Details

Time bar (total: 7.7m)

sample38.0ms

Algorithm
intervals
Results
12.0ms49×body1280valid
9.0ms47×body640valid
7.0ms127×body80valid
3.0ms22×body320valid
1.0ms11×body160valid

simplify83.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
83.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize13.0ms

Local error

Found 3 expressions with local error:

3.3b
(- (/ 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
65.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
34.0ms
(/ (+ x 1) (- x 1))
14.0ms
(/ x (+ x 1))

series209.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
138.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
38.0ms
(/ (+ x 1) (- x 1))
33.0ms
(/ x (+ x 1))

simplify5.7m

Counts
1423 → 762
Calls
1423 calls:
Slowest
894.0ms
(fma (/ 1 (sqrt (+ x 1))) (/ x (sqrt (+ x 1))) (- (* (/ (+ x 1) (cbrt (- x 1))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))))))
877.0ms
(fma (/ (* (cbrt x) (cbrt x)) 1) (/ (cbrt x) (+ x 1)) (- (* (/ (cbrt (+ x 1)) (sqrt (- x 1))) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (sqrt (- x 1))))))
872.0ms
(fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (* (sqrt (/ (+ x 1) (- x 1))) (sqrt (/ (+ x 1) (- x 1))))))
872.0ms
(fma (- (/ (+ x 1) (sqrt (- x 1)))) (/ 1 (sqrt (- x 1))) (* (/ (+ x 1) (sqrt (- x 1))) (/ 1 (sqrt (- x 1)))))
826.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))

prune5.9s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

3.2b
(fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (cbrt x) (cbrt (+ x 1))) (- (/ (+ x 1) (- x 1))))
0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 53
Calls
4 calls:
Slowest
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (cbrt x) (cbrt (+ x 1))) (- (/ (+ x 1) (- x 1))))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
317.0ms
(fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (cbrt x) (cbrt (+ x 1))) (- (/ (+ x 1) (- x 1))))
274.0ms
(cbrt x)
263.0ms
(cbrt x)
257.0ms
(cbrt x)

simplify4.2s

Counts
71 → 65
Calls
71 calls:
Slowest
546.0ms
(* (* (fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (cbrt x) (cbrt (+ x 1))) (- (/ (+ x 1) (- x 1)))) (fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (cbrt x) (cbrt (+ x 1))) (- (/ (+ x 1) (- x 1))))) (fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (cbrt x) (cbrt (+ x 1))) (- (/ (+ x 1) (- x 1)))))
295.0ms
(real->posit16 (fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (cbrt x) (cbrt (+ x 1))) (- (/ (+ x 1) (- x 1)))))
284.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
281.0ms
(exp (fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (cbrt x) (cbrt (+ x 1))) (- (/ (+ x 1) (- x 1)))))
252.0ms
(log1p (fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (cbrt x) (cbrt (+ x 1))) (- (/ (+ x 1) (- x 1)))))

prune801.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

5.8b
(+ (- (/ -3 x) (/ 1 (* x x))) (/ (/ -3 x) (* x x)))
0.3b
(/ 1 (* x x))
0.1b
(/ (/ -3 x) (* x x))
0.0b
(- (/ -3 x) (/ 1 (* x x)))

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
265×times-frac
204×add-sqr-sqrt
199×*-un-lft-identity
182×prod-diff
178×add-cube-cbrt
93×associate-+l+
51×div-inv
27×add-exp-log
21×add-cbrt-cube
16×associate-/l*
13×fma-neg
12×pow1 fma-def difference-of-squares
11×add-log-exp
10×div-exp
8×cbrt-undiv
6×pow-flip distribute-lft-out--
5×prod-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u distribute-lft-out
3×distribute-rgt-out-- frac-add cbrt-unprod
2×rec-exp clear-num associate-/r* sum-log sub-neg frac-2neg flip3-- diff-log 1-exp frac-sub flip--
1×pow2 +-commutative flip3-+ pow-plus pow-prod-down pow-sqr pow-prod-up associate-+l- flip-+ inv-pow associate-/l/
Counts
4 → 341
Calls
4 calls:
Slowest
136.0ms
(+ (- (/ -3 x) (/ 1 (* x x))) (/ (/ -3 x) (* x x)))
18.0ms
(/ 1 (* x x))
16.0ms
(- (/ -3 x) (/ 1 (* x x)))
15.0ms
(/ (/ -3 x) (* x x))

