Details

Time bar (total: 40.0s)

sample1.2s

Algorithm
intervals
Results
1.0s212×body10240exit
83.0ms372×body80nan
34.0ms238×body80valid
9.0ms22×body160valid

simplify354.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
353.0ms
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite35.0ms

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
16.0ms
(+ (exp x) 1)
16.0ms
(sqrt (+ (exp x) 1))

series95.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
68.0ms
(sqrt (+ (exp x) 1))
27.0ms
(+ (exp x) 1)

simplify789.0ms

Counts
16 → 36
Calls
16 calls:
Slowest
401.0ms
(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
92.0ms
(sqrt (- (* (exp x) (exp x)) (* 1 1)))
86.0ms
(sqrt (+ (pow (exp x) 3) (pow 1 3)))
81.0ms
(+ x (+ (* 1/2 (pow x 2)) 2))
18.0ms
(* (exp (exp x)) (exp 1))

prune299.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (sqrt (+ (exp x) 1))) (sqrt (sqrt (+ (exp x) 1))))
0.0b
(+ (exp x) 1)
0.0b
(+ (exp x) 1)
0.0b
(sqrt (+ (exp x) 1))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
86×sqrt-prod
48×add-sqr-sqrt
37×*-un-lft-identity
33×sqrt-pow1
28×pow1
26×sqrt-div
18×swap-sqr
17×pow1/2 add-cube-cbrt
10×associate-*r* associate-*l*
9×flip3-+ pow-prod-up flip-+ distribute-lft-out unswap-sqr
8×add-log-exp
6×add-cbrt-cube add-exp-log
5×pow-prod-down pow-sqr
4×frac-times insert-posit16
2×+-commutative sum-log associate-*l/ associate-*r/
1×pow2 rem-sqrt-square rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 132
Calls
4 calls:
Slowest
52.0ms
(* (sqrt (sqrt (+ (exp x) 1))) (sqrt (sqrt (+ (exp x) 1))))
7.0ms
(sqrt (+ (exp x) 1))
7.0ms
(+ (exp x) 1)
6.0ms
(+ (exp x) 1)

series112.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
51.0ms
(sqrt (+ (exp x) 1))
38.0ms
(* (sqrt (sqrt (+ (exp x) 1))) (sqrt (sqrt (+ (exp x) 1))))
14.0ms
(+ (exp x) 1)
8.0ms
(+ (exp x) 1)

simplify4.7s

Counts
150 → 144
Calls
150 calls:
Slowest
322.0ms
(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
320.0ms
(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
277.0ms
(* (sqrt (sqrt (+ (pow (exp x) 3) (pow 1 3)))) (sqrt (sqrt (- (* (exp x) (exp x)) (* 1 1)))))
251.0ms
(* (sqrt (sqrt (- (* (exp x) (exp x)) (* 1 1)))) (sqrt (sqrt (+ (pow (exp x) 3) (pow 1 3)))))
224.0ms
(* (* (* (sqrt (sqrt (+ (exp x) 1))) (sqrt (sqrt (+ (exp x) 1)))) (sqrt (sqrt (+ (exp x) 1)))) (* (* (sqrt (sqrt (+ (exp x) 1))) (sqrt (sqrt (+ (exp x) 1)))) (sqrt (sqrt (+ (exp x) 1)))))

prune1.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (exp x) 1) (+ (exp x) 1))
0.0b
(+ (exp x) 1)
0.0b
(+ (exp x) 1)
0.0b
(pow (* (+ (exp x) 1) (+ (exp x) 1)) 1/4)

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
19×pow1
11×add-sqr-sqrt
9×add-exp-log add-cube-cbrt
8×flip3-+ flip-+ distribute-lft-out add-log-exp
6×pow-pow add-cbrt-cube swap-sqr
4×frac-times associate-*r* associate-*l* insert-posit16
3×pow-unpow
2×pow2 +-commutative sum-log pow-plus pow-prod-down associate-*l/ pow-exp prod-exp associate-*r/ pow-sqr pow-prod-up
1×distribute-rgt-in pow-to-exp unpow-prod-down distribute-lft-in *-commutative cbrt-unprod unswap-sqr sqr-pow
Counts
4 → 89
Calls
4 calls:
Slowest
38.0ms
(* (+ (exp x) 1) (+ (exp x) 1))
28.0ms
(pow (* (+ (exp x) 1) (+ (exp x) 1)) 1/4)
9.0ms
(+ (exp x) 1)
6.0ms
(+ (exp x) 1)

