Details

Time bar (total: 20.9s)

sample574.0ms

Algorithm
intervals
Results
337.0ms210×body10240exit
56.0ms389×body80nan
34.0ms241×body80valid
7.0ms22×body160valid

simplify377.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
376.0ms
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
8×add-sqr-sqrt
4×add-cube-cbrt sqrt-prod add-log-exp
3×pow1 fma-def
2×expm1-log1p-u flip3-+ add-cbrt-cube sqrt-div add-exp-log flip-+ hypot-def insert-posit16 log1p-expm1-u distribute-lft-out
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2
Counts
2 → 39
Calls
2 calls:
Slowest
11.0ms
(sqrt (+ (exp x) 1))
7.0ms
(+ (exp x) 1)

series59.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
47.0ms
(sqrt (+ (exp x) 1))
12.0ms
(+ (exp x) 1)

simplify973.0ms

Counts
20 → 45
Calls
20 calls:
Slowest
518.0ms
(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
106.0ms
(sqrt (- (* (exp x) (exp x)) (* 1 1)))
104.0ms
(sqrt (+ (pow (exp x) 3) (pow 1 3)))
94.0ms
(+ x (+ (* 1/2 (pow x 2)) 2))
18.0ms
(sqrt (* (cbrt (+ (exp x) 1)) (cbrt (+ (exp x) 1))))

prune400.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt
4×*-un-lft-identity sqrt-pow1 add-cube-cbrt
3×pow1 exp-prod sqrt-prod
2×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
1×rem-sqrt-square hypot-udef pow1/2
Counts
2 → 30
Calls
2 calls:
Slowest
2.0ms
(sqrt (exp x))
0.0ms
(hypot (sqrt (exp x)) 1)

series132.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
118.0ms
(hypot (sqrt (exp x)) 1)
13.0ms
(sqrt (exp x))

simplify637.0ms

Counts
14 → 36
Calls
14 calls:
Slowest
457.0ms
(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
110.0ms
(+ (* 1/2 x) (+ (* 1/8 (pow x 2)) 1))
20.0ms
(exp (* (cbrt x) (cbrt x)))
10.0ms
(sqrt (+ (exp x) 1))
8.0ms
(sqrt (+ (exp x) 1))

prune334.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 2 expressions with local error:

0.0b
(pow E (/ x 2))
0.0b
(hypot (pow E (/ x 2)) 1)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
13×pow-unpow
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
3×pow1 unpow-prod-down add-exp-log
2×expm1-log1p-u add-cbrt-cube pow-exp insert-posit16 log1p-expm1-u add-log-exp
1×pow-to-exp e-exp-1 hypot-udef pow-pow div-inv sqr-pow
Counts
2 → 42
Calls
2 calls:
Slowest
5.0ms
(pow E (/ x 2))
0.0ms
(hypot (pow E (/ x 2)) 1)

series126.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
102.0ms
(hypot (pow E (/ x 2)) 1)
24.0ms
(pow E (/ x 2))

simplify1.5s

Counts
24 → 48
Calls
24 calls:
Slowest
493.0ms
(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
373.0ms
(sqrt (+ (pow (exp (* 1/2 x)) 2) 1))
348.0ms
(sqrt (+ (pow (exp (* 1/2 x)) 2) 1))
88.0ms
(+ (* 1/2 x) (+ (* 1/8 (pow x 2)) 1))
36.0ms
(pow (* (cbrt E) (cbrt E)) (/ x 2))

prune475.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
31×pow1
15×add-sqr-sqrt
11×*-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
7×hypot-udef pow-plus pow-prod-up
6×associate-*r*
4×expm1-log1p-u sqrt-pow1 associate-*l* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×pow2 exp-prod sqrt-unprod swap-sqr pow-sqr sqrt-prod
2×pow3 *-commutative unswap-sqr
1×cbrt-prod rem-sqrt-square rem-square-sqrt pow1/2 pow1/3 rem-cbrt-cube
Counts
4 → 94
Calls
4 calls:
Slowest
36.0ms
(* (* (hypot (sqrt (exp x)) 1) (hypot (sqrt (exp x)) 1)) (hypot (sqrt (exp x)) 1))
16.0ms
(cbrt (* (* (hypot (sqrt (exp x)) 1) (hypot (sqrt (exp x)) 1)) (hypot (sqrt (exp x)) 1)))
6.0ms
(* (hypot (sqrt (exp x)) 1) (hypot (sqrt (exp x)) 1))
5.0ms
(sqrt (exp x))

series404.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
154.0ms
(* (hypot (sqrt (exp x)) 1) (hypot (sqrt (exp x)) 1))
147.0ms
(* (* (hypot (sqrt (exp x)) 1) (hypot (sqrt (exp x)) 1)) (hypot (sqrt (exp x)) 1))
78.0ms
(cbrt (* (* (hypot (sqrt (exp x)) 1) (hypot (sqrt (exp x)) 1)) (hypot (sqrt (exp x)) 1)))
24.0ms
(sqrt (exp x))

simplify4.3s

Counts
72 → 106
Calls
72 calls:
Slowest
729.0ms
(* (* (+ (* (sqrt (exp x)) (sqrt (exp x))) (* 1 1)) (+ (* (sqrt (exp x)) (sqrt (exp x))) (* 1 1))) (+ (* (sqrt (exp x)) (sqrt (exp x))) (* 1 1)))
508.0ms
(* (* (* (* (hypot (sqrt (exp x)) 1) (hypot (sqrt (exp x)) 1)) (* (hypot (sqrt (exp x)) 1) (hypot (sqrt (exp x)) 1))) (* (hypot (sqrt (exp x)) 1) (hypot (sqrt (exp x)) 1))) (* (* (hypot (sqrt (exp x)) 1) (hypot (sqrt (exp x)) 1)) (hypot (sqrt (exp x)) 1)))
441.0ms
(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
405.0ms
(* (* (* (* (hypot (sqrt (exp x)) 1) (hypot (sqrt (exp x)) 1)) (hypot (sqrt (exp x)) 1)) (* (* (hypot (sqrt (exp x)) 1) (hypot (sqrt (exp x)) 1)) (hypot (sqrt (exp x)) 1))) (* (* (hypot (sqrt (exp x)) 1) (hypot (sqrt (exp x)) 1)) (hypot (sqrt (exp x)) 1)))
291.0ms
(sqrt (pow (+ (exp x) 1) 3))

prune1.1s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes22.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample9.3s

Algorithm
intervals
Results
5.3s6851×body10240exit
1.8s12876×body80nan
1.5s7419×body80valid
227.0ms708×body160valid