series154.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
53.0ms
(- (/ -3 x) (/ 1 (* x x)))
46.0ms
(/ (/ -3 x) (* x x))
37.0ms
(+ (- (/ -3 x) (/ 1 (* x x))) (/ (/ -3 x) (* x x)))
17.0ms
(/ 1 (* x x))

simplify52.4s

Counts
462 → 353
Calls
462 calls:
Slowest
753.0ms
(+ (fma (- (cbrt (/ 1 (* x x)))) (* (cbrt (/ 1 (* x x))) (cbrt (/ 1 (* x x)))) (* (cbrt (/ 1 (* x x))) (* (cbrt (/ 1 (* x x))) (cbrt (/ 1 (* x x)))))) (/ (/ -3 x) (* x x)))
700.0ms
(* (* (/ 1 (* x x)) (/ 1 (* x x))) (/ 1 (* x x)))
429.0ms
(/ (* (* 1 1) 1) (* (* (* x x) (* x x)) (* x x)))
411.0ms
(+ (* (- (* (/ -3 x) (/ -3 x)) (* (/ 1 (* x x)) (/ 1 (* x x)))) (* x x)) (* (+ (/ -3 x) (/ 1 (* x x))) (/ -3 x)))
398.0ms
(* (* (/ (/ -3 x) (* x x)) (/ (/ -3 x) (* x x))) (/ (/ -3 x) (* x x)))

prune1.7s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 3 expressions with local error:

5.8b
(+ (* (/ 1 x) (- -3 (/ 1 x))) (/ (/ -3 x) (* x x)))
0.2b
(* (/ 1 x) (- -3 (/ 1 x)))
0.1b
(/ (/ -3 x) (* x x))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
175×add-sqr-sqrt
167×*-un-lft-identity
161×add-cube-cbrt
156×prod-diff
153×times-frac
82×distribute-rgt-in associate-+l+ distribute-lft-in
24×add-exp-log
20×add-cbrt-cube
17×div-inv
13×associate-*l* associate-/l*
8×div-exp associate-*r*
7×cbrt-undiv
6×prod-exp
5×pow1 frac-add add-log-exp
4×frac-times sub-neg flip3-- associate-*r/ cbrt-unprod flip--
3×expm1-log1p-u insert-posit16 log1p-expm1-u difference-of-squares unswap-sqr
2×associate-*l/ distribute-lft-out--
1×+-commutative rec-exp clear-num associate-/r* sum-log fma-def frac-2neg flip3-+ 1-exp pow-prod-down *-commutative flip-+ distribute-lft-out associate-/l/
Counts
3 → 281
Calls
3 calls:
Slowest
31.0ms
(* (/ 1 x) (- -3 (/ 1 x)))
22.0ms
(+ (* (/ 1 x) (- -3 (/ 1 x))) (/ (/ -3 x) (* x x)))
9.0ms
(/ (/ -3 x) (* x x))

series134.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
62.0ms
(* (/ 1 x) (- -3 (/ 1 x)))
45.0ms
(/ (/ -3 x) (* x x))
27.0ms
(+ (* (/ 1 x) (- -3 (/ 1 x))) (/ (/ -3 x) (* x x)))

simplify50.3s

Counts
395 → 290
Calls
395 calls:
Slowest
535.0ms
(* (* (* (/ 1 x) (/ 1 x)) (/ 1 x)) (* (* (- -3 (/ 1 x)) (- -3 (/ 1 x))) (- -3 (/ 1 x))))
508.0ms
(* (* (* (/ 1 x) (- -3 (/ 1 x))) (* (/ 1 x) (- -3 (/ 1 x)))) (* (/ 1 x) (- -3 (/ 1 x))))
487.0ms
(* (fma (* (cbrt -3) (cbrt -3)) (cbrt -3) (- (* (/ 1 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))) (/ 1 x))
453.0ms
(+ (* (fma (- (sqrt (/ 1 x))) (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt (/ 1 x)))) (/ 1 x)) (/ (/ -3 x) (* x x)))
373.0ms
(+ (* (* (/ 1 x) (- (* -3 -3) (* (/ 1 x) (/ 1 x)))) (* x x)) (* (+ -3 (/ 1 x)) (/ -3 x)))

prune1.3s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes30.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.1b

bsearch112.0ms

end0.0ms

sample1.6s

Algorithm
intervals
Results
496.0ms1693×body1280valid
394.0ms656×body320valid
297.0ms1225×body640valid
263.0ms4133×body80valid
45.0ms293×body160valid