Details

Time bar (total: 2.6m)

sample100.0ms

Algorithm
intervals
Results
36.0ms67×body640valid
31.0ms139×body80valid
11.0ms16×body1280valid
10.0ms25×body320valid
2.0ms9×body160valid

simplify65.0ms

Calls
1 calls:
Slowest
65.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.3b

localize17.0ms

Local error

Found 4 expressions with local error:

1.7b
(+ (- (/ 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))

rewrite332.0ms

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
227.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
67.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
9.0ms
(/ 1 (- x 1))
8.0ms
(/ 1 (+ x 1))

series197.0ms

Calls
4 calls:
Slowest
120.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
36.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
25.0ms
(/ 1 (- x 1))
16.0ms
(/ 1 (+ x 1))

simplify2.1m

Calls
879 calls:
Slowest
689.0ms
(fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x)))))
573.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (+ x 1)) (- (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x))))))
567.0ms
(fma (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
538.0ms
(+ (* (- (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (* (/ 2 x) (/ 2 x))) (- x 1)) (* (+ (/ 1 (+ x 1)) (/ 2 x)) 1))
535.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (+ x 1))) (/ (cbrt 1) (sqrt (+ x 1))) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))

prune3.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

27.5b
(fma (* (cbrt (- (/ 1 (+ x 1)) (/ 2 x))) (cbrt (- (/ 1 (+ x 1)) (/ 2 x)))) (cbrt (- (/ 1 (+ x 1)) (/ 2 x))) (/ 1 (- x 1)))
0.6b
(cbrt (- (/ 1 (+ x 1)) (/ 2 x)))
0.6b
(cbrt (- (/ 1 (+ x 1)) (/ 2 x)))
0.6b
(cbrt (- (/ 1 (+ x 1)) (/ 2 x)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
49×*-un-lft-identity
39×cbrt-prod
33×times-frac
18×difference-of-squares
12×distribute-lft-out--
9×cbrt-div
7×add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×flip3-- pow1/3 frac-sub div-inv flip-- distribute-lft-out
1×fma-udef
Calls
4 calls:
Slowest
18.0ms
(cbrt (- (/ 1 (+ x 1)) (/ 2 x)))
14.0ms
(cbrt (- (/ 1 (+ x 1)) (/ 2 x)))
14.0ms
(cbrt (- (/ 1 (+ x 1)) (/ 2 x)))
0.0ms
(fma (* (cbrt (- (/ 1 (+ x 1)) (/ 2 x))) (cbrt (- (/ 1 (+ x 1)) (/ 2 x)))) (cbrt (- (/ 1 (+ x 1)) (/ 2 x))) (/ 1 (- x 1)))

series321.0ms

Calls
4 calls:
Slowest
142.0ms
(fma (* (cbrt (- (/ 1 (+ x 1)) (/ 2 x))) (cbrt (- (/ 1 (+ x 1)) (/ 2 x)))) (cbrt (- (/ 1 (+ x 1)) (/ 2 x))) (/ 1 (- x 1)))
61.0ms
(cbrt (- (/ 1 (+ x 1)) (/ 2 x)))
61.0ms
(cbrt (- (/ 1 (+ x 1)) (/ 2 x)))
56.0ms
(cbrt (- (/ 1 (+ x 1)) (/ 2 x)))

simplify4.0s

Calls
60 calls:
Slowest
299.0ms
(cbrt (- (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (* (/ 2 x) (/ 2 x))))
298.0ms
(cbrt (- (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (* (/ 2 x) (/ 2 x))))
295.0ms
(cbrt (- (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (* (/ 2 x) (/ 2 x))))
252.0ms
(- (+ (* 1/2 (* (exp (* 1/3 (- (log 4) (* 2 (log x))))) (* (pow x 2) (exp (* 1/3 (- (log -2) (log x))))))) (* (exp (* 1/3 (- (log 4) (* 2 (log x))))) (exp (* 1/3 (- (log -2) (log x)))))) (+ (* 1/2 (* (exp (* 1/3 (- (log 4) (* 2 (log x))))) (* (exp (* 1/3 (- (log -2) (log x)))) x))) (+ (pow x 2) (+ x 1))))
189.0ms
(- (+ (* (pow (/ 1 (pow x 5)) 1/3) (exp (* 1/3 (+ (log (/ 1 x)) (log -1))))) (+ (* (pow (/ 1 (pow x 2)) 1/3) (exp (* 1/3 (+ (log (/ 1 x)) (log -1))))) (+ (/ 1 (pow x 2)) (/ 1 x)))) (* (pow (/ 1 (pow x 8)) 1/3) (exp (* 1/3 (+ (log (/ 1 x)) (log -1))))))

