Details

Time bar (total: 44.4s)

sample385.0ms

Algorithm
intervals
Results
181.0ms187×body10240exit
94.0ms392×body80nan
29.0ms234×body80valid
6.0ms26×body160valid

simplify307.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
307.0ms
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (exp x) 1)
0.0b
(sqrt (+ (exp x) 1))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
7×*-un-lft-identity
4×add-sqr-sqrt sqrt-prod add-log-exp
3×pow1 add-cube-cbrt
2×flip3-+ add-cbrt-cube sqrt-div add-exp-log flip-+ insert-posit16 distribute-lft-out
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2
Counts
2 → 30
Calls
2 calls:
Slowest
11.0ms
(+ (exp x) 1)
8.0ms
(sqrt (+ (exp x) 1))

series63.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
42.0ms
(sqrt (+ (exp x) 1))
21.0ms
(+ (exp x) 1)

simplify783.0ms

Counts
16 → 36
Calls
16 calls:
Slowest
405.0ms
(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
85.0ms
(+ x (+ (* 1/2 (pow x 2)) 2))
76.0ms
(sqrt (+ (pow (exp x) 3) (pow 1 3)))
54.0ms
(sqrt (- (* (exp x) (exp x)) (* 1 1)))
21.0ms
(sqrt (* (cbrt (+ (exp x) 1)) (cbrt (+ (exp x) 1))))

prune305.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (sqrt (+ (exp x) 1)))
0.0b
(cbrt (sqrt (+ (exp x) 1)))
0.0b
(cbrt (sqrt (+ (exp x) 1)))
0.0b
(* (cbrt (sqrt (+ (exp x) 1))) (cbrt (sqrt (+ (exp x) 1))))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
69×cbrt-prod
44×add-sqr-sqrt
42×*-un-lft-identity
40×sqrt-prod
22×add-cube-cbrt
18×cbrt-div sqrt-div
14×swap-sqr
11×pow1
10×associate-*r* associate-*l*
9×flip3-+ pow1/3 flip-+ distribute-lft-out unswap-sqr
6×add-exp-log
4×frac-times add-cbrt-cube insert-posit16 add-log-exp
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 124
Calls
4 calls:
Slowest
70.0ms
(* (cbrt (sqrt (+ (exp x) 1))) (cbrt (sqrt (+ (exp x) 1))))
8.0ms
(cbrt (sqrt (+ (exp x) 1)))
5.0ms
(cbrt (sqrt (+ (exp x) 1)))
5.0ms
(cbrt (sqrt (+ (exp x) 1)))

series548.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
154.0ms
(cbrt (sqrt (+ (exp x) 1)))
141.0ms
(* (cbrt (sqrt (+ (exp x) 1))) (cbrt (sqrt (+ (exp x) 1))))
133.0ms
(cbrt (sqrt (+ (exp x) 1)))
120.0ms
(cbrt (sqrt (+ (exp x) 1)))

simplify5.2s

Counts
129 → 136
Calls
129 calls:
Slowest
295.0ms
(* (cbrt (sqrt (+ (pow (exp x) 3) (pow 1 3)))) (cbrt (sqrt (- (* (exp x) (exp x)) (* 1 1)))))
265.0ms
(* (cbrt (sqrt (- (* (exp x) (exp x)) (* 1 1)))) (cbrt (sqrt (+ (pow (exp x) 3) (pow 1 3)))))
251.0ms
(* (cbrt (sqrt (+ (pow (exp x) 3) (pow 1 3)))) (cbrt (sqrt (+ (exp x) 1))))
247.0ms
(+ (* 1/12 (* x (pow 2 1/6))) (+ (pow 2 1/6) (* 7/288 (* (pow x 2) (pow 2 1/6)))))
227.0ms
(+ (* 1/12 (* x (pow 2 1/6))) (+ (pow 2 1/6) (* 7/288 (* (pow x 2) (pow 2 1/6)))))

