Details

Time bar (total: 34.8s)

sample34.0ms

Algorithm
intervals
Results
12.0ms60×body640valid
7.0ms132×body80valid
6.0ms42×body320valid
2.0ms22×body160valid

simplify20.0ms

Calls
1 calls:
Slowest
20.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize25.0ms

Local error

Found 3 expressions with local error:

3.5b
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
0.0b
(/ 1 (+ x 1))
0.0b
(/ 1 (- x 1))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
36×prod-diff
32×associate-/r/
22×*-un-lft-identity
20×add-sqr-sqrt
19×div-inv
18×add-cube-cbrt
9×flip-+ flip--
8×flip3-+ flip3--
6×associate-/r* fma-neg
5×pow1 add-exp-log distribute-lft-out-- add-log-exp
3×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
2×rec-exp clear-num frac-2neg pow-flip inv-pow
1×sub-neg diff-log frac-sub difference-of-squares
Calls
3 calls:
Slowest
16.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
2.0ms
(/ 1 (- x 1))
2.0ms
(/ 1 (+ x 1))

series118.0ms

Calls
3 calls:
Slowest
87.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
17.0ms
(/ 1 (+ x 1))
14.0ms
(/ 1 (- x 1))

simplify14.5s

Calls
108 calls:
Slowest
754.0ms
(fma (/ 1 (- (* x x) (* 1 1))) (- x 1) (- (* (+ x 1) (/ 1 (- (* x x) (* 1 1))))))
578.0ms
(fma (- (+ x 1)) (/ 1 (- (* x x) (* 1 1))) (* (+ x 1) (/ 1 (- (* x x) (* 1 1)))))
574.0ms
(fma (- (+ x 1)) (/ 1 (- (* x x) (* 1 1))) (* (+ x 1) (/ 1 (- (* x x) (* 1 1)))))
566.0ms
(fma (- (+ x 1)) (/ 1 (- (* x x) (* 1 1))) (* (+ x 1) (/ 1 (- (* x x) (* 1 1)))))
539.0ms
(fma (- (+ x 1)) (/ 1 (- (* x x) (* 1 1))) (* (+ x 1) (/ 1 (- (* x x) (* 1 1)))))

prune895.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ -2 (fma x (+ x -1) (+ x -1)))
0.0b
(fma x (+ x -1) (+ x -1))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt associate-/r* *-un-lft-identity add-cube-cbrt
2×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
1×clear-num frac-2neg fma-udef div-inv
Calls
2 calls:
Slowest
1.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))
0.0ms
(fma x (+ x -1) (+ x -1))

series219.0ms

Calls
2 calls:
Slowest
137.0ms
(fma x (+ x -1) (+ x -1))
82.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))

simplify1.1s

Calls
9 calls:
Slowest
389.0ms
(- (+ (* 2 (/ 1 (pow x 4))) (+ (* 2 (/ 1 (pow x 6))) (* 2 (/ 1 (pow x 2))))))
345.0ms
(- (+ (* 2 (/ 1 (pow x 4))) (+ (* 2 (/ 1 (pow x 6))) (* 2 (/ 1 (pow x 2))))))
109.0ms
(+ (* 2 (pow x 2)) (+ (* 2 (pow x 4)) 2))
66.0ms
(cbrt (fma x (+ x -1) (+ x -1)))
56.0ms
(sqrt (fma x (+ x -1) (+ x -1)))

prune267.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

15.0b
(cbrt (fma x (+ x -1) (+ x -1)))
15.0b
(cbrt (fma x (+ x -1) (+ x -1)))
15.0b
(cbrt (fma x (+ x -1) (+ x -1)))
0.2b
(* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×pow1
7×pow1/3
6×associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
11.0ms
(* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1))))
1.0ms
(cbrt (fma x (+ x -1) (+ x -1)))
1.0ms
(cbrt (fma x (+ x -1) (+ x -1)))
1.0ms
(cbrt (fma x (+ x -1) (+ x -1)))

series728.0ms

Calls
4 calls:
Slowest
205.0ms
(cbrt (fma x (+ x -1) (+ x -1)))
186.0ms
(cbrt (fma x (+ x -1) (+ x -1)))
178.0ms
(cbrt (fma x (+ x -1) (+ x -1)))
159.0ms
(* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1))))

simplify7.3s

Calls
41 calls:
Slowest
355.0ms
(+ (log (cbrt (fma x (+ x -1) (+ x -1)))) (log (cbrt (fma x (+ x -1) (+ x -1)))))
341.0ms
(* (fma x (+ x -1) (+ x -1)) (fma x (+ x -1) (+ x -1)))
328.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
324.0ms
(cbrt (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))))
322.0ms
(cbrt (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))))

prune954.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

10.0b
(cbrt (* (* (/ -2 (fma x (+ x -1) (+ x -1))) (/ -2 (fma x (+ x -1) (+ x -1)))) (/ -2 (fma x (+ x -1) (+ x -1)))))
0.1b
(/ -2 (fma x (+ x -1) (+ x -1)))
0.1b
(/ -2 (fma x (+ x -1) (+ x -1)))
0.1b
(/ -2 (fma x (+ x -1) (+ x -1)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
9×associate-/r*
7×add-sqr-sqrt cbrt-div *-un-lft-identity add-cube-cbrt
5×frac-times associate-*l/
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*r/ div-inv
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Calls
4 calls:
Slowest
14.0ms
(cbrt (* (* (/ -2 (fma x (+ x -1) (+ x -1))) (/ -2 (fma x (+ x -1) (+ x -1)))) (/ -2 (fma x (+ x -1) (+ x -1)))))
1.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))
1.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))
1.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))

series371.0ms

Calls
4 calls:
Slowest
146.0ms
(cbrt (* (* (/ -2 (fma x (+ x -1) (+ x -1))) (/ -2 (fma x (+ x -1) (+ x -1)))) (/ -2 (fma x (+ x -1) (+ x -1)))))
83.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))
74.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))
68.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))

simplify5.9s

Calls
29 calls:
Slowest
875.0ms
(cbrt (* (* (/ -2 (fma x (+ x -1) (+ x -1))) (/ -2 (fma x (+ x -1) (+ x -1)))) -2))
450.0ms
(cbrt (* (* (/ -2 (fma x (+ x -1) (+ x -1))) -2) (/ -2 (fma x (+ x -1) (+ x -1)))))
396.0ms
(cbrt (* (/ -2 (fma x (+ x -1) (+ x -1))) (/ -2 (fma x (+ x -1) (+ x -1)))))
365.0ms
(- (+ (* 2 (/ 1 (pow x 4))) (+ (* 2 (/ 1 (pow x 6))) (* 2 (/ 1 (pow x 2))))))
351.0ms
(cbrt (* (* -2 (/ -2 (fma x (+ x -1) (+ x -1)))) -2))

prune683.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes23.0ms

Accuracy

0% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch1.0ms

end0.0ms

sample1.6s

Algorithm
intervals
Results
723.0ms1991×body640valid
377.0ms4184×body80valid
326.0ms1215×body320valid
86.0ms610×body160valid