Details

Time bar (total: 8.0m)

sample65.0ms

Algorithm
intervals
Results
21.0ms57×body640valid
12.0ms125×body80valid
11.0ms22×body1280valid
10.0ms34×body320valid
3.0ms18×body160valid

simplify92.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
92.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.3b

localize38.0ms

Local error

Found 4 expressions with local error:

3.4b
(+ (- (/ 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))

rewrite340.0ms

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
197.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
73.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
19.0ms
(/ 1 (+ x 1))
16.0ms
(/ 1 (- x 1))

series222.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
155.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
25.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
21.0ms
(/ 1 (- x 1))
21.0ms
(/ 1 (+ x 1))

simplify2.3m

Counts
879 → 660
Calls
879 calls:
Slowest
914.0ms
(fma (/ (sqrt 1) 1) (/ (sqrt 1) (+ x 1)) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
815.0ms
(fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))
630.0ms
(fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))
556.0ms
(fma (/ (sqrt 1) 1) (/ (sqrt 1) (+ x 1)) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
555.0ms
(fma (/ (sqrt 1) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (sqrt 1) (cbrt (+ x 1))) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))

prune3.8s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

61.0b
(fma (- (/ (cbrt 2) x)) (/ (* (cbrt 2) (cbrt 2)) 1) (* (/ (cbrt 2) x) (/ (* (cbrt 2) (cbrt 2)) 1)))
3.4b
(+ (- (/ 1 (+ 1 x)) (/ 2 x)) (+ (fma (- (/ (cbrt 2) x)) (/ (* (cbrt 2) (cbrt 2)) 1) (* (/ (cbrt 2) x) (/ (* (cbrt 2) (cbrt 2)) 1))) (/ 1 (- x 1))))
1.0b
(cbrt 2)
1.0b
(cbrt 2)

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
353×*-un-lft-identity
329×times-frac
254×add-sqr-sqrt
237×add-cube-cbrt
236×associate-+l+
234×prod-diff
55×distribute-lft-out
38×div-inv
26×associate-/r/
17×flip3-+ flip-+
16×add-log-exp
13×fma-def
10×distribute-lft-out--
6×cbrt-prod sum-log frac-add difference-of-squares
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
2×flip3-- pow1/3 diff-log frac-sub flip--
1×+-commutative associate-+r+ sub-neg associate-+l- fma-udef
Counts
4 → 322
Calls
4 calls:
Slowest
156.0ms
(+ (- (/ 1 (+ 1 x)) (/ 2 x)) (+ (fma (- (/ (cbrt 2) x)) (/ (* (cbrt 2) (cbrt 2)) 1) (* (/ (cbrt 2) x) (/ (* (cbrt 2) (cbrt 2)) 1))) (/ 1 (- x 1))))
1.0ms
(cbrt 2)
1.0ms
(cbrt 2)
0.0ms
(fma (- (/ (cbrt 2) x)) (/ (* (cbrt 2) (cbrt 2)) 1) (* (/ (cbrt 2) x) (/ (* (cbrt 2) (cbrt 2)) 1)))

series521.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
331.0ms
(+ (- (/ 1 (+ 1 x)) (/ 2 x)) (+ (fma (- (/ (cbrt 2) x)) (/ (* (cbrt 2) (cbrt 2)) 1) (* (/ (cbrt 2) x) (/ (* (cbrt 2) (cbrt 2)) 1))) (/ 1 (- x 1))))
190.0ms
(fma (- (/ (cbrt 2) x)) (/ (* (cbrt 2) (cbrt 2)) 1) (* (/ (cbrt 2) x) (/ (* (cbrt 2) (cbrt 2)) 1)))
0.0ms
(cbrt 2)
0.0ms
(cbrt 2)

simplify41.7s

Counts
287 → 330
Calls
287 calls:
Slowest
565.0ms
(fma (/ 1 (- (* 1 1) (* x x))) (- 1 x) (- (* (/ (cbrt 2) x) (/ (* (cbrt 2) (cbrt 2)) 1))))
508.0ms
(+ (* (- (* (/ 1 (+ 1 x)) (/ 1 (+ 1 x))) (* (/ 2 x) (/ 2 x))) (+ (* (fma (- (/ (cbrt 2) x)) (/ (* (cbrt 2) (cbrt 2)) 1) (* (/ (cbrt 2) x) (/ (* (cbrt 2) (cbrt 2)) 1))) (fma (- (/ (cbrt 2) x)) (/ (* (cbrt 2) (cbrt 2)) 1) (* (/ (cbrt 2) x) (/ (* (cbrt 2) (cbrt 2)) 1)))) (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (fma (- (/ (cbrt 2) x)) (/ (* (cbrt 2) (cbrt 2)) 1) (* (/ (cbrt 2) x) (/ (* (cbrt 2) (cbrt 2)) 1))) (/ 1 (- x 1)))))) (* (+ (/ 1 (+ 1 x)) (/ 2 x)) (+ (pow (fma (- (/ (cbrt 2) x)) (/ (* (cbrt 2) (cbrt 2)) 1) (* (/ (cbrt 2) x) (/ (* (cbrt 2) (cbrt 2)) 1))) 3) (pow (/ 1 (- x 1)) 3))))
399.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (+ 1 x)) (cbrt (+ 1 x)))) (/ (cbrt 1) (cbrt (+ 1 x))) (- (* (/ 2 x) 1)))
375.0ms
(+ (* (- (* 1 x) (* (+ 1 x) 2)) (+ (* (fma (- (/ (cbrt 2) x)) (/ (* (cbrt 2) (cbrt 2)) 1) (* (/ (cbrt 2) x) (/ (* (cbrt 2) (cbrt 2)) 1))) (fma (- (/ (cbrt 2) x)) (/ (* (cbrt 2) (cbrt 2)) 1) (* (/ (cbrt 2) x) (/ (* (cbrt 2) (cbrt 2)) 1)))) (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (fma (- (/ (cbrt 2) x)) (/ (* (cbrt 2) (cbrt 2)) 1) (* (/ (cbrt 2) x) (/ (* (cbrt 2) (cbrt 2)) 1))) (/ 1 (- x 1)))))) (* (* (+ 1 x) x) (+ (pow (fma (- (/ (cbrt 2) x)) (/ (* (cbrt 2) (cbrt 2)) 1) (* (/ (cbrt 2) x) (/ (* (cbrt 2) (cbrt 2)) 1))) 3) (pow (/ 1 (- x 1)) 3))))
351.0ms
(fma (/ (sqrt 1) (* (cbrt (+ 1 x)) (cbrt (+ 1 x)))) (/ (sqrt 1) (cbrt (+ 1 x))) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))

