Details

Time bar (total: 26.0s)

sample738.0ms

Algorithm
intervals
Results
476.0ms241×body10240exit
127.0ms423×body80nan
32.0ms234×body80valid
8.0ms26×body160valid

simplify258.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
257.0ms
(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
(sqrt (+ (exp x) 1))
0.0b
(+ (exp x) 1)

rewrite38.0ms

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
19.0ms
(sqrt (+ (exp x) 1))
16.0ms
(+ (exp x) 1)

series72.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
45.0ms
(sqrt (+ (exp x) 1))
26.0ms
(+ (exp x) 1)

simplify2.3s

Counts
45 → 45
Calls
45 calls:
Slowest
594.0ms
(* (* (+ (exp x) 1) (+ (exp x) 1)) (+ (exp x) 1))
485.0ms
(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
159.0ms
(+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))
130.0ms
(sqrt (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
114.0ms
(sqrt (+ (pow (exp x) 3) (pow 1 3)))

prune417.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 2 expressions with local error:

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

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)

series123.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
99.0ms
(hypot (sqrt (exp x)) 1)
23.0ms
(sqrt (exp x))

simplify935.0ms

Counts
37 → 36
Calls
37 calls:
Slowest
462.0ms
(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
89.0ms
(+ (* 1/2 x) (+ (* 1/8 (pow x 2)) 1))
79.0ms
(* (* (hypot (sqrt (exp x)) 1) (hypot (sqrt (exp x)) 1)) (hypot (sqrt (exp x)) 1))
44.0ms
(* (* (sqrt (exp x)) (sqrt (exp x))) (sqrt (exp x)))
18.0ms
(log1p (hypot (sqrt (exp x)) 1))

prune331.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

6.2b
(- 1 (exp x))
0.0b
(* (exp x) (exp x))
0.0b
(fma (* (exp x) (exp x)) (exp x) 1)
0.0b
(fma (exp x) (exp x) (- 1 (exp x)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
24×*-un-lft-identity
21×add-cube-cbrt
18×exp-prod
11×pow1
9×prod-diff
6×add-cbrt-cube add-log-exp
4×expm1-log1p-u pow-prod-down add-exp-log pow-sqr pow-prod-up insert-posit16 log1p-expm1-u
3×fma-neg swap-sqr associate-*r* associate-*l*
2×fma-udef difference-of-squares
1×pow2 sub-neg pow-plus flip3-- diff-log prod-exp *-commutative cbrt-unprod flip-- distribute-lft-out-- unswap-sqr
Counts
4 → 89
Calls
4 calls:
Slowest
32.0ms
(* (exp x) (exp x))
14.0ms
(- 1 (exp x))
0.0ms
(fma (* (exp x) (exp x)) (exp x) 1)
0.0ms
(fma (exp x) (exp x) (- 1 (exp x)))

series148.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
51.0ms
(fma (* (exp x) (exp x)) (exp x) 1)
45.0ms
(fma (exp x) (exp x) (- 1 (exp x)))
27.0ms
(- 1 (exp x))
24.0ms
(* (exp x) (exp x))

simplify6.4s

Counts
116 → 101
Calls
116 calls:
Slowest
773.0ms
(* (* (fma (* (exp x) (exp x)) (exp x) 1) (fma (* (exp x) (exp x)) (exp x) 1)) (fma (* (exp x) (exp x)) (exp x) 1))
340.0ms
(- (+ (pow (exp x) 2) 1) (exp x))
317.0ms
(- (+ (pow (exp x) 2) 1) (exp x))
255.0ms
(- (+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2)))))
252.0ms
(* (* (* (exp x) (exp x)) (* (exp x) (exp x))) (* (exp x) (exp x)))

prune1.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(log (exp (sqrt (exp x))))
0.0b
(hypot (log (exp (sqrt (exp x)))) 1)
0.0b
(exp (sqrt (exp x)))
0.0b
(sqrt (exp x))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
15×exp-prod
12×add-sqr-sqrt
11×*-un-lft-identity add-cube-cbrt
9×sqrt-prod
7×log-pow
6×pow1
5×add-log-exp
4×expm1-log1p-u sqrt-pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×log-prod
1×rem-sqrt-square hypot-udef pow1/2 rem-log-exp rem-exp-log
Counts
4 → 68
Calls
4 calls:
Slowest
8.0ms
(exp (sqrt (exp x)))
8.0ms
(log (exp (sqrt (exp x))))
5.0ms
(sqrt (exp x))
0.0ms
(hypot (log (exp (sqrt (exp x)))) 1)

series215.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
130.0ms
(hypot (log (exp (sqrt (exp x)))) 1)
45.0ms
(exp (sqrt (exp x)))
23.0ms
(log (exp (sqrt (exp x))))
17.0ms
(sqrt (exp x))

simplify1.9s

Counts
82 → 80
Calls
82 calls:
Slowest
450.0ms
(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
255.0ms
(+ (* 1/4 (* (pow x 2) E)) (+ E (* 1/2 (* x E))))
130.0ms
(log (exp (* (cbrt (sqrt (exp x))) (cbrt (sqrt (exp x))))))
95.0ms
(exp (* (cbrt (sqrt (exp x))) (cbrt (sqrt (exp x)))))
84.0ms
(+ (* 1/2 x) (+ (* 1/8 (pow x 2)) 1))

prune803.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes44.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample9.9s

Algorithm
intervals
Results
6.2s6855×body10240exit
1.7s12828×body80nan
1.4s7452×body80valid
200.0ms674×body160valid