Details

Time bar (total: 2.7m)

sample44.0ms

Algorithm
intervals
Results
14.0ms49×body1280valid
10.0ms39×body640valid
8.0ms138×body80valid
4.0ms21×body320valid
1.0ms9×body160valid

simplify309.0ms

Counts
1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize13.0ms

Local error

Found 3 expressions with local error:

2.7b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b
(/ (+ x 1) (- x 1))
0.0b
(/ x (+ x 1))

rewrite163.0ms

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
71.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
36.0ms
(/ (+ x 1) (- x 1))
17.0ms
(/ x (+ x 1))

series197.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
111.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
46.0ms
(/ x (+ x 1))
40.0ms
(/ (+ x 1) (- x 1))

simplify1.1s

Counts
762 → 762

prune9.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

28.5b
(fma x (/ 1 (+ x 1)) (- (* (cbrt (/ (+ x 1) (- x 1))) (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))))))
1.9b
(fma (- (cbrt (/ (+ x 1) (- x 1)))) (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))) (* (cbrt (/ (+ x 1) (- x 1))) (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1))))))
0.0b
(* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1))))
0.0b
(* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1))))

rewrite188.0ms

Algorithm
rewrite-expression-head
Rules
624×*-un-lft-identity
448×cbrt-prod
388×add-sqr-sqrt times-frac
150×swap-sqr
132×add-cube-cbrt
116×distribute-lft-out
104×difference-of-squares
74×associate-*r* associate-*l*
64×difference-of-sqr-1 distribute-lft-out--
18×pow1 unswap-sqr
16×associate-/r/
12×pow1/3
8×cbrt-div flip3-- add-exp-log div-inv flip--
4×expm1-log1p-u add-cbrt-cube pow-prod-down pow-sqr pow-prod-up insert-posit16 log1p-expm1-u add-log-exp
2×pow2 frac-times pow-plus associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod fma-udef
Counts
4 → 386
Calls
4 calls:
Slowest
89.0ms
(* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1))))
81.0ms
(* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1))))
0.0ms
(fma x (/ 1 (+ x 1)) (- (* (cbrt (/ (+ x 1) (- x 1))) (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))))))
0.0ms
(fma (- (cbrt (/ (+ x 1) (- x 1)))) (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))) (* (cbrt (/ (+ x 1) (- x 1))) (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1))))))

series936.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
526.0ms
(fma (- (cbrt (/ (+ x 1) (- x 1)))) (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))) (* (cbrt (/ (+ x 1) (- x 1))) (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1))))))
149.0ms
(fma x (/ 1 (+ x 1)) (- (* (cbrt (/ (+ x 1) (- x 1))) (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))))))
141.0ms
(* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1))))
120.0ms
(* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1))))

simplify2.0s

Counts
398 → 398

prune5.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 3 expressions with local error:

14.8b
(/ (- (* x x) (* 1 1)) (* (- x 1) (- x 1)))
2.7b
(- (/ x (+ x 1)) (/ (- (* x x) (* 1 1)) (* (- x 1) (- x 1))))
0.0b
(/ x (+ x 1))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
298×*-un-lft-identity
296×times-frac
288×prod-diff
196×add-sqr-sqrt
188×associate-/r/
186×add-cube-cbrt
116×flip3-- flip--
76×frac-times
55×distribute-lft-out
38×associate-*l/ associate-*r/
37×div-inv
24×difference-of-squares
18×flip3-+ fma-neg flip-+
10×add-cbrt-cube add-exp-log
7×associate-/l*
5×associate-/r* add-log-exp
3×expm1-log1p-u pow1 cbrt-undiv div-exp insert-posit16 log1p-expm1-u
2×clear-num frac-2neg div-sub associate-/l/
1×sub-neg diff-log prod-exp frac-sub cbrt-unprod distribute-lft-out-- associate--r-
Counts
3 → 401
Calls
3 calls:
Slowest
77.0ms
(- (/ x (+ x 1)) (/ (- (* x x) (* 1 1)) (* (- x 1) (- x 1))))
42.0ms
(/ (- (* x x) (* 1 1)) (* (- x 1) (- x 1)))
8.0ms
(/ x (+ x 1))

series226.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
113.0ms
(- (/ x (+ x 1)) (/ (- (* x x) (* 1 1)) (* (- x 1) (- x 1))))
61.0ms
(/ (- (* x x) (* 1 1)) (* (- x 1) (- x 1)))
52.0ms
(/ x (+ x 1))

simplify855.0ms

Counts
410 → 410

prune4.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize83.0ms

Local error

Found 4 expressions with local error:

