Details

Time bar (total: 2.9m)

sample69.0ms

Algorithm
intervals
Results
21.0ms59×body640valid
12.0ms136×body80valid
11.0ms13×body160valid
9.0ms37×body320valid
5.0ms11×body1280valid

simplify89.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
89.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.7b

localize38.0ms

Local error

Found 4 expressions with local error:

2.1b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
0.0b
(/ 1 (- x 1))
0.0b
(/ 1 (+ x 1))
0.0b
(- (/ 1 (+ x 1)) (/ 2 x))

rewrite299.0ms

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-
Counts
4 → 648
Calls
4 calls:
Slowest
194.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
52.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
18.0ms
(/ 1 (- x 1))
10.0ms
(/ 1 (+ x 1))

series190.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
110.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
43.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
23.0ms
(/ 1 (- x 1))
15.0ms
(/ 1 (+ x 1))

simplify2.3m

Counts
927 → 660
Calls
927 calls:
Slowest
749.0ms
(+ (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) (/ 1 (- x 1)))
690.0ms
(/ (* (* 1 1) 1) (* (* (+ x 1) (+ x 1)) (+ x 1)))
616.0ms
(+ (fma (- (/ (sqrt 2) (cbrt x))) (/ (sqrt 2) (* (cbrt x) (cbrt x))) (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1)))
565.0ms
(fma (* (cbrt (/ 1 (+ x 1))) (cbrt (/ 1 (+ x 1)))) (cbrt (/ 1 (+ x 1))) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
564.0ms
(* (* (+ x 1) x) (- x 1))

prune3.6s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

29.4b
(fma x (+ x 1) (- (* (fma -2 (+ x 1) x) x) (fma -2 (+ x 1) x)))
0.0b
(* (fma x x -1) x)
0.0b
(/ (fma x (+ x 1) (- (* (fma -2 (+ x 1) x) x) (fma -2 (+ x 1) x))) (* (fma x x -1) x))
0.0b
(- (* (fma -2 (+ x 1) x) x) (fma -2 (+ x 1) x))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cbrt-cube add-exp-log
9×*-un-lft-identity add-cube-cbrt
6×pow1 add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×times-frac associate-*r* associate-*l* prod-diff associate-/l*
2×cbrt-undiv div-exp prod-exp cbrt-unprod fma-udef
1×clear-num associate-/r* sub-neg frac-2neg flip3-- fma-neg diff-log pow-prod-down *-commutative div-inv flip-- associate--r+ unswap-sqr
Counts
4 → 76
Calls
4 calls:
Slowest
7.0ms
(- (* (fma -2 (+ x 1) x) x) (fma -2 (+ x 1) x))
7.0ms
(/ (fma x (+ x 1) (- (* (fma -2 (+ x 1) x) x) (fma -2 (+ x 1) x))) (* (fma x x -1) x))
6.0ms
(* (fma x x -1) x)
0.0ms
(fma x (+ x 1) (- (* (fma -2 (+ x 1) x) x) (fma -2 (+ x 1) x)))

series578.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
265.0ms
(/ (fma x (+ x 1) (- (* (fma -2 (+ x 1) x) x) (fma -2 (+ x 1) x))) (* (fma x x -1) x))
189.0ms
(fma x (+ x 1) (- (* (fma -2 (+ x 1) x) x) (fma -2 (+ x 1) x)))
79.0ms
(* (fma x x -1) x)
45.0ms
(- (* (fma -2 (+ x 1) x) x) (fma -2 (+ x 1) x))

simplify14.6s

Counts
97 → 88
Calls
97 calls:
Slowest
644.0ms
(cbrt (fma x (+ x 1) (- (* (fma -2 (+ x 1) x) x) (fma -2 (+ x 1) x))))
457.0ms
(+ (* (* (fma -2 (+ x 1) x) x) (* (fma -2 (+ x 1) x) x)) (+ (* (fma -2 (+ x 1) x) (fma -2 (+ x 1) x)) (* (* (fma -2 (+ x 1) x) x) (fma -2 (+ x 1) x))))
426.0ms
(/ (sqrt (fma x (+ x 1) (- (* (fma -2 (+ x 1) x) x) (fma -2 (+ x 1) x)))) x)
421.0ms
(* (cbrt (fma x (+ x 1) (- (* (fma -2 (+ x 1) x) x) (fma -2 (+ x 1) x)))) (cbrt (fma x (+ x 1) (- (* (fma -2 (+ x 1) x) x) (fma -2 (+ x 1) x)))))
421.0ms
(* (* (* (fma x x -1) x) (* (fma x x -1) x)) (* (fma x x -1) x))

prune584.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ 2 (* (fma x x -1) x))
0.0b
(* (fma x x -1) x)

rewrite15.0ms

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
Counts
2 → 45
Calls
2 calls:
Slowest
8.0ms
(* (fma x x -1) x)
6.0ms
(/ 2 (* (fma x x -1) x))

series125.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
78.0ms
(* (fma x x -1) x)
46.0ms
(/ 2 (* (fma x x -1) x))

simplify4.4s

Counts
55 → 51
Calls
55 calls:
Slowest
671.0ms
(* (* (* (fma x x -1) x) (* (fma x x -1) x)) (* (fma x x -1) x))
452.0ms
(* (* (/ 2 (* (fma x x -1) x)) (/ 2 (* (fma x x -1) x))) (/ 2 (* (fma x x -1) x)))
284.0ms
(* (* (* (fma x x -1) (fma x x -1)) (fma x x -1)) (* (* x x) x))
166.0ms
(- (+ (* 2 x) (+ (* 2 (pow x 3)) (* 2 (/ 1 x)))))
159.0ms
(log (/ 2 (* (fma x x -1) x)))

prune258.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ 1 (fma x x -1))
0.1b
(* (/ 1 (fma x x -1)) (/ 2 x))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
34×times-frac
28×add-exp-log
26×*-un-lft-identity
24×add-cube-cbrt
16×add-cbrt-cube
13×associate-*r* associate-*l*
10×div-exp
8×prod-exp
6×unswap-sqr
5×pow1 cbrt-undiv
4×cbrt-unprod
3×rec-exp associate-/r* 1-exp div-inv associate-/l*
2×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative pow-flip inv-pow
Counts
2 → 93
Calls
2 calls:
Slowest
12.0ms
(* (/ 1 (fma x x -1)) (/ 2 x))
4.0ms
(/ 1 (fma x x -1))

series83.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
45.0ms
(* (/ 1 (fma x x -1)) (/ 2 x))
38.0ms
(/ 1 (fma x x -1))

simplify12.3s

Counts
114 → 99
Calls
114 calls:
Slowest
560.0ms
(* (* (* (/ 1 (fma x x -1)) (/ 2 x)) (* (/ 1 (fma x x -1)) (/ 2 x))) (* (/ 1 (fma x x -1)) (/ 2 x)))
406.0ms
(* (* (* (/ 1 (fma x x -1)) (/ 1 (fma x x -1))) (/ 1 (fma x x -1))) (* (* (/ 2 x) (/ 2 x)) (/ 2 x)))
339.0ms
(* (/ 1 (fma x x -1)) (/ (* (cbrt 2) (cbrt 2)) (sqrt x)))
332.0ms
(* (/ 1 (fma x x -1)) (/ (sqrt 2) (* (cbrt x) (cbrt x))))
315.0ms
(+ (- 0 (log (fma x x -1))) (- (log 2) (log x)))

prune495.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes25.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch1.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
900.0ms1867×body640valid
326.0ms4161×body80valid
199.0ms579×body1280valid
173.0ms957×body320valid
53.0ms438×body160valid