Details

Time bar (total: 20.1s)

sample613.0ms

Algorithm
intervals
Results
283.0ms191×body10240exit
81.0ms376×body80nan
29.0ms227×body80valid
8.0ms30×body160valid

simplify326.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
326.0ms
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))

prune16.0ms

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))

rewrite32.0ms

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
17.0ms
(+ (exp x) 1)
9.0ms
(sqrt (+ (exp x) 1))

series55.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
39.0ms
(sqrt (+ (exp x) 1))
16.0ms
(+ (exp x) 1)

simplify808.0ms

Counts
20 → 45
Calls
20 calls:
Slowest
427.0ms
(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
104.0ms
(sqrt (+ (pow (exp x) 3) (pow 1 3)))
71.0ms
(sqrt (- (* (exp x) (exp x)) (* 1 1)))
68.0ms
(+ x (+ (* 1/2 (pow x 2)) 2))
16.0ms
(sqrt (* (cbrt (+ (exp x) 1)) (cbrt (+ (exp x) 1))))

prune383.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b
(sqrt (exp x))
0.0b
(hypot (sqrt (exp x)) 1)

rewrite5.0ms

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
4.0ms
(sqrt (exp x))
0.0ms
(hypot (sqrt (exp x)) 1)

series141.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
115.0ms
(hypot (sqrt (exp x)) 1)
26.0ms
(sqrt (exp x))

simplify570.0ms

Counts
14 → 36
Calls
14 calls:
Slowest
418.0ms
(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
76.0ms
(+ (* 1/2 x) (+ (* 1/8 (pow x 2)) 1))
24.0ms
(exp (* (cbrt x) (cbrt x)))
16.0ms
(sqrt (+ (exp x) 1))
9.0ms
(sqrt (+ (exp x) 1))

prune320.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (exp x))
0.3b
(cbrt (exp x))
0.3b
(cbrt (exp x))
0.1b
(* (cbrt (exp x)) (cbrt (exp x)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 85
Calls
4 calls:
Slowest
15.0ms
(* (cbrt (exp x)) (cbrt (exp x)))
3.0ms
(cbrt (exp x))
3.0ms
(cbrt (exp x))
2.0ms
(cbrt (exp x))

series475.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
136.0ms
(* (cbrt (exp x)) (cbrt (exp x)))
136.0ms
(cbrt (exp x))
111.0ms
(cbrt (exp x))
91.0ms
(cbrt (exp x))

simplify929.0ms

Counts
65 → 97
Calls
65 calls:
Slowest
125.0ms
(+ (* 1/3 x) (+ (* 1/18 (pow x 2)) 1))
117.0ms
(+ (* 2/3 x) (+ (* 2/9 (pow x 2)) 1))
106.0ms
(* (* (cbrt (cbrt (exp x))) (cbrt (cbrt (exp x)))) (* (cbrt (cbrt (exp x))) (cbrt (cbrt (exp x)))))
85.0ms
(+ (* 1/3 x) (+ (* 1/18 (pow x 2)) 1))
83.0ms
(+ (* 1/3 x) (+ (* 1/18 (pow x 2)) 1))

prune1.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

5.8b
(- (* 1 1) (* (exp x) 1))
0.3b
(sqrt (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
0.2b
(sqrt (fma (exp x) (* (exp x) (exp x)) 1))
0.1b
(* (exp x) (exp x))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
18×exp-prod
16×*-un-lft-identity add-cube-cbrt
13×pow1
6×add-cbrt-cube sqrt-prod add-log-exp
4×expm1-log1p-u pow-prod-down add-exp-log pow-sqr pow-prod-up insert-posit16 log1p-expm1-u
3×swap-sqr associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 pow1/2 sqrt-div
1×pow2 sub-neg flip3-+ pow-plus flip3-- distribute-rgt-out-- fma-neg diff-log prod-diff prod-exp *-commutative cbrt-unprod flip-+ hypot-def flip-- unswap-sqr
Counts
4 → 90
Calls
4 calls:
Slowest
59.0ms
(sqrt (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
15.0ms
(* (exp x) (exp x))
11.0ms
(- (* 1 1) (* (exp x) 1))
1.0ms
(sqrt (fma (exp x) (* (exp x) (exp x)) 1))

series156.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
68.0ms
(sqrt (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
55.0ms
(sqrt (fma (exp x) (* (exp x) (exp x)) 1))
17.0ms
(* (exp x) (exp x))
17.0ms
(- (* 1 1) (* (exp x) 1))

simplify3.8s

Counts
67 → 102
Calls
67 calls:
Slowest
590.0ms
(* (exp (* (cbrt x) (cbrt x))) (exp (* (cbrt x) (cbrt x))))
329.0ms
(- (+ (sqrt 2) (+ (* 9/4 (/ (pow x 2) (sqrt 2))) (* 3/2 (/ x (sqrt 2))))) (* 9/8 (/ (pow x 2) (pow (sqrt 2) 3))))
242.0ms
(sqrt (- (+ (pow (exp x) 2) 1) (exp x)))
230.0ms
(sqrt (- (+ (pow (exp x) 2) 1) (exp x)))
217.0ms
(sqrt (- (* (* (exp x) (exp x)) (* (exp x) (exp x))) (* (- (* 1 1) (* (exp x) 1)) (- (* 1 1) (* (exp x) 1)))))

prune1.1s

Pruning

3 alts after pruning (0 fresh and 3 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

sample9.2s

Algorithm
intervals
Results
5.7s6454×body10240exit
1.7s12430×body80nan
1.1s7395×body80valid
226.0ms717×body160valid