Details

Time bar (total: 1.3m)

sample342.0ms

Algorithm
intervals
Results
113.0ms191×body10240exit
66.0ms376×body80nan
22.0ms227×body80valid
7.0ms30×body160valid

simplify391.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
390.0ms
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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
17.0ms
(+ (exp x) 1)
16.0ms
(sqrt (+ (exp x) 1))

series79.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
43.0ms
(sqrt (+ (exp x) 1))
36.0ms
(+ (exp x) 1)

simplify733.0ms

Counts
16 → 36
Calls
16 calls:
Slowest
375.0ms
(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
102.0ms
(sqrt (+ (pow (exp x) 3) (pow 1 3)))
76.0ms
(+ x (+ (* 1/2 (pow x 2)) 2))
63.0ms
(sqrt (- (* (exp x) (exp x)) (* 1 1)))
17.0ms
(sqrt (sqrt (+ (exp x) 1)))

prune247.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite280.0ms

Algorithm
rewrite-expression-head
Rules
120×sqrt-div
61×flip3-+ flip-+
60×frac-times
59×pow1
32×*-un-lft-identity
31×pow-prod-up sqrt-prod
30×associate-*l/
29×sqrt-pow1 pow1/2
28×add-sqr-sqrt
26×cbrt-div
18×associate-*r/
14×associate-*r* add-cube-cbrt
11×add-cbrt-cube swap-sqr add-exp-log
10×pow-prod-down
9×pow-sqr
8×associate-*l* distribute-lft-out
7×pow-plus
6×add-log-exp unswap-sqr
4×prod-exp cbrt-unprod insert-posit16
3×pow2 sqrt-unprod
2×pow3 *-commutative
1×cbrt-prod +-commutative sum-log rem-square-sqrt pow1/3 rem-cbrt-cube
Counts
4 → 188
Calls
4 calls:
Slowest
114.0ms
(* (* (sqrt (+ (exp x) 1)) (sqrt (+ (exp x) 1))) (sqrt (+ (exp x) 1)))
87.0ms
(cbrt (* (* (sqrt (+ (exp x) 1)) (sqrt (+ (exp x) 1))) (sqrt (+ (exp x) 1))))
58.0ms
(* (sqrt (+ (exp x) 1)) (sqrt (+ (exp x) 1)))
14.0ms
(+ (exp x) 1)

series151.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
90.0ms
(* (* (sqrt (+ (exp x) 1)) (sqrt (+ (exp x) 1))) (sqrt (+ (exp x) 1)))
42.0ms
(cbrt (* (* (sqrt (+ (exp x) 1)) (sqrt (+ (exp x) 1))) (sqrt (+ (exp x) 1))))
9.0ms
(* (sqrt (+ (exp x) 1)) (sqrt (+ (exp x) 1)))
9.0ms
(+ (exp x) 1)

simplify22.0s

Counts
223 → 200
Calls
223 calls:
Slowest
741.0ms
(cbrt (* (* (sqrt (- (* (exp x) (exp x)) (* 1 1))) (sqrt (+ (exp x) 1))) (sqrt (+ (pow (exp x) 3) (pow 1 3)))))
449.0ms
(cbrt (* (* (sqrt (+ (pow (exp x) 3) (pow 1 3))) (sqrt (+ (pow (exp x) 3) (pow 1 3)))) (sqrt (- (* (exp x) (exp x)) (* 1 1)))))
415.0ms
(* (* (sqrt (+ (pow (exp x) 3) (pow 1 3))) (sqrt (+ (pow (exp x) 3) (pow 1 3)))) (sqrt (+ (pow (exp x) 3) (pow 1 3))))
407.0ms
(* (* (* (sqrt (+ (exp x) 1)) (sqrt (+ (exp x) 1))) (sqrt (+ (exp x) 1))) (* (* (sqrt (+ (exp x) 1)) (sqrt (+ (exp x) 1))) (sqrt (+ (exp x) 1))))
395.0ms
(* (* (sqrt (+ (pow (exp x) 3) (pow 1 3))) (sqrt (+ (pow (exp x) 3) (pow 1 3)))) (sqrt (- (* (exp x) (exp x)) (* 1 1))))

prune2.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

5.8b
(- (* 1 1) (* (exp x) 1))
0.3b
(/ (+ (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
0.1b
(pow (exp x) 3)
0.1b
(* (exp x) (exp x))

rewrite205.0ms

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
144.0ms
(/ (+ (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
27.0ms
(- (* 1 1) (* (exp x) 1))
26.0ms
(* (exp x) (exp x))
3.0ms
(pow (exp x) 3)

