Local error

Found 3 expressions with local error:

3.1b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b
(/ (+ x 1) (- x 1))
0.0b
(/ x (+ x 1))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
110×*-un-lft-identity
60×times-frac
57×add-sqr-sqrt
25×add-cube-cbrt
20×distribute-lft-out
18×distribute-lft-out--
14×difference-of-squares
11×associate-/r*
7×add-cbrt-cube add-exp-log associate-/l*
5×difference-of-sqr-1 add-log-exp
4×associate-/r/
3×pow1 insert-posit16
2×cbrt-undiv clear-num frac-2neg flip3-+ flip3-- div-exp flip-+ div-inv flip-- associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 117
Calls
3 calls:
Slowest
63.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
20.0ms
(/ (+ x 1) (- x 1))
8.0ms
(/ x (+ x 1))

series149.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
102.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
24.0ms
(/ (+ x 1) (- x 1))
23.0ms
(/ x (+ x 1))

simplify8.4s

Counts
175 → 126
Calls
175 calls:
Slowest
476.0ms
(* (- x 1) (+ (* x x) (- (* 1 1) (* x 1))))
394.0ms
(* (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1)))
359.0ms
(+ (* (/ x (+ x 1)) (/ x (+ x 1))) (+ (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (* (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
352.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
350.0ms
(/ (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (- x 1) (- x 1)) (- x 1)))

prune987.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

19.4b
(- (/ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ (+ x 1) (- x 1)))
0.2b
(cbrt (+ x 1))
0.2b
(cbrt (+ x 1))
0.2b
(cbrt (+ x 1))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
35×*-un-lft-identity
25×times-frac
16×cbrt-prod
10×difference-of-squares
7×add-cube-cbrt distribute-lft-out--
6×cbrt-div add-log-exp
5×distribute-lft-out
4×pow1 add-cbrt-cube add-exp-log insert-posit16
3×flip3-+ pow1/3 flip-+
1×sub-neg flip3-- diff-log frac-sub flip--
Counts
4 → 74
Calls
4 calls:
Slowest
110.0ms
(- (/ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ (+ x 1) (- x 1)))
3.0ms
(cbrt (+ x 1))
3.0ms
(cbrt (+ x 1))
3.0ms
(cbrt (+ x 1))

series248.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
113.0ms
(- (/ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ (+ x 1) (- x 1)))
47.0ms
(cbrt (+ x 1))
44.0ms
(cbrt (+ x 1))
43.0ms
(cbrt (+ x 1))

simplify8.1s

Counts
114 → 86
Calls
114 calls:
Slowest
393.0ms
(+ (* (/ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1)))) (+ (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (* (/ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ (+ x 1) (- x 1)))))
306.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
300.0ms
(- (* (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (- x 1)) (* (cbrt (+ x 1)) (+ x 1)))
269.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
250.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))

prune709.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

19.4b
(- (/ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ (+ x 1) (- x 1)))
19.4b
(- (/ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ (+ x 1) (- x 1)))
0.2b
(cbrt (+ x 1))
0.2b
(cbrt (+ x 1))

rewrite328.0ms

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt
54×*-un-lft-identity
50×times-frac
20×difference-of-squares
16×cbrt-prod
14×distribute-lft-out--
8×add-log-exp
6×add-cube-cbrt distribute-lft-out
4×pow1 cbrt-div add-cbrt-cube add-exp-log insert-posit16
2×sub-neg flip3-+ flip3-- pow1/3 diff-log frac-sub flip-+ flip--
Counts
4 → 88
Calls
4 calls:
Slowest
168.0ms
(- (/ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ (+ x 1) (- x 1)))
147.0ms
(- (/ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ (+ x 1) (- x 1)))
5.0ms
(cbrt (+ x 1))
5.0ms
(cbrt (+ x 1))

series318.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
107.0ms
(- (/ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ (+ x 1) (- x 1)))
105.0ms
(- (/ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ (+ x 1) (- x 1)))
64.0ms
(cbrt (+ x 1))
42.0ms
(cbrt (+ x 1))

simplify12.9s

Counts
136 → 100
Calls
136 calls:
Slowest
456.0ms
(+ (/ (sqrt (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (sqrt (+ x 1)))) (/ (sqrt (+ x 1)) (sqrt (- x 1))))
454.0ms
(+ (* (/ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1)))) (+ (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (* (/ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ (+ x 1) (- x 1)))))
355.0ms
(+ (* (/ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1)))) (+ (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (* (/ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ (+ x 1) (- x 1)))))
348.0ms
(- (* (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (- x 1)) (* (cbrt (+ x 1)) (+ x 1)))
324.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))

prune1.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

5.6b
(- (/ (/ -3 x) (* x x)) (- (/ 1 (* x x)) (/ -3 x)))
0.5b
(/ 1 (* x x))
0.1b
(/ (/ -3 x) (* x x))
0.0b
(- (/ 1 (* x x)) (/ -3 x))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
47×times-frac
40×add-sqr-sqrt
35×*-un-lft-identity
27×add-exp-log
21×add-cbrt-cube
20×add-cube-cbrt
16×associate-/l*
12×pow1
11×add-log-exp
10×div-exp
9×difference-of-squares
8×cbrt-undiv div-inv distribute-lft-out--
6×pow-flip
5×prod-exp frac-sub
4×diff-log insert-posit16
3×sub-neg flip3-- cbrt-unprod flip--
2×rec-exp clear-num associate-/r* frac-2neg distribute-rgt-out-- 1-exp associate--r+
1×pow2 pow-plus pow-prod-down pow-sqr pow-prod-up inv-pow associate--r- associate-/l/
Counts
4 → 130
Calls
4 calls:
Slowest
67.0ms
(- (/ (/ -3 x) (* x x)) (- (/ 1 (* x x)) (/ -3 x)))
24.0ms
(- (/ 1 (* x x)) (/ -3 x))
11.0ms
(/ 1 (* x x))
10.0ms
(/ (/ -3 x) (* x x))

series189.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
64.0ms
(/ (/ -3 x) (* x x))
57.0ms
(- (/ 1 (* x x)) (/ -3 x))
35.0ms
(/ 1 (* x x))
33.0ms
(- (/ (/ -3 x) (* x x)) (- (/ 1 (* x x)) (/ -3 x)))

simplify13.1s

Counts
176 → 142
Calls
176 calls:
Slowest
783.0ms
(* (* (- (/ (/ -3 x) (* x x)) (- (/ 1 (* x x)) (/ -3 x))) (- (/ (/ -3 x) (* x x)) (- (/ 1 (* x x)) (/ -3 x)))) (- (/ (/ -3 x) (* x x)) (- (/ 1 (* x x)) (/ -3 x))))
625.0ms
(* (* (/ 1 (* x x)) (/ 1 (* x x))) (/ 1 (* x x)))
455.0ms
(+ (* (/ 1 (* x x)) (/ 1 (* x x))) (+ (* (/ -3 x) (/ -3 x)) (* (/ 1 (* x x)) (/ -3 x))))
418.0ms
(- (* (/ -3 x) (* (* x x) x)) (* (* x x) (- (* 1 x) (* (* x x) -3))))
417.0ms
(/ (* (* 1 1) 1) (* (* (* x x) (* x x)) (* x x)))

prune1.0s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.6b

bsearch122.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
824.0ms1693×body1280valid
720.0ms4120×body80valid
535.0ms1261×body640valid
143.0ms617×body320valid
52.0ms309×body160valid