Details

Time bar (total: 1.2m)

sample15.0ms

Algorithm
intervals
Results
10.0ms256×body80valid

simplify9.0ms

Calls
1 calls:
Slowest
8.0ms
(/ x (+ (* x x) 1))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize6.0ms

Local error

Found 1 expressions with local error:

14.5b
(/ x (fma x 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
Calls
1 calls:
Slowest
4.0ms
(/ x (fma x x 1))

series66.0ms

Calls
1 calls:
Slowest
66.0ms
(/ x (fma x x 1))

simplify1.2s

Calls
28 calls:
Slowest
262.0ms
(- (+ x (pow x 5)) (pow x 3))
190.0ms
(/ (* (* x x) x) (* (* (fma x x 1) (fma x x 1)) (fma x x 1)))
188.0ms
(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
187.0ms
(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
62.0ms
(/ (* (cbrt x) (cbrt x)) (* (cbrt (fma x x 1)) (cbrt (fma x x 1))))

prune216.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

14.4b
(sqrt (fma x x 1))
14.4b
(sqrt (fma x x 1))
0.0b
(/ (/ x (sqrt (fma x x 1))) (sqrt (fma x x 1)))
0.0b
(/ x (sqrt (fma x x 1)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
160×add-sqr-sqrt
158×*-un-lft-identity add-cube-cbrt
150×sqrt-prod
25×associate-/l*
12×associate-/r*
11×add-cbrt-cube add-exp-log
9×div-inv
6×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
1×associate-/l/
Calls
4 calls:
Slowest
13.0ms
(/ (/ x (sqrt (fma x x 1))) (sqrt (fma x x 1)))
5.0ms
(/ x (sqrt (fma x x 1)))
1.0ms
(sqrt (fma x x 1))
1.0ms
(sqrt (fma x x 1))

series310.0ms

Calls
4 calls:
Slowest
128.0ms
(/ x (sqrt (fma x x 1)))
67.0ms
(sqrt (fma x x 1))
64.0ms
(/ (/ x (sqrt (fma x x 1))) (sqrt (fma x x 1)))
51.0ms
(sqrt (fma x x 1))

simplify15.9s

Calls
362 calls:
Slowest
834.0ms
(/ (/ (* (* x x) x) (* (* (sqrt (fma x x 1)) (sqrt (fma x x 1))) (sqrt (fma x x 1)))) (* (* (sqrt (fma x x 1)) (sqrt (fma x x 1))) (sqrt (fma x x 1))))
398.0ms
(/ (* (* x x) x) (* (* (sqrt (fma x x 1)) (sqrt (fma x x 1))) (sqrt (fma x x 1))))
324.0ms
(/ (* (* (/ x (sqrt (fma x x 1))) (/ x (sqrt (fma x x 1)))) (/ x (sqrt (fma x x 1)))) (* (* (sqrt (fma x x 1)) (sqrt (fma x x 1))) (sqrt (fma x x 1))))
254.0ms
(- (+ x (pow x 5)) (pow x 3))
236.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))

prune2.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 1 expressions with local error:

14.5b
(/ x (fma x 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
Calls
1 calls:
Slowest
4.0ms
(/ x (fma x x 1))

series80.0ms

Calls
1 calls:
Slowest
80.0ms
(/ x (fma x x 1))

simplify1.2s

Calls
28 calls:
Slowest
262.0ms
(- (+ x (pow x 5)) (pow x 3))
204.0ms
(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
178.0ms
(/ (* (* x x) x) (* (* (fma x x 1) (fma x x 1)) (fma x x 1)))
176.0ms
(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
59.0ms
(/ (* (cbrt x) (cbrt x)) (* (cbrt (fma x x 1)) (cbrt (fma x x 1))))

prune246.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

18.6b
(- (+ (/ 1 x) (/ 1 (pow x 5))) (/ 1 (* (* x x) x)))
0.3b
(/ 1 (pow x 5))
0.3b
(/ 1 (* (* x x) x))
0.1b
(* (* x x) x)

rewrite254.0ms

Algorithm
rewrite-expression-head
Rules
162×*-un-lft-identity
102×times-frac
70×add-sqr-sqrt prod-diff
67×add-cube-cbrt
64×distribute-lft-out
57×div-inv
43×pow1
39×add-exp-log
20×add-cbrt-cube
13×pow-flip
12×unpow-prod-down pow-plus div-exp prod-exp pow-prod-up
10×fma-neg distribute-lft-out--
9×add-log-exp
8×associate-/r*
6×rec-exp 1-exp pow-prod-down cbrt-unprod associate-/l*
4×pow2 expm1-log1p-u cbrt-undiv pow-sqr insert-posit16 log1p-expm1-u sqr-pow
3×pow-to-exp associate-*r* pow-exp frac-sub
2×clear-num frac-2neg diff-log pow3 inv-pow
1×sum-log sub-neg flip3-+ flip3-- associate-*l* frac-add associate--l+ *-commutative flip-+ flip-- difference-of-squares unswap-sqr
Calls
4 calls:
Slowest
191.0ms
(- (+ (/ 1 x) (/ 1 (pow x 5))) (/ 1 (* (* x x) x)))
24.0ms
(/ 1 (* (* x x) x))
23.0ms
(* (* x x) x)
8.0ms
(/ 1 (pow x 5))

series193.0ms

Calls
4 calls:
Slowest
57.0ms
(/ 1 (pow x 5))
49.0ms
(- (+ (/ 1 x) (/ 1 (pow x 5))) (/ 1 (* (* x x) x)))
47.0ms
(/ 1 (* (* x x) x))
39.0ms
(* (* x x) x)

simplify49.2s

Calls
280 calls:
Slowest
980.0ms
(/ (* (* 1 1) 1) (* (* (* (* x x) x) (* (* x x) x)) (* (* x x) x)))
960.0ms
(/ (* (* 1 1) 1) (* (* (* (* x x) x) (* (* x x) x)) (* (* x x) x)))
688.0ms
(fma (/ 1 1) (+ (/ 1 x) (/ 1 (pow x 5))) (- (* (/ (sqrt 1) x) (/ (sqrt 1) (* x x)))))
546.0ms
(* (+ (* (/ 1 x) (/ 1 x)) (- (* (/ 1 (pow x 5)) (/ 1 (pow x 5))) (* (/ 1 x) (/ 1 (pow x 5))))) (* (* x x) x))
510.0ms
(/ (* (cbrt 1) (cbrt 1)) (pow (* (cbrt x) (cbrt x)) 5))

prune2.6s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes58.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.8b

bsearch131.0ms

end0.0ms

sample646.0ms

Algorithm
intervals
Results
558.0ms8000×body80valid