Details

Time bar (total: 1.7m)

sample29.0ms

Algorithm
intervals
Results
19.0ms256×body80valid

simplify10.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
10.0ms
(/ x (+ (* x x) 1))

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize8.0ms

Local error

Found 1 expressions with local error:

14.3b
(/ x (+ (* x x) 1))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
3×associate-/r* add-cbrt-cube add-exp-log associate-/l*
2×associate-/r/
1×pow1 cbrt-undiv clear-num frac-2neg flip3-+ div-exp flip-+ insert-posit16 div-inv add-log-exp
Counts
1 → 30
Calls
1 calls:
Slowest
10.0ms
(/ x (+ (* x x) 1))

series64.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
64.0ms
(/ x (+ (* x x) 1))

simplify2.8s

Counts
43 → 33
Calls
43 calls:
Slowest
439.0ms
(/ x (+ (pow (* x x) 3) (pow 1 3)))
410.0ms
(* (cbrt (/ x (+ (* x x) 1))) (cbrt (/ x (+ (* x x) 1))))
321.0ms
(/ (* (* x x) x) (* (* (+ (* x x) 1) (+ (* x x) 1)) (+ (* x x) 1)))
270.0ms
(* (* (/ x (+ (* x x) 1)) (/ x (+ (* x x) 1))) (/ x (+ (* x x) 1)))
238.0ms
(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))

prune227.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

14.3b
(sqrt (+ (* x x) 1))
14.3b
(sqrt (+ (* x x) 1))
0.0b
(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
0.0b
(/ x (sqrt (+ (* x x) 1)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
164×add-sqr-sqrt
162×*-un-lft-identity add-cube-cbrt
156×sqrt-prod
27×associate-/l*
22×sqrt-div
18×associate-/r/
12×associate-/r*
11×flip3-+ add-cbrt-cube add-exp-log flip-+
9×div-inv
6×pow1
4×cbrt-undiv div-exp insert-posit16 add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
1×associate-/l/
Counts
4 → 266
Calls
4 calls:
Slowest
35.0ms
(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
20.0ms
(/ x (sqrt (+ (* x x) 1)))
7.0ms
(sqrt (+ (* x x) 1))
7.0ms
(sqrt (+ (* x x) 1))

series240.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
86.0ms
(/ x (sqrt (+ (* x x) 1)))
56.0ms
(sqrt (+ (* x x) 1))
49.0ms
(sqrt (+ (* x x) 1))
49.0ms
(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))

simplify28.6s

Counts
448 → 278
Calls
448 calls:
Slowest
557.0ms
(/ (/ x (sqrt (+ (pow (* x x) 3) (pow 1 3)))) (sqrt (* (cbrt (+ (* x x) 1)) (cbrt (+ (* x x) 1)))))
548.0ms
(* (* (/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1))) (/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))) (/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1))))
532.0ms
(/ (/ x (sqrt (+ (pow (* x x) 3) (pow 1 3)))) (sqrt 1))
499.0ms
(/ (/ x (sqrt (+ (pow (* x x) 3) (pow 1 3)))) 1)
490.0ms
(/ (/ (* (* x x) x) (* (* (sqrt (+ (* x x) 1)) (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))) (* (* (sqrt (+ (* x x) 1)) (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1))))

prune2.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

20.4b
(* (/ x (+ (* (* x x) (* x x)) -1)) (- (* x x) 1))
1.6b
(/ x (+ (* (* x x) (* x x)) -1))
0.1b
(* (* x x) (* x x))
0.0b
(- (* x x) 1)

rewrite250.0ms

Algorithm
rewrite-expression-head
Rules
117×pow1
36×pow-prod-up
29×add-sqr-sqrt
25×times-frac
24×*-un-lft-identity pow-prod-down
23×add-cbrt-cube add-exp-log
22×pow-sqr add-cube-cbrt
19×associate-*l*
18×pow-plus
13×pow2
10×prod-exp cbrt-unprod
7×difference-of-sqr--1 associate-*r*
6×add-log-exp
4×associate-/r* associate-/r/ insert-posit16 difference-of-squares
3×sub-neg flip3-- flip-- associate-/l* unswap-sqr
2×distribute-rgt-in frac-times cbrt-undiv distribute-lft-in flip3-+ difference-of-sqr-1 div-exp associate-*r/ *-commutative flip-+ div-inv
1×clear-num frac-2neg diff-log swap-sqr associate-*l/
Counts
4 → 163
Calls
4 calls:
Slowest
175.0ms
(* (/ x (+ (* (* x x) (* x x)) -1)) (- (* x x) 1))
42.0ms
(/ x (+ (* (* x x) (* x x)) -1))
24.0ms
(* (* x x) (* x x))
7.0ms
(- (* x x) 1)

