Details

Time bar (total: 40.3s)

sample36.0ms

Algorithm
intervals
Results
14.0ms68×body640valid
7.0ms127×body80valid
6.0ms42×body320valid
2.0ms19×body160valid

simplify14.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
14.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize12.0ms

Local error

Found 3 expressions with local error:

3.3b
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
0.0b
(/ 1 (+ x 1))
0.0b
(/ 1 (- x 1))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
98×*-un-lft-identity
72×add-sqr-sqrt
69×times-frac
32×add-cube-cbrt
27×distribute-lft-out--
17×difference-of-squares
11×associate-/r* add-exp-log
10×distribute-lft-out
7×add-cbrt-cube
6×associate-/r/ div-inv associate-/l*
5×pow1 add-log-exp
4×difference-of-sqr-1 div-exp
3×insert-posit16 flip--
2×cbrt-undiv rec-exp clear-num frac-2neg flip3-- 1-exp flip-+ pow-flip inv-pow
1×sub-neg flip3-+ diff-log frac-sub
Counts
3 → 128
Calls
3 calls:
Slowest
45.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
16.0ms
(/ 1 (- x 1))
15.0ms
(/ 1 (+ x 1))

series125.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
78.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
25.0ms
(/ 1 (- x 1))
23.0ms
(/ 1 (+ x 1))

simplify5.2s

Counts
153 → 137
Calls
153 calls:
Slowest
395.0ms
(/ (* (* 1 1) 1) (* (* (+ x 1) (+ x 1)) (+ x 1)))
383.0ms
(- (+ (* 2 (/ 1 (pow x 4))) (+ (* 2 (/ 1 (pow x 6))) (* 2 (/ 1 (pow x 2))))))
383.0ms
(- (+ (* 2 (/ 1 (pow x 4))) (+ (* 2 (/ 1 (pow x 6))) (* 2 (/ 1 (pow x 2))))))
331.0ms
(/ (* (* 1 1) 1) (* (* (- x 1) (- x 1)) (- x 1)))
250.0ms
(- (+ (/ 1 (pow x 3)) (/ 1 x)) (/ 1 (pow x 2)))

prune889.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ 1 (- (* x x) 1))
0.0b
(* (/ 1 (- (* x x) 1)) -2)

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt times-frac
32×*-un-lft-identity
24×associate-*l* add-cube-cbrt
15×add-exp-log
14×difference-of-squares
9×add-cbrt-cube
7×difference-of-sqr-1
6×associate-/r*
5×pow1
4×div-exp prod-exp associate-/r/
3×associate-*r* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp flip3-- 1-exp cbrt-unprod insert-posit16 div-inv flip-- add-log-exp
1×clear-num frac-2neg pow-prod-down associate-*l/ *-commutative pow-flip inv-pow
Counts
2 → 93
Calls
2 calls:
Slowest
43.0ms
(* (/ 1 (- (* x x) 1)) -2)
13.0ms
(/ 1 (- (* x x) 1))

series69.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
37.0ms
(/ 1 (- (* x x) 1))
32.0ms
(* (/ 1 (- (* x x) 1)) -2)

simplify8.8s

Counts
94 → 99
Calls
94 calls:
Slowest
580.0ms
(+ (/ 1 (pow x 4)) (+ (/ 1 (pow x 6)) (/ 1 (pow x 2))))
488.0ms
(* (/ (* (* 1 1) 1) (* (* (- (* x x) 1) (- (* x x) 1)) (- (* x x) 1))) (* (* -2 -2) -2))
435.0ms
(* (* (* (/ 1 (- (* x x) 1)) (/ 1 (- (* x x) 1))) (/ 1 (- (* x x) 1))) (* (* -2 -2) -2))
406.0ms
(- (+ (* 2 (/ 1 (pow x 4))) (+ (* 2 (/ 1 (pow x 6))) (* 2 (/ 1 (pow x 2))))))
399.0ms
(- (+ (* 2 (/ 1 (pow x 4))) (+ (* 2 (/ 1 (pow x 6))) (* 2 (/ 1 (pow x 2))))))