prune706.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 2 (pow x 5))
0.1b
(/ (/ 2 x) (* x x))
0.0b
(/ 2 (pow x 7))
0.0b
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))

rewrite297.0ms

Algorithm
rewrite-expression-head
Rules
95×times-frac
60×*-un-lft-identity
58×add-sqr-sqrt add-cube-cbrt
26×add-exp-log
24×unpow-prod-down
20×add-cbrt-cube
19×associate-/l*
17×fma-def
15×associate-/r*
12×div-exp
8×cbrt-undiv sqr-pow
7×div-inv
6×add-log-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×clear-num frac-2neg
2×pow-to-exp pow-exp prod-exp cbrt-unprod
1×+-commutative sum-log flip3-+ frac-add flip-+ distribute-lft-out associate-/l/
Calls
4 calls:
Slowest
276.0ms
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))
9.0ms
(/ (/ 2 x) (* x x))
5.0ms
(/ 2 (pow x 5))
5.0ms
(/ 2 (pow x 7))

series282.0ms

Calls
4 calls:
Slowest
128.0ms
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))
62.0ms
(/ 2 (pow x 7))
50.0ms
(/ 2 (pow x 5))
41.0ms
(/ (/ 2 x) (* x x))

simplify7.6s

Calls
187 calls:
Slowest
235.0ms
(/ (* (* 2 2) 2) (* (* (pow x 5) (pow x 5)) (pow x 5)))
234.0ms
(/ (* (* 2 2) 2) (* (* (pow x 7) (pow x 7)) (pow x 7)))
172.0ms
(* (exp (/ (/ 2 x) (* x x))) (exp (/ 2 (pow x 5))))
164.0ms
(/ (* (cbrt 2) (cbrt 2)) (* (cbrt (pow x 5)) (cbrt (pow x 5))))
164.0ms
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))

prune1.3s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 2 (pow x 5))
0.1b
(/ (/ 1 x) x)
0.1b
(fma (/ 2 x) (/ (/ 1 x) x) (/ 2 (pow x 5)))
0.0b
(/ 2 (pow x 7))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
117×times-frac
78×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
24×unpow-prod-down
23×add-exp-log
19×associate-/l*
17×associate-/r*
13×add-cbrt-cube
12×div-exp
8×sqr-pow
7×pow1 div-inv
5×cbrt-undiv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×pow-to-exp pow-exp pow-div
1×rec-exp 1-exp fma-udef pow-flip inv-pow associate-/l/
Calls
4 calls:
Slowest
7.0ms
(/ 2 (pow x 5))
7.0ms
(/ (/ 1 x) x)
5.0ms
(/ 2 (pow x 7))
0.0ms
(fma (/ 2 x) (/ (/ 1 x) x) (/ 2 (pow x 5)))

series258.0ms

Calls
4 calls:
Slowest
126.0ms
(fma (/ 2 x) (/ (/ 1 x) x) (/ 2 (pow x 5)))
62.0ms
(/ 2 (pow x 7))
50.0ms
(/ 2 (pow x 5))
19.0ms
(/ (/ 1 x) x)

simplify7.9s

Calls
221 calls:
Slowest
341.0ms
(/ (/ (* (* 1 1) 1) (* (* x x) x)) (* (* x x) x))
283.0ms
(/ (* (* (/ 1 x) (/ 1 x)) (/ 1 x)) (* (* x x) x))
235.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt x) (cbrt x))) (* (cbrt x) (cbrt x)))
232.0ms
(/ (* (* 2 2) 2) (* (* (pow x 7) (pow x 7)) (pow x 7)))
227.0ms
(/ (* (* 2 2) 2) (* (* (pow x 5) (pow x 5)) (pow x 5)))

prune1.4s

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0b

regimes84.0ms

Accuracy

99.5% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 9.9b

bsearch123.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
919.0ms1869×body640valid
372.0ms4169×body80valid
207.0ms922×body320valid
206.0ms568×body1280valid
62.0ms474×body160valid