Details

Time bar (total: 6.0m)

sample101.0ms

Algorithm
intervals
Results
54.0ms51×body640valid
19.0ms43×body1280valid
11.0ms133×body80valid
5.0ms21×body320valid
1.0ms8×body160valid

simplify42.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
41.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize16.0ms

Local error

Found 3 expressions with local error:

1.9b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b
(/ (+ x 1) (- x 1))
0.0b
(/ x (+ x 1))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
1284×*-un-lft-identity
984×times-frac
841×add-sqr-sqrt
612×prod-diff
521×add-cube-cbrt
251×distribute-lft-out
158×difference-of-squares
110×associate-/r/
90×distribute-lft-out--
77×difference-of-sqr-1
55×div-inv
37×flip3-+ flip-+
20×flip3-- flip--
18×fma-neg
11×associate-/r*
7×add-cbrt-cube add-exp-log associate-/l*
5×add-log-exp
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
2×cbrt-undiv clear-num frac-2neg div-exp associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 753
Calls
3 calls:
Slowest
83.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
20.0ms
(/ (+ x 1) (- x 1))
7.0ms
(/ x (+ x 1))

series205.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
124.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
43.0ms
(/ (+ x 1) (- x 1))
38.0ms
(/ x (+ x 1))

simplify5.2m

Counts
1382 → 762
Calls
1382 calls:
Slowest
844.0ms
(fma (/ (sqrt x) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (sqrt x) (cbrt (+ x 1))) (- (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1))))))
797.0ms
(fma (/ (sqrt x) 1) (/ (sqrt x) (+ x 1)) (- (* (/ (+ x 1) (cbrt (- x 1))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))))))
794.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
757.0ms
(fma (- (/ (+ x 1) (sqrt (- x 1)))) (/ 1 (sqrt (- x 1))) (* (/ (+ x 1) (sqrt (- x 1))) (/ 1 (sqrt (- x 1)))))
755.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))

prune4.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

1.9b
(- (/ x (+ x 1)) (* (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))) (cbrt (/ (+ x 1) (- x 1)))))
0.0b
(cbrt (/ (+ x 1) (- x 1)))
0.0b
(cbrt (/ (+ x 1) (- x 1)))
0.0b
(cbrt (/ (+ x 1) (- x 1)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
146×*-un-lft-identity
108×times-frac
104×add-sqr-sqrt
102×cbrt-prod
56×add-cube-cbrt
27×distribute-lft-out
24×difference-of-squares
18×fma-neg prod-diff
15×cbrt-div
12×difference-of-sqr-1 distribute-lft-out--
10×associate-/r/
7×frac-sub
6×add-log-exp
5×frac-times associate-*l/ div-inv
4×expm1-log1p-u pow1 flip3-- add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u flip--
3×pow1/3 associate-*r/
2×flip3-+ flip-+
1×sub-neg diff-log
Counts
4 → 196
Calls
4 calls:
Slowest
45.0ms
(- (/ x (+ x 1)) (* (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))) (cbrt (/ (+ x 1) (- x 1)))))
5.0ms
(cbrt (/ (+ x 1) (- x 1)))
5.0ms
(cbrt (/ (+ x 1) (- x 1)))
5.0ms
(cbrt (/ (+ x 1) (- x 1)))

series361.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
108.0ms
(- (/ x (+ x 1)) (* (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))) (cbrt (/ (+ x 1) (- x 1)))))
87.0ms
(cbrt (/ (+ x 1) (- x 1)))
84.0ms
(cbrt (/ (+ x 1) (- x 1)))
83.0ms
(cbrt (/ (+ x 1) (- x 1)))

simplify10.9s

Counts
184 → 208
Calls
184 calls:
Slowest
333.0ms
(* (+ x 1) (* (* (cbrt (- x 1)) (cbrt (- x 1))) (cbrt (- x 1))))
252.0ms
(cbrt (/ (+ x 1) (- (pow x 3) (pow 1 3))))
250.0ms
(cbrt (/ (+ x 1) (- (pow x 3) (pow 1 3))))
248.0ms
(cbrt (/ (+ x 1) (- (pow x 3) (pow 1 3))))
227.0ms
(fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (cbrt x) (cbrt (+ x 1))) (- (* (cbrt (/ (+ x 1) (- x 1))) (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))))))

