Details

Time bar (total: 3.1m)

sample57.0ms

Algorithm
intervals
Results
19.0ms56×body640valid
12.0ms133×body80valid
9.0ms19×body1280valid
8.0ms32×body320valid
3.0ms16×body160valid

simplify103.0ms

Calls
1 calls:
Slowest
103.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.7b

localize30.0ms

Local error

Found 4 expressions with local error:

2.5b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
0.0b
(- (/ 1 (+ x 1)) (/ 2 x))
0.0b
(/ 1 (+ x 1))
0.0b
(/ 1 (- x 1))

rewrite281.0ms

Algorithm
rewrite-expression-head
Rules
743×*-un-lft-identity
715×times-frac
544×add-sqr-sqrt
494×add-cube-cbrt
468×prod-diff
236×associate-+l+
99×distribute-lft-out
72×div-inv
58×associate-/r/
29×flip3-+ flip-+
22×distribute-lft-out--
20×difference-of-squares
18×fma-neg
13×fma-def
12×add-exp-log
11×associate-/r* add-log-exp
8×add-cbrt-cube
6×pow1 associate-/l*
4×expm1-log1p-u difference-of-sqr-1 div-exp insert-posit16 log1p-expm1-u
3×flip3-- frac-add flip--
2×cbrt-undiv rec-exp clear-num sum-log sub-neg frac-2neg diff-log 1-exp frac-sub pow-flip inv-pow
1×+-commutative associate-+l-
Calls
4 calls:
Slowest
208.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
38.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
8.0ms
(/ 1 (- x 1))
8.0ms
(/ 1 (+ x 1))

series202.0ms

Calls
4 calls:
Slowest
128.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
33.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
23.0ms
(/ 1 (+ x 1))
19.0ms
(/ 1 (- x 1))

simplify2.1m

Calls
879 calls:
Slowest
839.0ms
(fma (/ (sqrt 1) (sqrt (+ x 1))) (/ (sqrt 1) (sqrt (+ x 1))) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
574.0ms
(fma (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
565.0ms
(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ 1 (cbrt (+ x 1))) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
552.0ms
(fma (/ (sqrt 1) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (sqrt 1) (cbrt (+ x 1))) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
542.0ms
(* (* (+ x 1) x) (- x 1))

prune3.6s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

60.0b
(fma (- (/ (sqrt 2) x)) (/ (sqrt 2) 1) (* (/ (sqrt 2) x) (/ (sqrt 2) 1)))
2.5b
(+ (- (/ 1 (+ 1 x)) (/ 2 x)) (+ (fma (- (/ (sqrt 2) x)) (/ (sqrt 2) 1) (* (/ (sqrt 2) x) (/ (sqrt 2) 1))) (/ 1 (- x 1))))
0.5b
(/ (sqrt 2) x)
0.5b
(/ (sqrt 2) x)

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
381×*-un-lft-identity
365×times-frac
282×add-sqr-sqrt
265×add-cube-cbrt
236×associate-+l+
234×prod-diff
55×distribute-lft-out
40×div-inv
26×associate-/r/
24×sqrt-prod
17×flip3-+ flip-+
16×add-log-exp
13×fma-def
12×associate-/l*
10×distribute-lft-out--
8×add-cbrt-cube add-exp-log
6×associate-/r* sum-log frac-add difference-of-squares
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
2×cbrt-undiv clear-num frac-2neg flip3-- diff-log div-exp frac-sub flip--
1×+-commutative associate-+r+ sub-neg associate-+l- fma-udef
Calls
4 calls:
Slowest
152.0ms
(+ (- (/ 1 (+ 1 x)) (/ 2 x)) (+ (fma (- (/ (sqrt 2) x)) (/ (sqrt 2) 1) (* (/ (sqrt 2) x) (/ (sqrt 2) 1))) (/ 1 (- x 1))))
6.0ms
(/ (sqrt 2) x)
4.0ms
(/ (sqrt 2) x)
0.0ms
(fma (- (/ (sqrt 2) x)) (/ (sqrt 2) 1) (* (/ (sqrt 2) x) (/ (sqrt 2) 1)))

series485.0ms

Calls
4 calls:
Slowest
251.0ms
(+ (- (/ 1 (+ 1 x)) (/ 2 x)) (+ (fma (- (/ (sqrt 2) x)) (/ (sqrt 2) 1) (* (/ (sqrt 2) x) (/ (sqrt 2) 1))) (/ 1 (- x 1))))
135.0ms
(fma (- (/ (sqrt 2) x)) (/ (sqrt 2) 1) (* (/ (sqrt 2) x) (/ (sqrt 2) 1)))
49.0ms
(/ (sqrt 2) x)
48.0ms
(/ (sqrt 2) x)