series202.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
108.0ms
(/ (+ (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
46.0ms
(pow (exp x) 3)
24.0ms
(- (* 1 1) (* (exp x) 1))
24.0ms
(* (exp x) (exp x))

simplify14.6s

Counts
142 → 148
Calls
142 calls:
Slowest
367.0ms
(/ (* (* (+ (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)))))
285.0ms
(/ (+ (pow (exp x) 3) (pow 1 3)) (cbrt (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))))
283.0ms
(/ (+ (pow (exp x) 3) (pow 1 3)) (cbrt (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))))
282.0ms
(/ (sqrt (+ (pow (exp x) 3) (pow 1 3))) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
276.0ms
(/ (+ (pow (exp x) 3) (pow 1 3)) (cbrt (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))))

prune1.8s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

5.8b
(- (* 1 1) (* (exp x) 1))
5.8b
(- (* 1 1) (* (exp x) 1))
5.8b
(- (* 1 1) (* (exp x) 1))
0.3b
(/ (+ (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (* (* (cbrt (- (* 1 1) (* (exp x) 1))) (cbrt (- (* 1 1) (* (exp x) 1)))) (cbrt (- (* 1 1) (* (exp x) 1))))))

rewrite544.0ms

Algorithm
rewrite-expression-head
Rules
63×*-un-lft-identity
30×times-frac
24×distribute-lft-out
19×add-sqr-sqrt add-cube-cbrt
16×unpow-prod-down cube-prod
10×associate-/l* add-log-exp
6×add-cbrt-cube add-exp-log
4×cube-mult pow1 sum-cubes insert-posit16
3×associate-/r* sub-neg flip3-- distribute-rgt-out-- diff-log flip--
2×flip3-+ associate-/r/ flip-+ associate-/l/
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
4 → 102
Calls
4 calls:
Slowest
481.0ms
(/ (+ (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (* (* (cbrt (- (* 1 1) (* (exp x) 1))) (cbrt (- (* 1 1) (* (exp x) 1)))) (cbrt (- (* 1 1) (* (exp x) 1))))))
21.0ms
(- (* 1 1) (* (exp x) 1))
21.0ms
(- (* 1 1) (* (exp x) 1))
20.0ms
(- (* 1 1) (* (exp x) 1))

series152.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
96.0ms
(/ (+ (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (* (* (cbrt (- (* 1 1) (* (exp x) 1))) (cbrt (- (* 1 1) (* (exp x) 1)))) (cbrt (- (* 1 1) (* (exp x) 1))))))
20.0ms
(- (* 1 1) (* (exp x) 1))
19.0ms
(- (* 1 1) (* (exp x) 1))
16.0ms
(- (* 1 1) (* (exp x) 1))

simplify19.7s

Counts
94 → 114
Calls
94 calls:
Slowest
494.0ms
(/ (cbrt (+ (pow (exp x) 3) (pow 1 3))) (+ (* (exp x) (exp x)) (* (* (cbrt (- (* 1 1) (* (exp x) 1))) (cbrt (- (* 1 1) (* (exp x) 1)))) (cbrt (- (* 1 1) (* (exp x) 1))))))
492.0ms
(/ (+ (pow (exp x) 3) (pow 1 3)) (sqrt (+ (* (exp x) (exp x)) (* (* (cbrt (- (* 1 1) (* (exp x) 1))) (cbrt (- (* 1 1) (* (exp x) 1)))) (cbrt (- (* 1 1) (* (exp x) 1)))))))
487.0ms
(/ (+ (pow (exp x) 3) (pow 1 3)) (cbrt (+ (* (exp x) (exp x)) (* (* (cbrt (- (* 1 1) (* (exp x) 1))) (cbrt (- (* 1 1) (* (exp x) 1)))) (cbrt (- (* 1 1) (* (exp x) 1)))))))
474.0ms
(/ (+ (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (* (* (cbrt (- (* 1 1) (* (exp x) 1))) (cbrt (- (* 1 1) (* (exp x) 1)))) (cbrt (- (* 1 1) (* (exp x) 1))))))
468.0ms
(/ (+ (pow (exp x) 3) (pow 1 3)) (sqrt (+ (* (exp x) (exp x)) (* (* (cbrt (- (* 1 1) (* (exp x) 1))) (cbrt (- (* 1 1) (* (exp x) 1)))) (cbrt (- (* 1 1) (* (exp x) 1)))))))

prune1.6s

Pruning

2 alts after pruning (0 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

bsearch3.0ms

end4.0ms

sample9.7s

Algorithm
intervals
Results
6.4s6454×body10240exit
1.4s7395×body80valid
1.3s12430×body80nan
195.0ms717×body160valid