Details

Time bar (total: 5.7m)

sample40.0ms

Algorithm
intervals
Results
15.0ms59×body1280valid
8.0ms41×body640valid
7.0ms126×body80valid
3.0ms18×body320valid
1.0ms12×body160valid

simplify85.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
85.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize14.0ms

Local error

Found 3 expressions with local error:

3.4b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b
(/ x (+ x 1))
0.0b
(/ (+ x 1) (- x 1))

rewrite168.0ms

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
98.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
24.0ms
(/ (+ x 1) (- x 1))
16.0ms
(/ x (+ x 1))

series169.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
115.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
28.0ms
(/ (+ x 1) (- x 1))
26.0ms
(/ x (+ x 1))

simplify5.3m

Counts
1382 → 762
Calls
1382 calls:
Slowest
849.0ms
(fma (/ (* (cbrt x) (cbrt x)) 1) (/ (cbrt x) (+ x 1)) (- (* (/ (+ x 1) (cbrt (- x 1))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))))))
839.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
797.0ms
(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ x (cbrt (+ x 1))) (- (* (/ (+ x 1) (cbrt (- x 1))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))))))
787.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
776.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))

prune4.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

5.2b
(fma 3 (+ (/ -1 x) (/ (/ -1 x) (* x x))) (/ -1 (* x x)))
0.5b
(/ -1 (* x x))
0.1b
(/ (/ -1 x) (* x x))
0.0b
(+ (/ -1 x) (/ (/ -1 x) (* x x)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
43×times-frac
29×*-un-lft-identity
27×add-sqr-sqrt add-cube-cbrt
21×add-cbrt-cube add-exp-log
16×associate-/l*
13×fma-def
8×cbrt-undiv div-exp
6×add-log-exp
5×div-inv
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×prod-exp cbrt-unprod
2×clear-num associate-/r* frac-2neg
1×+-commutative sum-log flip3-+ frac-add flip-+ fma-udef distribute-lft-out associate-/l/
Counts
4 → 113
Calls
4 calls:
Slowest
14.0ms
(+ (/ -1 x) (/ (/ -1 x) (* x x)))
10.0ms
(/ -1 (* x x))
9.0ms
(/ (/ -1 x) (* x x))
0.0ms
(fma 3 (+ (/ -1 x) (/ (/ -1 x) (* x x))) (/ -1 (* x x)))

series148.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
53.0ms
(+ (/ -1 x) (/ (/ -1 x) (* x x)))
35.0ms
(/ (/ -1 x) (* x x))
31.0ms
(fma 3 (+ (/ -1 x) (/ (/ -1 x) (* x x))) (/ -1 (* x x)))
30.0ms
(/ -1 (* x x))

simplify3.2s

Counts
84 → 125
Calls
84 calls:
Slowest
422.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
277.0ms
(/ (* (* -1 -1) -1) (* (* (* x x) x) (* (* x x) x)))
242.0ms
(/ (* (* -1 -1) -1) (* (* (* x x) (* x x)) (* x x)))
168.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
167.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))

prune602.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

21.6b
(cbrt (* (* (/ -1 (* x x)) (/ -1 (* x x))) (/ -1 (* x x))))
5.2b
(fma 3 (+ (/ -1 x) (/ (/ -1 x) (* x x))) (cbrt (* (* (/ -1 (* x x)) (/ -1 (* x x))) (/ -1 (* x x)))))
0.5b
(/ -1 (* x x))
0.5b
(/ -1 (* x x))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
14×add-cbrt-cube add-exp-log
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×cbrt-div
6×times-frac associate-/l*
5×frac-times associate-*l/
4×expm1-log1p-u pow1 cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r/
2×clear-num associate-/r* frac-2neg prod-exp cbrt-unprod div-inv
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube fma-udef
Counts
4 → 79
Calls
4 calls:
Slowest
73.0ms
(cbrt (* (* (/ -1 (* x x)) (/ -1 (* x x))) (/ -1 (* x x))))
6.0ms
(/ -1 (* x x))
6.0ms
(/ -1 (* x x))
0.0ms
(fma 3 (+ (/ -1 x) (/ (/ -1 x) (* x x))) (cbrt (* (* (/ -1 (* x x)) (/ -1 (* x x))) (/ -1 (* x x)))))

