Details

Time bar (total: 4.9m)

sample47.0ms

Algorithm
intervals
Results
19.0ms66×body640valid
9.0ms129×body80valid
7.0ms41×body320valid
3.0ms20×body160valid

simplify33.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
33.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.4b

localize28.0ms

Local error

Found 3 expressions with local error:

3.3b
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
0.0b
(/ 1 (+ x 1))
0.0b
(/ 1 (- x 1))

rewrite138.0ms

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
84.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
17.0ms
(/ 1 (+ x 1))
16.0ms
(/ 1 (- x 1))

series123.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
73.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
26.0ms
(/ 1 (+ x 1))
24.0ms
(/ 1 (- x 1))

simplify3.8m

Counts
1178 → 647
Calls
1178 calls:
Slowest
863.0ms
(fma (* (cbrt (/ 1 (+ x 1))) (cbrt (/ 1 (+ x 1)))) (cbrt (/ 1 (+ x 1))) (- (* (/ (cbrt 1) (- (sqrt x) (sqrt 1))) (/ (* (cbrt 1) (cbrt 1)) (+ (sqrt x) (sqrt 1))))))
842.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (+ x 1))) (/ (cbrt 1) (sqrt (+ x 1))) (- (* (/ (cbrt 1) (- (sqrt x) (sqrt 1))) (/ (* (cbrt 1) (cbrt 1)) (+ (sqrt x) (sqrt 1))))))
791.0ms
(fma (- (/ (sqrt 1) (- (sqrt x) (sqrt 1)))) (/ (sqrt 1) (+ (sqrt x) (sqrt 1))) (* (/ (sqrt 1) (- (sqrt x) (sqrt 1))) (/ (sqrt 1) (+ (sqrt x) (sqrt 1)))))
768.0ms
(fma (/ 1 1) (/ 1 (+ x 1)) (- (* (/ (sqrt 1) (- (sqrt x) 1)) (/ (sqrt 1) (+ (sqrt x) 1)))))
712.0ms
(fma (/ (sqrt 1) 1) (/ (sqrt 1) (+ x 1)) (- (* (/ (sqrt 1) (- (sqrt x) 1)) (/ (sqrt 1) (+ (sqrt x) 1)))))

prune4.8s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 1 expressions with local error:

0.3b
(/ -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)))

series92.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
92.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))

simplify12.2s

Counts
43 → 33
Calls
43 calls:
Slowest
940.0ms
(/ (* (* -2 -2) -2) (* (* (fma x (+ x -1) (+ x -1)) (fma x (+ x -1) (+ x -1))) (fma x (+ x -1) (+ x -1))))
430.0ms
(real->posit16 (/ -2 (fma x (+ x -1) (+ x -1))))
411.0ms
(- (fma x (+ x -1) (+ x -1)))
402.0ms
(/ 1 (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))))
368.0ms
(/ (sqrt -2) (sqrt (fma x (+ x -1) (+ x -1))))

prune231.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

14.3b
(cbrt (fma x (+ x -1) (+ x -1)))
14.3b
(cbrt (fma x (+ x -1) (+ x -1)))
14.3b
(cbrt (fma x (+ x -1) (+ x -1)))
0.2b
(* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 85
Calls
4 calls:
Slowest
8.0ms
(* (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)))

series745.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
196.0ms
(cbrt (fma x (+ x -1) (+ x -1)))
191.0ms
(cbrt (fma x (+ x -1) (+ x -1)))
181.0ms
(cbrt (fma x (+ x -1) (+ x -1)))
175.0ms
(* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1))))

simplify28.9s

Counts
111 → 97
Calls
111 calls:
Slowest
674.0ms
(sqrt (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))))
529.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
512.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
469.0ms
(- 1 (+ (* 2/3 (pow x 2)) (* 1/9 (pow x 4))))
447.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))

prune1.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

14.3b
(cbrt (fma x (+ x -1) (+ x -1)))
14.3b
(cbrt (fma x (+ x -1) (+ x -1)))
14.3b
(cbrt (fma x (+ x -1) (+ x -1)))
14.3b
(cbrt (fma x (+ x -1) (+ x -1)))

rewrite6.0ms

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)))

series714.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
190.0ms
(cbrt (fma x (+ x -1) (+ x -1)))
178.0ms
(cbrt (fma x (+ x -1) (+ x -1)))
176.0ms
(cbrt (fma x (+ x -1) (+ x -1)))
169.0ms
(cbrt (fma x (+ x -1) (+ x -1)))

simplify17.3s

Counts
76 → 68
Calls
76 calls:
Slowest
490.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
476.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
460.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
439.0ms
(cbrt (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))))
420.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))

prune967.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes29.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
830.0ms4242×body80valid
624.0ms1855×body640valid
357.0ms1308×body320valid
122.0ms595×body160valid