prune1.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

17.7b
(- (* x (- x 1)) (* (+ x 1) (+ x 1)))
0.0b
(/ (- (* x (- x 1)) (* (+ x 1) (+ x 1))) (* (+ x 1) (- x 1)))
0.0b
(* (+ x 1) (+ x 1))
0.0b
(* x (- x 1))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
53×*-un-lft-identity
46×associate-*r/
44×add-sqr-sqrt
37×prod-diff
36×add-cube-cbrt
33×flip3-+ flip-+
32×frac-sub
24×distribute-rgt-in frac-times distribute-lft-in
22×flip3-- associate--l+ flip--
18×associate-/l/
13×pow1 add-cbrt-cube add-exp-log
12×associate-*l/
11×associate-*r*
8×associate-/r/
7×associate-*l*
6×swap-sqr distribute-lft-out add-log-exp
5×sub-neg
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×times-frac prod-exp cbrt-unprod associate-/l*
2×cbrt-undiv div-exp pow-prod-down *-commutative associate--r+ difference-of-squares unswap-sqr
1×pow2 clear-num associate-/r* frac-2neg pow-plus fma-neg diff-log difference-of-sqr-1 div-sub pow-sqr pow-prod-up div-inv distribute-lft-out--
Counts
4 → 200
Calls
4 calls:
Slowest
40.0ms
(/ (- (* x (- x 1)) (* (+ x 1) (+ x 1))) (* (+ x 1) (- x 1)))
21.0ms
(* (+ x 1) (+ x 1))
16.0ms
(- (* x (- x 1)) (* (+ x 1) (+ x 1)))
16.0ms
(* x (- x 1))

series138.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
49.0ms
(/ (- (* x (- x 1)) (* (+ x 1) (+ x 1))) (* (+ x 1) (- x 1)))
39.0ms
(- (* x (- x 1)) (* (+ x 1) (+ x 1)))
38.0ms
(* x (- x 1))
12.0ms
(* (+ x 1) (+ x 1))

simplify20.7s

Counts
191 → 212
Calls
191 calls:
Slowest
652.0ms
(- (* (* x (- (* x x) (* 1 1))) (* (- x 1) (- x 1))) (* (+ x 1) (* (- (* x x) (* 1 1)) (- (* x x) (* 1 1)))))
640.0ms
(fma (- (+ x 1)) (+ x 1) (* (+ x 1) (+ x 1)))
514.0ms
(* (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (+ x 1) (+ x 1)) (+ x 1)))
457.0ms
(/ (* x (- x 1)) (* (+ x 1) (- x 1)))
446.0ms
(* (+ (pow x 3) (pow 1 3)) (- (* x x) (* 1 1)))

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

15.1b
(/ (fma -3 x -1) (* (+ x 1) (- x 1)))
0.1b
(fma -3 x -1)
0.0b
(* (+ x 1) (- x 1))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
24×*-un-lft-identity
19×add-cube-cbrt
18×prod-diff
11×distribute-rgt-in distribute-lft-in
10×add-cbrt-cube add-exp-log
8×frac-times associate-/r/
7×associate-*r*
6×flip3-+ flip3-- flip-+ flip--
5×pow1
4×associate-*l* associate-*l/ associate-*r/
3×expm1-log1p-u times-frac insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×cbrt-undiv sub-neg div-exp prod-exp cbrt-unprod difference-of-squares
1×clear-num associate-/r* frac-2neg difference-of-sqr-1 pow-prod-down *-commutative fma-udef div-inv distribute-lft-out distribute-lft-out-- unswap-sqr
Counts
3 → 99
Calls
3 calls:
Slowest
23.0ms
(* (+ x 1) (- x 1))
12.0ms
(/ (fma -3 x -1) (* (+ x 1) (- x 1)))
0.0ms
(fma -3 x -1)

series156.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
79.0ms
(* (+ x 1) (- x 1))
43.0ms
(/ (fma -3 x -1) (* (+ x 1) (- x 1)))
34.0ms
(fma -3 x -1)

simplify5.7s

Counts
78 → 108
Calls
78 calls:
Slowest
521.0ms
(* (+ (pow x 3) (pow 1 3)) (- (pow x 3) (pow 1 3)))
440.0ms
(* (+ (pow x 3) (pow 1 3)) (- (* x x) (* 1 1)))
306.0ms
(* (- (* x x) (* 1 1)) (- (pow x 3) (pow 1 3)))
278.0ms
(* (+ (* x x) (- (* 1 1) (* x 1))) (+ (* x x) (+ (* 1 1) (* x 1))))
278.0ms
(* (+ (* x x) (- (* 1 1) (* x 1))) (+ (* x x) (+ (* 1 1) (* x 1))))

prune625.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes28.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.8b

bsearch113.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
841.0ms1687×body1280valid
376.0ms1260×body640valid
317.0ms4101×body80valid
128.0ms637×body320valid
36.0ms315×body160valid