prune620.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

16.6b
(cbrt (- (* x x) 1))
16.6b
(cbrt (- (* x x) 1))
16.6b
(cbrt (- (* x x) 1))
0.4b
(/ 1 (* (cbrt (- (* x x) 1)) (cbrt (- (* x x) 1))))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod cbrt-div
15×add-exp-log
12×add-sqr-sqrt pow1 *-un-lft-identity
9×flip3-- pow1/3 add-cube-cbrt pow-flip flip--
8×associate-/r/
7×add-cbrt-cube
6×difference-of-squares
4×frac-times div-exp insert-posit16 add-log-exp
3×times-frac difference-of-sqr-1 prod-exp associate-/l*
2×cbrt-undiv rec-exp 1-exp pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 clear-num associate-/r* frac-2neg pow-plus cbrt-unprod div-inv inv-pow
Counts
4 → 95
Calls
4 calls:
Slowest
64.0ms
(/ 1 (* (cbrt (- (* x x) 1)) (cbrt (- (* x x) 1))))
10.0ms
(cbrt (- (* x x) 1))
6.0ms
(cbrt (- (* x x) 1))
5.0ms
(cbrt (- (* x x) 1))

series574.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
164.0ms
(cbrt (- (* x x) 1))
144.0ms
(cbrt (- (* x x) 1))
143.0ms
(cbrt (- (* x x) 1))
123.0ms
(/ 1 (* (cbrt (- (* x x) 1)) (cbrt (- (* x x) 1))))

simplify7.4s

Counts
68 → 107
Calls
68 calls:
Slowest
408.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
358.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
306.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
292.0ms
(- (pow (/ 1 x) -2/3) (+ (* 1/9 (pow (/ 1 (pow x 10)) 1/3)) (* 1/3 (pow (/ 1 (pow x 4)) 1/3))))
262.0ms
(- (pow (/ -1 x) -2/3) (+ (* 1/9 (pow (/ 1 (pow x 10)) 1/3)) (* 1/3 (pow (/ 1 (pow x 4)) 1/3))))

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

16.6b
(cbrt (- (* x x) 1))
16.6b
(cbrt (- (* x x) 1))
0.2b
(pow (cbrt (- (* x x) 1)) -2)
0.2b
(/ 1 (cbrt (- (* x x) 1)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
42×cbrt-prod
34×add-sqr-sqrt *-un-lft-identity
27×times-frac add-cube-cbrt
14×difference-of-squares
9×associate-/r* unpow-prod-down add-exp-log
7×difference-of-sqr-1
6×pow1 cbrt-div
5×add-cbrt-cube
4×pow1/3 insert-posit16 add-log-exp
3×pow-unpow flip3-- flip-- associate-/l*
2×pow-pow div-exp associate-/r/ pow-flip
1×pow-to-exp cbrt-undiv rec-exp clear-num frac-2neg 1-exp pow-exp div-inv inv-pow sqr-pow
Counts
4 → 118
Calls
4 calls:
Slowest
14.0ms
(pow (cbrt (- (* x x) 1)) -2)
13.0ms
(/ 1 (cbrt (- (* x x) 1)))
11.0ms
(cbrt (- (* x x) 1))
11.0ms
(cbrt (- (* x x) 1))

series659.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
223.0ms
(pow (cbrt (- (* x x) 1)) -2)
147.0ms
(/ 1 (cbrt (- (* x x) 1)))
145.0ms
(cbrt (- (* x x) 1))
143.0ms
(cbrt (- (* x x) 1))

simplify10.9s

Counts
114 → 130
Calls
114 calls:
Slowest
453.0ms
(pow (* (cbrt (cbrt (- (* x x) 1))) (cbrt (cbrt (- (* x x) 1)))) -2)
366.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
361.0ms
(pow (cbrt (* (cbrt (- (* x x) 1)) (cbrt (- (* x x) 1)))) -2)
343.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
336.0ms
(pow (sqrt (cbrt (- (* x x) 1))) -2)

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes28.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch1.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
864.0ms4196×body80valid
686.0ms1912×body640valid
319.0ms1295×body320valid
122.0ms597×body160valid