Details

Time bar (total: 2.9m)

sample90.0ms

Algorithm
intervals
Results
31.0ms67×body640valid
15.0ms123×body80valid
14.0ms35×body320valid
13.0ms18×body160valid
8.0ms13×body1280valid

simplify95.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
95.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.8b

localize25.0ms

Local error

Found 4 expressions with local error:

2.4b
(+ (- (/ 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))

rewrite378.0ms

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
266.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
52.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
11.0ms
(/ 1 (- x 1))
9.0ms
(/ 1 (+ x 1))

series225.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
137.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
41.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
24.0ms
(/ 1 (+ x 1))
23.0ms
(/ 1 (- x 1))

simplify2.0m

Counts
879 → 660
Calls
879 calls:
Slowest
734.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (+ x 1)) (- (* (/ (cbrt 2) x) (/ (* (cbrt 2) (cbrt 2)) 1))))
692.0ms
(fma (* (cbrt (/ 1 (+ x 1))) (cbrt (/ 1 (+ x 1)))) (cbrt (/ 1 (+ x 1))) (- (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))))
552.0ms
(fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))
549.0ms
(fma (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
518.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (+ x 1)) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))

prune4.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

9.9b
(+ (- (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))) (/ 2 x)) (/ 1 (- x 1)))
0.1b
(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
0.1b
(/ 1 (sqrt (+ x 1)))
0.1b
(/ 1 (sqrt (+ x 1)))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
200×times-frac
193×add-sqr-sqrt
191×*-un-lft-identity
118×sqrt-prod
108×add-cube-cbrt
52×add-exp-log
41×swap-sqr
31×pow1
30×pow-flip
28×distribute-lft-out
27×associate-*r* associate-*l*
25×unswap-sqr
20×add-cbrt-cube div-exp
16×prod-exp
15×associate-+l+
14×associate-/r*
13×prod-diff
12×sqrt-div associate-/r/
10×rec-exp sqrt-pow1 pow1/2 1-exp div-inv inv-pow
9×pow-prod-up add-log-exp
7×flip3-+ flip-+
6×cbrt-undiv frac-add associate-/l*
5×fma-def pow-prod-down pow-sqr
4×expm1-log1p-u frac-sub cbrt-unprod insert-posit16 log1p-expm1-u
2×frac-times clear-num sum-log frac-2neg associate-*l/ associate-*r/ un-div-inv difference-of-squares
1×pow2 +-commutative sub-neg pow-plus flip3-- diff-log *-commutative associate-+l- flip--
Counts
4 → 328
Calls
4 calls:
Slowest
151.0ms
(+ (- (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))) (/ 2 x)) (/ 1 (- x 1)))
38.0ms
(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
10.0ms
(/ 1 (sqrt (+ x 1)))
9.0ms
(/ 1 (sqrt (+ x 1)))

series166.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
90.0ms
(+ (- (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))) (/ 2 x)) (/ 1 (- x 1)))
29.0ms
(/ 1 (sqrt (+ x 1)))
29.0ms
(/ 1 (sqrt (+ x 1)))
18.0ms
(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))

simplify12.8s

Counts
412 → 340
Calls
412 calls:
Slowest
452.0ms
(* (* (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt (+ x 1)))) (* (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt (+ x 1)))))
383.0ms
(+ (* (- (* (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (* (/ 2 x) (/ 2 x))) (- x 1)) (* (+ (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))) (/ 2 x)) 1))
310.0ms
(fma (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
298.0ms
(* (+ (* (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (* (/ 2 x) (/ 2 x)) (* (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))) (/ 2 x)))) (- x 1))
295.0ms
(* (/ (* (* 1 1) 1) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1)))) (/ (* (* 1 1) 1) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1)))))

prune2.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

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
32.0ms
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))
11.0ms
(/ (/ 2 x) (* x x))
6.0ms
(/ 2 (pow x 7))
5.0ms
(/ 2 (pow x 5))

series289.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
129.0ms
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))
65.0ms
(/ 2 (pow x 7))
53.0ms
(/ 2 (pow x 5))
42.0ms
(/ (/ 2 x) (* x x))

simplify7.9s

Counts
187 → 190
Calls
187 calls:
Slowest
240.0ms
(/ (* (* 2 2) 2) (* (* (pow x 7) (pow x 7)) (pow x 7)))
239.0ms
(/ (* (* 2 2) 2) (* (* (pow x 5) (pow x 5)) (pow x 5)))
177.0ms
(* (exp (/ (/ 2 x) (* x x))) (exp (/ 2 (pow x 5))))
172.0ms
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))
169.0ms
(/ (* (cbrt 2) (cbrt 2)) (* (cbrt (pow x 5)) (cbrt (pow x 5))))

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 2 x) x)
0.1b
(/ 2 (pow x 7))
0.1b
(/ (/ (/ 2 x) x) x)
0.1b
(/ 2 (pow x 5))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
510×times-frac
262×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
62×associate-/l*
28×add-exp-log
24×unpow-prod-down div-inv
22×add-cbrt-cube
20×associate-/r*
15×div-exp
11×cbrt-undiv
8×sqr-pow
4×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
2×pow-to-exp pow-exp associate-/l/
Counts
4 → 364
Calls
4 calls:
Slowest
12.0ms
(/ (/ (/ 2 x) x) x)
8.0ms
(/ (/ 2 x) x)
5.0ms
(/ 2 (pow x 5))
5.0ms
(/ 2 (pow x 7))

series197.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
64.0ms
(/ 2 (pow x 7))
55.0ms
(/ 2 (pow x 5))
46.0ms
(/ (/ (/ 2 x) x) x)
33.0ms
(/ (/ 2 x) x)

simplify19.0s

Counts
526 → 376
Calls
526 calls:
Slowest
311.0ms
(/ (sqrt 2) (pow (cbrt x) 5))
273.0ms
(/ (* (* (/ (/ 2 x) x) (/ (/ 2 x) x)) (/ (/ 2 x) x)) (* (* x x) x))
250.0ms
(/ (/ (/ (* (cbrt 2) (cbrt 2)) (sqrt x)) (* (cbrt x) (cbrt x))) (sqrt x))
241.0ms
(/ (/ (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (cbrt x) (cbrt x))) (sqrt x))
239.0ms
(/ (* (* 2 2) 2) (* (* (pow x 7) (pow x 7)) (pow x 7)))

prune2.8s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes42.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 26.6b

bsearch130.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
585.0ms1848×body640valid
509.0ms623×body1280valid
366.0ms4135×body80valid
243.0ms930×body320valid
63.0ms466×body160valid