series144.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
51.0ms
(cbrt (* (* (/ -1 (* x x)) (/ -1 (* x x))) (/ -1 (* x x))))
38.0ms
(fma 3 (+ (/ -1 x) (/ (/ -1 x) (* x x))) (cbrt (* (* (/ -1 (* x x)) (/ -1 (* x x))) (/ -1 (* x x)))))
30.0ms
(/ -1 (* x x))
25.0ms
(/ -1 (* x x))

simplify2.8s

Counts
44 → 91
Calls
44 calls:
Slowest
283.0ms
(/ (* (* -1 -1) -1) (* (* (* x x) x) (* (* x x) x)))
276.0ms
(/ (* (* -1 -1) -1) (* (* (* x x) x) (* (* x x) x)))
263.0ms
(cbrt (* (* (/ -1 (* x x)) (/ -1 (* x x))) -1))
248.0ms
(cbrt (* (* (/ -1 (* x x)) -1) (/ -1 (* x x))))
245.0ms
(/ (* (* -1 -1) -1) (* (* (* x x) (* x x)) (* x x)))

prune543.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

5.0b
(- (/ (cbrt -1) (* x x)) (fma (/ 3 x) (/ 1 (* x x)) (/ 3 x)))
0.5b
(/ (cbrt -1) (* x x))
0.5b
(/ 1 (* x x))
0.1b
(fma (/ 3 x) (/ 1 (* x x)) (/ 3 x))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
35×times-frac
34×*-un-lft-identity
32×add-cube-cbrt
30×prod-diff
20×add-exp-log
19×cbrt-prod
12×pow1 add-cbrt-cube
10×fma-neg
9×associate-/l*
6×div-exp div-inv pow-flip add-log-exp
4×expm1-log1p-u cbrt-undiv prod-exp insert-posit16 log1p-expm1-u
3×difference-of-squares
2×rec-exp clear-num associate-/r* frac-2neg 1-exp cbrt-unprod fma-udef
1×pow2 sub-neg pow-plus flip3-- diff-log pow-prod-down pow-sqr pow-prod-up flip-- associate--r+ distribute-lft-out-- inv-pow
Counts
4 → 136
Calls
4 calls:
Slowest
24.0ms
(- (/ (cbrt -1) (* x x)) (fma (/ 3 x) (/ 1 (* x x)) (/ 3 x)))
9.0ms
(/ 1 (* x x))
7.0ms
(/ (cbrt -1) (* x x))
0.0ms
(fma (/ 3 x) (/ 1 (* x x)) (/ 3 x))

series204.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
87.0ms
(fma (/ 3 x) (/ 1 (* x x)) (/ 3 x))
50.0ms
(/ (cbrt -1) (* x x))
43.0ms
(- (/ (cbrt -1) (* x x)) (fma (/ 3 x) (/ 1 (* x x)) (/ 3 x)))
23.0ms
(/ 1 (* x x))

simplify13.9s

Counts
131 → 148
Calls
131 calls:
Slowest
417.0ms
(- (/ (cbrt -1) (pow x 2)) (+ (* 3 (/ 1 (pow x 3))) (* 3 (/ 1 x))))
334.0ms
(fma (sqrt (/ (cbrt -1) (* x x))) (sqrt (/ (cbrt -1) (* x x))) (- (* (sqrt (fma (/ 3 x) (/ 1 (* x x)) (/ 3 x))) (sqrt (fma (/ 3 x) (/ 1 (* x x)) (/ 3 x))))))
236.0ms
(+ (* 3 (/ 1 (pow x 3))) (* 3 (/ 1 x)))
234.0ms
(/ (* (* 1 1) 1) (* (* (* x x) (* x x)) (* x x)))
234.0ms
(+ (* 3 (/ 1 (pow x 3))) (* 3 (/ 1 x)))

prune827.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes32.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.5b

bsearch110.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
606.0ms1707×body1280valid
302.0ms1255×body640valid
229.0ms4101×body80valid
91.0ms603×body320valid
33.0ms334×body160valid