prune3.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

14.3b
(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))
3.3b
(- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))
0.3b
(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
0.1b
(* (/ 1 (- x 1)) (/ 1 (- x 1)))

rewrite660.0ms

Algorithm
rewrite-expression-head
Rules
1672×*-un-lft-identity
1578×times-frac
1191×add-sqr-sqrt
1002×add-cube-cbrt
937×prod-diff
472×distribute-rgt-in distribute-lft-in associate--l+
196×frac-sub
172×distribute-lft-out
164×div-inv
146×distribute-lft-out--
117×associate-/r/
112×frac-times
87×difference-of-squares
80×flip3-- flip--
62×swap-sqr associate-/l/
58×associate-*l/ associate-*r/
52×flip3-+ flip-+
48×add-exp-log
40×associate-*r* associate-*l*
31×un-div-inv
26×pow1
20×add-cbrt-cube
18×difference-of-sqr-1
17×div-exp prod-exp
16×associate-/r*
10×unswap-sqr
8×rec-exp 1-exp pow-flip inv-pow
6×pow-prod-up add-log-exp
5×cbrt-undiv sub-neg cbrt-unprod
4×expm1-log1p-u pow-prod-down pow-sqr insert-posit16 log1p-expm1-u associate-/l*
2×pow2 pow-plus *-commutative
1×clear-num frac-2neg fma-neg diff-log div-sub
Counts
4 → 1422
Calls
4 calls:
Slowest
331.0ms
(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))
155.0ms
(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
92.0ms
(- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))
29.0ms
(* (/ 1 (- x 1)) (/ 1 (- x 1)))

series495.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
325.0ms
(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))
114.0ms
(- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))
37.0ms
(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
19.0ms
(* (/ 1 (- x 1)) (/ 1 (- x 1)))

simplify4.5m

Counts
1596 → 1434
Calls
1596 calls:
Slowest
679.0ms
(- (* (* (- (pow (/ 1 (+ x 1)) 3) (pow (/ 2 x) 3)) (- (pow (/ 1 (+ x 1)) 3) (pow (/ 2 x) 3))) (* (- x 1) (- x 1))) (* (* (+ (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (+ (* (/ 2 x) (/ 2 x)) (* (/ 1 (+ x 1)) (/ 2 x)))) (+ (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (+ (* (/ 2 x) (/ 2 x)) (* (/ 1 (+ x 1)) (/ 2 x))))) (* 1 1)))
625.0ms
(* (fma (/ 1 (+ (pow x 3) (pow 1 3))) (+ (* x x) (- (* 1 1) (* x 1))) (- (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x)))))) (- (/ 1 (+ x 1)) (/ 2 x)))
559.0ms
(* (fma (- (/ (cbrt 2) x)) (/ (* (cbrt 2) (cbrt 2)) 1) (* (/ (cbrt 2) x) (/ (* (cbrt 2) (cbrt 2)) 1))) (- (/ 1 (+ x 1)) (/ 2 x)))
544.0ms
(* (+ (/ 1 (+ x 1)) (/ 2 x)) (- x 1))
530.0ms
(/ (sqrt (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))

prune12.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 2 (pow x 5))
0.2b
(/ 2 (pow x 7))
0.1b
(/ (/ 2 x) (* x x))
0.0b
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))

rewrite46.0ms

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/
Counts
4 → 178
Calls
4 calls:
Slowest
27.0ms
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))
9.0ms
(/ (/ 2 x) (* x x))
4.0ms
(/ 2 (pow x 5))
4.0ms
(/ 2 (pow x 7))

series276.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
123.0ms
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))
60.0ms
(/ 2 (pow x 7))
52.0ms
(/ 2 (pow x 5))
40.0ms
(/ (/ 2 x) (* x x))

simplify7.2s

Counts
187 → 190
Calls
187 calls:
Slowest
221.0ms
(/ (* (* 2 2) 2) (* (* (pow x 7) (pow x 7)) (pow x 7)))
219.0ms
(/ (* (* 2 2) 2) (* (* (pow x 5) (pow x 5)) (pow x 5)))
166.0ms
(* (exp (/ (/ 2 x) (* x x))) (exp (/ 2 (pow x 5))))
157.0ms
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))
156.0ms
(/ (* (cbrt 2) (cbrt 2)) (* (cbrt (pow x 5)) (cbrt (pow x 5))))

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes48.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 19.3b

bsearch147.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
612.0ms4161×body80valid
546.0ms1846×body640valid
230.0ms585×body1280valid
202.0ms933×body320valid
104.0ms477×body160valid