30.9b
(fma (- (+ (* x x) (+ (* 1 1) (* x 1)))) (/ (- (* x x) (* 1 1)) (* (- (pow x 3) (pow 1 3)) (- x 1))) (* (+ (* x x) (+ (* 1 1) (* x 1))) (/ (- (* x x) (* 1 1)) (* (- (pow x 3) (pow 1 3)) (- x 1)))))
28.1b
(fma (/ (* (cbrt x) (cbrt x)) 1) (/ (cbrt x) (+ x 1)) (- (* (+ (* x x) (+ (* 1 1) (* x 1))) (/ (- (* x x) (* 1 1)) (* (- (pow x 3) (pow 1 3)) (- x 1))))))
22.1b
(/ (- (* x x) (* 1 1)) (* (- (pow x 3) (pow 1 3)) (- x 1)))
22.1b
(/ (- (* x x) (* 1 1)) (* (- (pow x 3) (pow 1 3)) (- x 1)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
16×associate-/r/
14×flip3-- add-cbrt-cube add-exp-log flip--
8×add-sqr-sqrt frac-times *-un-lft-identity times-frac add-cube-cbrt associate-/l*
4×expm1-log1p-u pow1 cbrt-undiv div-exp associate-*l/ associate-*r/ insert-posit16 log1p-expm1-u add-log-exp difference-of-squares associate-/l/
2×clear-num associate-/r* frac-2neg div-sub prod-exp cbrt-unprod fma-udef div-inv
Counts
4 → 96
Calls
4 calls:
Slowest
40.0ms
(/ (- (* x x) (* 1 1)) (* (- (pow x 3) (pow 1 3)) (- x 1)))
32.0ms
(/ (- (* x x) (* 1 1)) (* (- (pow x 3) (pow 1 3)) (- x 1)))
0.0ms
(fma (- (+ (* x x) (+ (* 1 1) (* x 1)))) (/ (- (* x x) (* 1 1)) (* (- (pow x 3) (pow 1 3)) (- x 1))) (* (+ (* x x) (+ (* 1 1) (* x 1))) (/ (- (* x x) (* 1 1)) (* (- (pow x 3) (pow 1 3)) (- x 1)))))
0.0ms
(fma (/ (* (cbrt x) (cbrt x)) 1) (/ (cbrt x) (+ x 1)) (- (* (+ (* x x) (+ (* 1 1) (* x 1))) (/ (- (* x x) (* 1 1)) (* (- (pow x 3) (pow 1 3)) (- x 1))))))

series928.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
433.0ms
(fma (- (+ (* x x) (+ (* 1 1) (* x 1)))) (/ (- (* x x) (* 1 1)) (* (- (pow x 3) (pow 1 3)) (- x 1))) (* (+ (* x x) (+ (* 1 1) (* x 1))) (/ (- (* x x) (* 1 1)) (* (- (pow x 3) (pow 1 3)) (- x 1)))))
281.0ms
(fma (/ (* (cbrt x) (cbrt x)) 1) (/ (cbrt x) (+ x 1)) (- (* (+ (* x x) (+ (* 1 1) (* x 1))) (/ (- (* x x) (* 1 1)) (* (- (pow x 3) (pow 1 3)) (- x 1))))))
111.0ms
(/ (- (* x x) (* 1 1)) (* (- (pow x 3) (pow 1 3)) (- x 1)))
103.0ms
(/ (- (* x x) (* 1 1)) (* (- (pow x 3) (pow 1 3)) (- x 1)))

simplify2.7s

Counts
108 → 108

prune2.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes83.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.6b

bsearch2.1m

end0.0ms

sample2.0s

Algorithm
intervals
Results
875.0ms1746×body1280valid
367.0ms1217×body640valid
348.0ms4041×body80valid
202.0ms667×body320valid
81.0ms329×body160valid