prune1.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (cbrt (cbrt (sqrt (+ (exp x) 1)))) (cbrt (cbrt (sqrt (+ (exp x) 1)))))
0.0b
(cbrt (sqrt (+ (exp x) 1)))
0.0b
(cbrt (sqrt (+ (exp x) 1)))
0.0b
(cbrt (sqrt (+ (exp x) 1)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
145×cbrt-prod
62×add-sqr-sqrt
46×*-un-lft-identity
42×sqrt-prod
30×cbrt-div
26×add-cube-cbrt
18×sqrt-div
17×swap-sqr
16×unswap-sqr
13×associate-*r* associate-*l*
11×pow1
9×flip3-+ pow1/3 flip-+ distribute-lft-out
6×add-exp-log
4×frac-times add-cbrt-cube insert-posit16 add-log-exp
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 140
Calls
4 calls:
Slowest
51.0ms
(* (cbrt (cbrt (sqrt (+ (exp x) 1)))) (cbrt (cbrt (sqrt (+ (exp x) 1)))))
5.0ms
(cbrt (sqrt (+ (exp x) 1)))
5.0ms
(cbrt (sqrt (+ (exp x) 1)))
5.0ms
(cbrt (sqrt (+ (exp x) 1)))

series490.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
139.0ms
(* (cbrt (cbrt (sqrt (+ (exp x) 1)))) (cbrt (cbrt (sqrt (+ (exp x) 1)))))
122.0ms
(cbrt (sqrt (+ (exp x) 1)))
117.0ms
(cbrt (sqrt (+ (exp x) 1)))
112.0ms
(cbrt (sqrt (+ (exp x) 1)))

simplify6.5s

Counts
155 → 152
Calls
155 calls:
Slowest
681.0ms
(+ (* 1/12 (* x (pow 2 1/6))) (+ (pow 2 1/6) (* 7/288 (* (pow x 2) (pow 2 1/6)))))
294.0ms
(* (cbrt (cbrt (sqrt (- (* (exp x) (exp x)) (* 1 1))))) (cbrt (cbrt (sqrt (+ (pow (exp x) 3) (pow 1 3))))))
238.0ms
(+ (* 1/12 (* x (pow 2 1/6))) (+ (pow 2 1/6) (* 7/288 (* (pow x 2) (pow 2 1/6)))))
234.0ms
(+ (* 1/12 (* x (pow 2 1/6))) (+ (pow 2 1/6) (* 7/288 (* (pow x 2) (pow 2 1/6)))))
211.0ms
(* (cbrt (cbrt (sqrt (+ (pow (exp x) 3) (pow 1 3))))) (cbrt (cbrt (sqrt (+ (exp x) 1)))))

prune2.0s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

5.4b
(- (* 1 1) (* (exp x) 1))
0.2b
(/ (+ (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
0.1b
(pow (exp x) 3)
0.0b
(* (exp x) (exp x))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
77×*-un-lft-identity
35×add-sqr-sqrt
33×add-cube-cbrt
30×times-frac
24×distribute-lft-out
21×exp-prod
19×unpow-prod-down cube-prod
12×pow1
10×associate-/l*
9×add-cbrt-cube
6×add-exp-log add-log-exp
5×cube-mult
4×pow-pow pow-prod-down pow-sqr sum-cubes pow-prod-up insert-posit16
3×pow-unpow associate-/r* swap-sqr associate-*r* associate-*l*
2×flip3-+ associate-/r/ flip-+ associate-/l/
1×pow2 pow-to-exp cbrt-undiv clear-num sub-neg frac-2neg pow-plus flip3-- distribute-rgt-out-- diff-log unpow3 div-exp pow-exp prod-exp *-commutative cbrt-unprod div-inv flip-- rem-cube-cbrt unswap-sqr sqr-pow
Counts
4 → 136
Calls
4 calls:
Slowest
136.0ms
(/ (+ (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
15.0ms
(- (* 1 1) (* (exp x) 1))
12.0ms
(* (exp x) (exp x))
3.0ms
(pow (exp x) 3)

series171.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
100.0ms
(/ (+ (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
27.0ms
(pow (exp x) 3)
23.0ms
(* (exp x) (exp x))
21.0ms
(- (* 1 1) (* (exp x) 1))

simplify14.2s

Counts
142 → 148
Calls
142 calls:
Slowest
314.0ms
(/ (* (* (+ (pow (exp x) 3) (pow 1 3)) (+ (pow (exp x) 3) (pow 1 3))) (+ (pow (exp x) 3) (pow 1 3))) (* (* (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))))
294.0ms
(+ (pow (pow (exp x) 3) 3) (pow (pow 1 3) 3))
271.0ms
(/ (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))) (* (cbrt (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))) (cbrt (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))))
269.0ms
(/ (+ (pow (exp x) 3) (* 1 1)) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
258.0ms
(/ (+ (pow (exp x) 3) (pow 1 3)) (cbrt (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))))

prune1.7s

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes49.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample9.8s

Algorithm
intervals
Results
6.4s6420×body10240exit
1.5s12573×body80nan
1.4s7430×body80valid
171.0ms696×body160valid