Details

Time bar (total: 4.0m)

sample58.0ms

Algorithm
intervals
Results
28.0ms66×body640valid
11.0ms140×body80valid
7.0ms33×body320valid
2.0ms17×body160valid

simplify21.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
21.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize27.0ms

Local error

Found 2 expressions with local error:

2.2b
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
0.0b
(/ 1 (+ x 1))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
825×*-un-lft-identity
762×times-frac
681×add-sqr-sqrt
486×prod-diff
441×add-cube-cbrt
117×difference-of-squares
96×associate-/r/
94×distribute-lft-out
77×distribute-lft-out--
54×difference-of-sqr-1
51×div-inv
30×flip-+
29×flip3-+
20×flip--
19×flip3--
18×fma-neg
6×add-exp-log
4×associate-/r* add-cbrt-cube add-log-exp
3×pow1 associate-/l*
2×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u
1×cbrt-undiv rec-exp clear-num sub-neg frac-2neg diff-log 1-exp frac-sub pow-flip inv-pow
Counts
2 → 586
Calls
2 calls:
Slowest
93.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
8.0ms
(/ 1 (+ x 1))

series105.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
81.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
24.0ms
(/ 1 (+ x 1))

simplify3.4m

Counts
1081 → 592
Calls
1081 calls:
Slowest
870.0ms
(fma (- (+ x 1)) (/ 1 (- (* x x) (* 1 1))) (* (+ x 1) (/ 1 (- (* x x) (* 1 1)))))
748.0ms
(fma (/ 1 (- (* x x) (* 1 1))) (- x 1) (- (* (+ x 1) (/ 1 (- (* x x) (* 1 1))))))
736.0ms
(fma (/ (sqrt 1) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (sqrt 1) (cbrt (+ x 1))) (- (* (/ (cbrt 1) (cbrt (- x 1))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (- x 1)) (cbrt (- x 1)))))))
709.0ms
(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)))))
661.0ms
(fma (/ 1 (+ (pow x 3) (pow 1 3))) (+ (* x x) (- (* 1 1) (* x 1))) (- (* (/ (cbrt 1) (- (sqrt x) 1)) (/ (* (cbrt 1) (cbrt 1)) (+ (sqrt x) 1)))))

prune4.5s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

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))

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
8.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))
0.0ms
(fma x (+ x -1) (+ x -1))

series236.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
137.0ms
(fma x (+ x -1) (+ x -1))
99.0ms
(/ -2 (fma x (+ x -1) (+ x -1)))

simplify6.7s

Counts
31 → 47
Calls
31 calls:
Slowest
1.2s
(/ (* (* -2 -2) -2) (* (* (fma x (+ x -1) (+ x -1)) (fma x (+ x -1) (+ x -1))) (fma x (+ x -1) (+ x -1))))
415.0ms
(/ (cbrt -2) (cbrt (fma x (+ x -1) (+ x -1))))
381.0ms
(/ 1 (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))))
357.0ms
(/ (* (cbrt -2) (cbrt -2)) (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))))
355.0ms
(/ (sqrt -2) (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))))

prune328.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

14.5b
(cbrt (fma x (+ x -1) (+ x -1)))
14.5b
(cbrt (fma x (+ x -1) (+ x -1)))
14.5b
(cbrt (fma x (+ x -1) (+ x -1)))
0.4b
(/ 1 (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))))

rewrite26.0ms

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
23.0ms
(/ 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)))

series738.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
204.0ms
(cbrt (fma x (+ x -1) (+ x -1)))
184.0ms
(/ 1 (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))))
178.0ms
(cbrt (fma x (+ x -1) (+ x -1)))
171.0ms
(cbrt (fma x (+ x -1) (+ x -1)))

simplify8.7s

Counts
45 → 92
Calls
45 calls:
Slowest
410.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
400.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
386.0ms
(- (log 1) (log (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1))))))
367.0ms
(cbrt (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))))
352.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

14.5b
(cbrt (fma x (+ x -1) (+ x -1)))
14.5b
(cbrt (fma x (+ x -1) (+ x -1)))
14.5b
(cbrt (fma x (+ x -1) (+ x -1)))
14.5b
(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)))

series793.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
234.0ms
(cbrt (fma x (+ x -1) (+ x -1)))
206.0ms
(cbrt (fma x (+ x -1) (+ x -1)))
195.0ms
(cbrt (fma x (+ x -1) (+ x -1)))
158.0ms
(cbrt (fma x (+ x -1) (+ x -1)))

simplify5.8s

Counts
24 → 68
Calls
24 calls:
Slowest
417.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
408.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
398.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
368.0ms
(cbrt (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))))
363.0ms
(cbrt (* (cbrt (fma x (+ x -1) (+ x -1))) (cbrt (fma x (+ x -1) (+ x -1)))))

prune892.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes60.0ms

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
1.0s1949×body640valid
393.0ms4138×body80valid
346.0ms1278×body320valid
96.0ms635×body160valid