series307.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
124.0ms
(/ x (+ (* (* x x) (* x x)) -1))
93.0ms
(* (/ x (+ (* (* x x) (* x x)) -1)) (- (* x x) 1))
49.0ms
(- (* x x) 1)
41.0ms
(* (* x x) (* x x))

simplify36.2s

Counts
200 → 175
Calls
200 calls:
Slowest
847.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
675.0ms
(* (sqrt (/ x (+ (* (* x x) (* x x)) -1))) (sqrt (- (* x x) 1)))
640.0ms
(* (/ x (+ (* (* x x) (* x x)) -1)) (- 1))
611.0ms
(* (- 1) (/ x (+ (* (* x x) (* x x)) -1)))
591.0ms
(* (* (* (* x x) (* x x)) (* (* x x) (* x x))) (* (* x x) (* x x)))

prune1.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

20.0b
(- (+ (/ 1 x) (/ 1 (pow x 5))) (/ 1 (* (* x x) x)))
0.3b
(/ 1 (pow x 5))
0.1b
(* (* x x) x)
0.1b
(/ 1 (* (* x x) x))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
43×pow1
39×add-exp-log
38×*-un-lft-identity
26×add-sqr-sqrt
24×times-frac
23×add-cube-cbrt
20×add-cbrt-cube
15×div-inv
13×pow-flip
12×unpow-prod-down pow-plus div-exp prod-exp pow-prod-up
10×distribute-lft-out--
9×add-log-exp
8×associate-/r* distribute-lft-out
6×rec-exp 1-exp pow-prod-down cbrt-unprod associate-/l*
4×pow2 cbrt-undiv pow-sqr insert-posit16 sqr-pow
3×pow-to-exp associate-*r* pow-exp frac-sub
2×clear-num frac-2neg diff-log pow3 inv-pow
1×sum-log sub-neg flip3-+ flip3-- associate-*l* frac-add associate--l+ *-commutative flip-+ flip-- difference-of-squares unswap-sqr
Counts
4 → 155
Calls
4 calls:
Slowest
125.0ms
(- (+ (/ 1 x) (/ 1 (pow x 5))) (/ 1 (* (* x x) x)))
24.0ms
(/ 1 (* (* x x) x))
23.0ms
(* (* x x) x)
11.0ms
(/ 1 (pow x 5))

series196.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
67.0ms
(/ 1 (pow x 5))
50.0ms
(* (* x x) x)
41.0ms
(/ 1 (* (* x x) x))
37.0ms
(- (+ (/ 1 x) (/ 1 (pow x 5))) (/ 1 (* (* x x) x)))

simplify25.0s

Counts
196 → 167
Calls
196 calls:
Slowest
1.2s
(/ (* (* 1 1) 1) (* (* (* (* x x) x) (* (* x x) x)) (* (* x x) x)))
977.0ms
(/ (* (* 1 1) 1) (* (* (* (* x x) x) (* (* x x) x)) (* (* x x) x)))
879.0ms
(* (* (- (+ (/ 1 x) (/ 1 (pow x 5))) (/ 1 (* (* x x) x))) (- (+ (/ 1 x) (/ 1 (pow x 5))) (/ 1 (* (* x x) x)))) (- (+ (/ 1 x) (/ 1 (pow x 5))) (/ 1 (* (* x x) x))))
669.0ms
(- (* (- (* (/ 1 x) (/ 1 x)) (* (/ 1 (pow x 5)) (/ 1 (pow x 5)))) (* (* x x) x)) (* (- (/ 1 x) (/ 1 (pow x 5))) 1))
631.0ms
(/ (* (cbrt 1) (cbrt 1)) (pow (* (cbrt x) (cbrt x)) 5))

prune1.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes49.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.7b

bsearch121.0ms

end0.0ms

sample708.0ms

Algorithm
intervals
Results
561.0ms8000×body80valid