series195.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
144.0ms
(pow (* (+ (exp x) 1) (+ (exp x) 1)) 1/4)
23.0ms
(* (+ (exp x) 1) (+ (exp x) 1))
14.0ms
(+ (exp x) 1)
14.0ms
(+ (exp x) 1)

simplify5.9s

Counts
69 → 101
Calls
69 calls:
Slowest
523.0ms
(* (+ (pow (exp x) 3) (pow 1 3)) (- (* (exp x) (exp x)) (* 1 1)))
487.0ms
(* (+ (pow (exp x) 3) (pow 1 3)) (+ (pow (exp x) 3) (pow 1 3)))
480.0ms
(* (- (exp x) 1) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
471.0ms
(* (- (* (exp x) (exp x)) (* 1 1)) (- (* (exp x) (exp x)) (* 1 1)))
405.0ms
(* (* (* (+ (exp x) 1) (+ (exp x) 1)) (+ (exp x) 1)) (* (* (+ (exp x) 1) (+ (exp x) 1)) (+ (exp x) 1)))

prune869.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

5.5b
(- (* 1 1) (* (exp x) 1))
0.3b
(/ (+ (+ (exp x) 1) (* (* (exp x) (exp x)) (+ (* (exp x) (exp x)) (exp x)))) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
0.0b
(* (* (exp x) (exp x)) (+ (* (exp x) (exp x)) (exp x)))
0.0b
(* (exp x) (exp x))

rewrite341.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
24×*-un-lft-identity
23×add-cube-cbrt
18×exp-prod
16×pow1
13×add-cbrt-cube
9×times-frac add-exp-log
8×associate-*r*
7×flip3-+ pow-prod-down flip-+
6×associate-*r/ add-log-exp associate-/l/
4×associate-*l* frac-add prod-exp pow-sqr pow-prod-up cbrt-unprod insert-posit16
3×associate-/r* swap-sqr associate-/l*
2×associate-/r/ *-commutative unswap-sqr
1×pow2 distribute-rgt-in cbrt-undiv clear-num sub-neg frac-2neg distribute-lft-in distribute-lft1-in pow-plus distribute-rgt-out flip3-- distribute-rgt-out-- diff-log div-exp div-inv flip--
Counts
4 → 111
Calls
4 calls:
Slowest
198.0ms
(/ (+ (+ (exp x) 1) (* (* (exp x) (exp x)) (+ (* (exp x) (exp x)) (exp x)))) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
101.0ms
(* (* (exp x) (exp x)) (+ (* (exp x) (exp x)) (exp x)))
21.0ms
(- (* 1 1) (* (exp x) 1))
19.0ms
(* (exp x) (exp x))

series257.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
166.0ms
(/ (+ (+ (exp x) 1) (* (* (exp x) (exp x)) (+ (* (exp x) (exp x)) (exp x)))) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
60.0ms
(* (* (exp x) (exp x)) (+ (* (exp x) (exp x)) (exp x)))
16.0ms
(- (* 1 1) (* (exp x) 1))
14.0ms
(* (exp x) (exp x))

simplify13.0s

Counts
103 → 123
Calls
103 calls:
Slowest
1.0s
(/ (* (* (+ (+ (exp x) 1) (* (* (exp x) (exp x)) (+ (* (exp x) (exp x)) (exp x)))) (+ (+ (exp x) 1) (* (* (exp x) (exp x)) (+ (* (exp x) (exp x)) (exp x))))) (+ (+ (exp x) 1) (* (* (exp x) (exp x)) (+ (* (exp x) (exp x)) (exp x))))) (* (* (+ (* (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)))))
466.0ms
(/ (+ (+ (exp x) 1) (* (* (exp x) (exp x)) (+ (* (exp x) (exp x)) (exp x)))) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
454.0ms
(+ (* (+ (pow (exp x) 3) (pow 1 3)) (+ (* (* (exp x) (exp x)) (* (exp x) (exp x))) (- (* (exp x) (exp x)) (* (* (exp x) (exp x)) (exp x))))) (* (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))) (* (* (exp x) (exp x)) (+ (pow (* (exp x) (exp x)) 3) (pow (exp x) 3)))))
446.0ms
(* (pow (exp x) 2) (+ (pow (exp x) 2) (exp x)))
422.0ms
(* (pow (exp x) 2) (+ (pow (exp x) 2) (exp x)))

prune1.8s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes25.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch1.0ms

end0.0ms

sample8.3s

Algorithm
intervals
Results
4.8s6700×body10240exit
2.2s12876×body80nan
736.0ms7372×body80valid
196.0ms737×body160valid