Details

Time bar (total: 4.2m)

sample36.0ms

Algorithm
intervals
Results
13.0ms65×body640valid
9.0ms136×body80valid
6.0ms37×body320valid
2.0ms18×body160valid

simplify20.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
850×*-un-lft-identity
783×times-frac
710×add-sqr-sqrt
486×prod-diff
454×add-cube-cbrt
125×difference-of-squares
98×associate-/r/
94×distribute-lft-out
81×distribute-lft-out--
58×difference-of-sqr-1
52×div-inv
30×flip-+
29×flip3-+
21×flip--
20×flip3--
18×fma-neg
11×associate-/r* add-exp-log
7×add-cbrt-cube
6×associate-/l*
5×pow1 add-log-exp
4×div-exp
3×expm1-log1p-u insert-posit16 log1p-expm1-u
2×cbrt-undiv rec-exp clear-num frac-2neg 1-exp pow-flip inv-pow
1×sub-neg diff-log frac-sub
Counts
3 → 638
Calls
3 calls:
Slowest
70.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
16.0ms
(/ 1 (+ x 1))
10.0ms
(/ 1 (- x 1))

series117.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
80.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
20.0ms
(/ 1 (+ x 1))
18.0ms
(/ 1 (- x 1))

simplify3.6m

Counts
1141 → 647
Calls
1141 calls:
Slowest
899.0ms
(fma (/ 1 (- (* x x) (* 1 1))) (- x 1) (- (* (/ (cbrt 1) (cbrt (- x 1))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (- x 1)) (cbrt (- x 1)))))))
799.0ms
(fma (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1))) (- (* (/ 1 (- (sqrt x) (sqrt 1))) (/ 1 (+ (sqrt x) (sqrt 1))))))
772.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (+ x 1)) (- (* (/ 1 (- (sqrt x) 1)) (/ 1 (+ (sqrt x) 1)))))
771.0ms
(fma (/ (sqrt 1) (sqrt (+ x 1))) (/ (sqrt 1) (sqrt (+ x 1))) (- (* (+ (* x x) (+ (* 1 1) (* x 1))) (/ 1 (- (pow x 3) (pow 1 3))))))
675.0ms
(fma (- (+ (* x x) (+ (* 1 1) (* x 1)))) (/ 1 (- (pow x 3) (pow 1 3))) (* (+ (* x x) (+ (* 1 1) (* x 1))) (/ 1 (- (pow x 3) (pow 1 3)))))

prune4.9s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 2 expressions with local error:

1.0b
(/ -2 (fma x (+ x -1) (+ x -1)))
0.0b
(fma x (+ x -1) (+ x -1))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log
3×associate-/r* associate-/l*
2×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Counts
2 → 41
Calls
2 calls:
Slowest
7.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))
0.0ms
(fma x (+ x -1) (+ x -1))

series231.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
135.0ms
(fma x (+ x -1) (+ x -1))
97.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))

simplify6.6s

Counts
31 → 47
Calls
31 calls:
Slowest
788.0ms
(/ (* (* -2 -2) -2) (* (* (fma x (+ x -1) (+ x -1)) (fma x (+ x -1) (+ x -1))) (fma x (+ x -1) (+ x -1))))
444.0ms
(/ (* (cbrt -2) (cbrt -2)) (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))))
390.0ms
(/ (sqrt -2) (sqrt (fma x (+ x -1) (+ x -1))))
380.0ms
(/ 1 (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))))
364.0ms
(/ (sqrt -2) (cbrt (fma x (+ x -1) (+ x -1))))

prune283.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

15.5b
(cbrt (fma x (+ x -1) (+ x -1)))
15.5b
(cbrt (fma x (+ x -1) (+ x -1)))
15.5b
(cbrt (fma x (+ x -1) (+ x -1)))
0.4b
(/ 1 (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
15×add-exp-log
12×pow1
9×cbrt-prod add-sqr-sqrt *-un-lft-identity pow1/3 add-cube-cbrt pow-flip
7×add-cbrt-cube
4×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u add-log-exp
3×times-frac prod-exp associate-/l*
2×cbrt-undiv rec-exp 1-exp pow-prod-down pow-sqr pow-prod-up
1×pow2 clear-num associate-/r* frac-2neg pow-plus cbrt-unprod div-inv inv-pow
Counts
4 → 80
Calls
4 calls:
Slowest
17.0ms
(/ 1 (* (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)))

series716.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
191.0ms
(/ 1 (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))))
186.0ms
(cbrt (fma x (+ x -1) (+ x -1)))
181.0ms
(cbrt (fma x (+ x -1) (+ x -1)))
158.0ms
(cbrt (fma x (+ x -1) (+ x -1)))

simplify10.1s

Counts
45 → 92
Calls
45 calls:
Slowest
656.0ms
(/ (* (* 1 1) 1) (* (fma x (+ x -1) (+ x -1)) (fma x (+ x -1) (+ x -1))))
516.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
473.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
456.0ms
(- (log 1) (+ (log (cbrt (fma x (+ x -1) (+ x -1)))) (log (cbrt (fma x (+ x -1) (+ x -1))))))
441.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))

prune971.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

15.5b
(cbrt (fma x (+ x -1) (+ x -1)))
15.5b
(cbrt (fma x (+ x -1) (+ x -1)))
15.5b
(cbrt (fma x (+ x -1) (+ x -1)))
15.5b
(cbrt (fma x (+ x -1) (+ x -1)))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube pow1/3 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 56
Calls
4 calls:
Slowest
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)))
1.0ms
(cbrt (fma x (+ x -1) (+ x -1)))

series810.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
224.0ms
(cbrt (fma x (+ x -1) (+ x -1)))
210.0ms
(cbrt (fma x (+ x -1) (+ x -1)))
195.0ms
(cbrt (fma x (+ x -1) (+ x -1)))
180.0ms
(cbrt (fma x (+ x -1) (+ x -1)))

simplify6.4s

Counts
24 → 68
Calls
24 calls:
Slowest
510.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
469.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
444.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
436.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
358.0ms
(cbrt (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))))

prune884.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes46.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch2.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
795.0ms4200×body80valid
704.0ms1938×body640valid
290.0ms1231×body320valid
90.0ms631×body160valid