Details

Time bar (total: 4.3m)

sample61.0ms

Algorithm
intervals
Results
22.0ms56×body640valid
14.0ms146×body80valid
12.0ms40×body320valid
3.0ms14×body160valid

simplify15.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
15.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize21.0ms

Local error

Found 3 expressions with local error:

2.8b
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
0.0b
(/ 1 (- x 1))
0.0b
(/ 1 (+ x 1))

rewrite126.0ms

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
77.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
8.0ms
(/ 1 (- x 1))
8.0ms
(/ 1 (+ x 1))

series111.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
81.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
15.0ms
(/ 1 (- x 1))
14.0ms
(/ 1 (+ x 1))

simplify3.6m

Counts
1141 → 647
Calls
1141 calls:
Slowest
829.0ms
(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ 1 (cbrt (+ x 1))) (- (* (+ x 1) (/ 1 (- (* x x) (* 1 1))))))
711.0ms
(fma (- (/ (sqrt 1) (cbrt (- x 1)))) (/ (sqrt 1) (* (cbrt (- x 1)) (cbrt (- x 1)))) (* (/ (sqrt 1) (cbrt (- x 1))) (/ (sqrt 1) (* (cbrt (- x 1)) (cbrt (- x 1))))))
695.0ms
(fma 1 (/ 1 (+ x 1)) (- (* (/ (sqrt 1) (- (sqrt x) 1)) (/ (sqrt 1) (+ (sqrt x) 1)))))
659.0ms
(fma (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1))) (- (* (/ (cbrt 1) (- (sqrt x) 1)) (/ (* (cbrt 1) (cbrt 1)) (+ (sqrt x) 1)))))
638.0ms
(fma (- (+ x 1)) (/ 1 (- (* x x) (* 1 1))) (* (+ x 1) (/ 1 (- (* x x) (* 1 1)))))

prune3.3s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
3×associate-/r* add-cbrt-cube add-exp-log associate-/l*
1×expm1-log1p-u pow1 cbrt-undiv clear-num frac-2neg div-exp insert-posit16 log1p-expm1-u div-inv add-log-exp
Counts
1 → 30
Calls
1 calls:
Slowest
4.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))

series66.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
65.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))

simplify4.6s

Counts
28 → 33
Calls
28 calls:
Slowest
602.0ms
(/ (* (* -2 -2) -2) (* (* (fma x (+ x -1) (+ x -1)) (fma x (+ x -1) (+ x -1))) (fma x (+ x -1) (+ x -1))))
267.0ms
(/ (* (cbrt -2) (cbrt -2)) (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))))
250.0ms
(/ (sqrt -2) (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))))
245.0ms
(/ (sqrt -2) (sqrt (fma x (+ x -1) (+ x -1))))
244.0ms
(/ 1 (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))))

prune161.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

8.9b
(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)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
27×times-frac
10×add-cbrt-cube add-exp-log
9×associate-/r* associate-/l*
7×cbrt-div
5×frac-times associate-*l/
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv clear-num frac-2neg div-exp associate-*r/ div-inv
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Counts
4 → 110
Calls
4 calls:
Slowest
21.0ms
(cbrt (* (* (/ -2 (fma x (+ x -1) (+ x -1))) (/ -2 (fma x (+ x -1) (+ x -1)))) (/ -2 (fma x (+ x -1) (+ x -1)))))
7.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))
3.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))
3.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))

series298.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
109.0ms
(cbrt (* (* (/ -2 (fma x (+ x -1) (+ x -1))) (/ -2 (fma x (+ x -1) (+ x -1)))) (/ -2 (fma x (+ x -1) (+ x -1)))))
65.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))
64.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))
60.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))

simplify16.6s

Counts
95 → 122
Calls
95 calls:
Slowest
621.0ms
(/ (* (* -2 -2) -2) (* (* (fma x (+ x -1) (+ x -1)) (fma x (+ x -1) (+ x -1))) (fma x (+ x -1) (+ x -1))))
609.0ms
(/ (* (* -2 -2) -2) (* (* (fma x (+ x -1) (+ x -1)) (fma x (+ x -1) (+ x -1))) (fma x (+ x -1) (+ x -1))))
603.0ms
(/ (* (* -2 -2) -2) (* (* (fma x (+ x -1) (+ x -1)) (fma x (+ x -1) (+ x -1))) (fma x (+ x -1) (+ x -1))))
492.0ms
(/ (sqrt -2) (sqrt (fma x (+ x -1) (+ x -1))))
367.0ms
(cbrt (* (* (/ -2 (fma x (+ x -1) (+ x -1))) (/ -2 (fma x (+ x -1) (+ x -1)))) -2))

prune723.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

14.7b
(cbrt (fma x (+ x -1) (+ x -1)))
14.4b
(cbrt (* (* (/ -2 (fma x (+ x -1) (+ x -1))) (/ -2 (fma x (+ x -1) (+ x -1)))) -2))
0.1b
(/ -2 (fma x (+ x -1) (+ x -1)))
0.1b
(/ -2 (fma x (+ x -1) (+ x -1)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac
8×add-cbrt-cube add-exp-log
6×associate-/r* associate-/l*
4×cbrt-prod expm1-log1p-u pow1 associate-*l/ insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-div
2×cbrt-undiv clear-num frac-2neg pow1/3 div-exp div-inv
1×frac-times associate-*r/
Counts
4 → 89
Calls
4 calls:
Slowest
21.0ms
(cbrt (* (* (/ -2 (fma x (+ x -1) (+ x -1))) (/ -2 (fma x (+ x -1) (+ x -1)))) -2))
4.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))
4.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))
1.0ms
(cbrt (fma x (+ x -1) (+ x -1)))

series444.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
186.0ms
(cbrt (* (* (/ -2 (fma x (+ x -1) (+ x -1))) (/ -2 (fma x (+ x -1) (+ x -1)))) -2))
136.0ms
(cbrt (fma x (+ x -1) (+ x -1)))
62.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))
60.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))

simplify12.0s

Counts
69 → 101
Calls
69 calls:
Slowest
607.0ms
(/ (* (* -2 -2) -2) (* (* (fma x (+ x -1) (+ x -1)) (fma x (+ x -1) (+ x -1))) (fma x (+ x -1) (+ x -1))))
603.0ms
(/ (* (* -2 -2) -2) (* (* (fma x (+ x -1) (+ x -1)) (fma x (+ x -1) (+ x -1))) (fma x (+ x -1) (+ x -1))))
424.0ms
(- (+ (* 2 (/ 1 (pow x 4))) (+ (* 2 (/ 1 (pow x 6))) (* 2 (/ 1 (pow x 2))))))
299.0ms
(+ (cbrt -8) (+ (* 5/9 (* (cbrt -8) (pow x 4))) (* 2/3 (* (cbrt -8) (pow x 2)))))
297.0ms
(cbrt (* (/ -2 (fma x (+ x -1) (+ x -1))) (/ -2 (fma x (+ x -1) (+ x -1)))))

prune699.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes22.0ms

Accuracy

0% (0.4b remaining)

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

bsearch1.0ms

end0.0ms

sample1.2s

Algorithm
intervals
Results
538.0ms1917×body640valid
302.0ms4248×body80valid
220.0ms1209×body320valid
70.0ms626×body160valid