simplify38.9s

Calls
375 calls:
Slowest
567.0ms
(+ (* (- (* (/ 1 (+ 1 x)) (/ 1 (+ 1 x))) (* (/ 2 x) (/ 2 x))) (+ (* (fma (- (/ (sqrt 2) x)) (/ (sqrt 2) 1) (* (/ (sqrt 2) x) (/ (sqrt 2) 1))) (fma (- (/ (sqrt 2) x)) (/ (sqrt 2) 1) (* (/ (sqrt 2) x) (/ (sqrt 2) 1)))) (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (fma (- (/ (sqrt 2) x)) (/ (sqrt 2) 1) (* (/ (sqrt 2) x) (/ (sqrt 2) 1))) (/ 1 (- x 1)))))) (* (+ (/ 1 (+ 1 x)) (/ 2 x)) (+ (pow (fma (- (/ (sqrt 2) x)) (/ (sqrt 2) 1) (* (/ (sqrt 2) x) (/ (sqrt 2) 1))) 3) (pow (/ 1 (- x 1)) 3))))
475.0ms
(fma (/ 1 (- (* 1 1) (* x x))) (- 1 x) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
417.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (+ 1 x)) (- (* (/ (cbrt 2) (sqrt x)) (/ (* (cbrt 2) (cbrt 2)) (sqrt x)))))
340.0ms
(+ (* (- (* 1 x) (* (+ 1 x) 2)) (+ (* (fma (- (/ (sqrt 2) x)) (/ (sqrt 2) 1) (* (/ (sqrt 2) x) (/ (sqrt 2) 1))) (fma (- (/ (sqrt 2) x)) (/ (sqrt 2) 1) (* (/ (sqrt 2) x) (/ (sqrt 2) 1)))) (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (fma (- (/ (sqrt 2) x)) (/ (sqrt 2) 1) (* (/ (sqrt 2) x) (/ (sqrt 2) 1))) (/ 1 (- x 1)))))) (* (* (+ 1 x) x) (+ (pow (fma (- (/ (sqrt 2) x)) (/ (sqrt 2) 1) (* (/ (sqrt 2) x) (/ (sqrt 2) 1))) 3) (pow (/ 1 (- x 1)) 3))))
340.0ms
(fma (/ (sqrt 1) (* (cbrt (+ 1 x)) (cbrt (+ 1 x)))) (/ (sqrt 1) (cbrt (+ 1 x))) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))

prune3.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

31.3b
(fma (- x (fma x 2 2)) (- x 1) (fma x x x))
0.0b
(* (fma x x -1) x)
0.0b
(/ (fma (- x (fma x 2 2)) (- x 1) (fma x x x)) (* (fma x x -1) x))
0.0b
(- x (fma x 2 2))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
17×*-un-lft-identity
15×add-cube-cbrt
11×add-cbrt-cube add-exp-log
9×prod-diff
6×pow1 add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×times-frac fma-neg associate-*r* associate-*l* associate-/l*
2×cbrt-undiv div-exp prod-exp cbrt-unprod fma-udef
1×clear-num associate-/r* sub-neg frac-2neg flip3-- diff-log pow-prod-down *-commutative div-inv flip-- associate--r+ distribute-lft-out-- difference-of-squares unswap-sqr
Calls
4 calls:
Slowest
6.0ms
(/ (fma (- x (fma x 2 2)) (- x 1) (fma x x x)) (* (fma x x -1) x))
6.0ms
(* (fma x x -1) x)
5.0ms
(- x (fma x 2 2))
0.0ms
(fma (- x (fma x 2 2)) (- x 1) (fma x x x))

series567.0ms

Calls
4 calls:
Slowest
256.0ms
(/ (fma (- x (fma x 2 2)) (- x 1) (fma x x x)) (* (fma x x -1) x))
177.0ms
(fma (- x (fma x 2 2)) (- x 1) (fma x x x))
78.0ms
(* (fma x x -1) x)
56.0ms
(- x (fma x 2 2))

simplify5.7s

Calls
57 calls:
Slowest
442.0ms
(/ (sqrt (fma (- x (fma x 2 2)) (- x 1) (fma x x x))) x)
438.0ms
(/ (cbrt (fma (- x (fma x 2 2)) (- x 1) (fma x x x))) x)
429.0ms
(* (cbrt (fma (- x (fma x 2 2)) (- x 1) (fma x x x))) (cbrt (fma (- x (fma x 2 2)) (- x 1) (fma x x x))))
406.0ms
(/ (fma (- x (fma x 2 2)) (- x 1) (fma x x x)) x)
404.0ms
(sqrt (fma (- x (fma x 2 2)) (- x 1) (fma x x x)))

prune671.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ 2 (* (fma x x -1) x))
0.0b
(* (fma x x -1) x)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
9×add-cbrt-cube add-exp-log
8×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt
4×pow1
3×times-frac associate-*r* associate-*l* associate-/l*
2×expm1-log1p-u cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
1×clear-num associate-/r* frac-2neg pow-prod-down *-commutative div-inv unswap-sqr
Calls
2 calls:
Slowest
6.0ms
(/ 2 (* (fma x x -1) x))
5.0ms
(* (fma x x -1) x)

series131.0ms

Calls
2 calls:
Slowest
81.0ms
(* (fma x x -1) x)
50.0ms
(/ 2 (* (fma x x -1) x))

simplify1.4s

Calls
27 calls:
Slowest
271.0ms
(* (* (* (fma x x -1) (fma x x -1)) (fma x x -1)) (* (* x x) x))
174.0ms
(- (+ (* 2 x) (+ (* 2 (pow x 3)) (* 2 (/ 1 x)))))
145.0ms
(- (log 2) (log (* (fma x x -1) x)))
135.0ms
(/ (* (* 2 2) 2) (* (* (* (fma x x -1) x) (* (fma x x -1) x)) (* (fma x x -1) x)))
134.0ms
(+ (* 2 (/ 1 (pow x 7))) (+ (* 2 (/ 1 (pow x 3))) (* 2 (/ 1 (pow x 5)))))

prune245.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes24.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch1.0ms

end0.0ms

sample1.9s

Algorithm
intervals
Results
581.0ms1913×body640valid
509.0ms877×body320valid
328.0ms4144×body80valid
289.0ms612×body1280valid
82.0ms456×body160valid