Details

Time bar (total: 34.0s)

sample299.0ms

Algorithm
intervals
Results
91.0ms203×body10240exit
54.0ms362×body80nan
17.0ms229×body80valid
4.0ms28×body160valid

simplify333.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
332.0ms
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

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
16.0ms
(sqrt (+ (exp x) 1))
7.0ms
(+ (exp x) 1)

series54.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
45.0ms
(sqrt (+ (exp x) 1))
9.0ms
(+ (exp x) 1)

simplify2.2s

Counts
45 → 45
Calls
45 calls:
Slowest
537.0ms
(* (* (+ (exp x) 1) (+ (exp x) 1)) (+ (exp x) 1))
496.0ms
(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
151.0ms
(+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))
142.0ms
(sqrt (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
123.0ms
(* (* (sqrt (+ (exp x) 1)) (sqrt (+ (exp x) 1))) (sqrt (+ (exp x) 1)))

prune359.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
15×add-sqr-sqrt
14×log-prod
12×sqrt-prod
11×add-cube-cbrt
9×pow1
7×exp-sum
6×exp-prod sqrt-div log-pow add-log-exp
5×add-exp-log
4×expm1-log1p-u log-div flip3-+ add-cbrt-cube flip-+ insert-posit16 log1p-expm1-u distribute-lft-out
3×fma-def sqrt-pow1 pow1/2
2×exp-diff hypot-def
1×+-commutative rem-sqrt-square sum-log rem-log-exp rem-exp-log
Counts
4 → 88
Calls
4 calls:
Slowest
15.0ms
(exp (log (sqrt (+ (exp x) 1))))
11.0ms
(log (sqrt (+ (exp x) 1)))
9.0ms
(sqrt (+ (exp x) 1))
7.0ms
(+ (exp x) 1)

series213.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
121.0ms
(log (sqrt (+ (exp x) 1)))
39.0ms
(exp (log (sqrt (+ (exp x) 1))))
38.0ms
(sqrt (+ (exp x) 1))
14.0ms
(+ (exp x) 1)

simplify5.1s

Counts
116 → 100
Calls
116 calls:
Slowest
637.0ms
(* (* (+ (exp x) 1) (+ (exp x) 1)) (+ (exp x) 1))
471.0ms
(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
435.0ms
(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
219.0ms
(- (+ (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2))) (+ (log (sqrt 2)) (* 1/2 (/ x (pow (sqrt 2) 2))))) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 4))))
212.0ms
(exp (log (sqrt (+ (pow (exp x) 3) (pow 1 3)))))

prune1.4s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

6.2b
(- 1 (exp x))
0.2b
(/ (fma (* (exp x) (exp x)) (exp x) 1) (fma (exp x) (exp x) (- 1 (exp x))))
0.0b
(* (exp x) (exp x))
0.0b
(sqrt (/ (fma (* (exp x) (exp x)) (exp x) 1) (fma (exp x) (exp x) (- 1 (exp x)))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
39×*-un-lft-identity
36×add-cube-cbrt
19×times-frac
18×exp-prod
13×sqrt-prod
12×pow1
9×prod-diff
8×add-cbrt-cube
6×add-exp-log add-log-exp
4×expm1-log1p-u pow-prod-down pow-sqr pow-prod-up insert-posit16 log1p-expm1-u
3×associate-/r* fma-neg swap-sqr associate-*r* associate-*l* associate-/l*
2×rem-sqrt-square div-inv difference-of-squares
1×pow2 cbrt-undiv clear-num sub-neg frac-2neg sqrt-pow1 pow-plus flip3-- pow1/2 sqrt-div diff-log div-exp prod-exp *-commutative cbrt-unprod flip-- distribute-lft-out-- unswap-sqr
Counts
4 → 125
Calls
4 calls:
Slowest
13.0ms
(* (exp x) (exp x))
7.0ms
(- 1 (exp x))
4.0ms
(/ (fma (* (exp x) (exp x)) (exp x) 1) (fma (exp x) (exp x) (- 1 (exp x))))
2.0ms
(sqrt (/ (fma (* (exp x) (exp x)) (exp x) 1) (fma (exp x) (exp x) (- 1 (exp x)))))

series246.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
130.0ms
(sqrt (/ (fma (* (exp x) (exp x)) (exp x) 1) (fma (exp x) (exp x) (- 1 (exp x)))))
87.0ms
(/ (fma (* (exp x) (exp x)) (exp x) 1) (fma (exp x) (exp x) (- 1 (exp x))))
15.0ms
(- 1 (exp x))
15.0ms
(* (exp x) (exp x))

simplify12.6s

Counts
173 → 137
Calls
173 calls:
Slowest
509.0ms
(/ (* (* (fma (* (exp x) (exp x)) (exp x) 1) (fma (* (exp x) (exp x)) (exp x) 1)) (fma (* (exp x) (exp x)) (exp x) 1)) (* (* (fma (exp x) (exp x) (- 1 (exp x))) (fma (exp x) (exp x) (- 1 (exp x)))) (fma (exp x) (exp x) (- 1 (exp x)))))
460.0ms
(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
275.0ms
(* (* (- 1 (exp x)) (- 1 (exp x))) (- 1 (exp x)))
249.0ms
(* (* (sqrt (/ (fma (* (exp x) (exp x)) (exp x) 1) (fma (exp x) (exp x) (- 1 (exp x))))) (sqrt (/ (fma (* (exp x) (exp x)) (exp x) 1) (fma (exp x) (exp x) (- 1 (exp x)))))) (sqrt (/ (fma (* (exp x) (exp x)) (exp x) 1) (fma (exp x) (exp x) (- 1 (exp x))))))
247.0ms
(* (exp (* (cbrt x) (cbrt x))) (exp (* (cbrt x) (cbrt x))))

prune1.5s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes38.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample9.5s

Algorithm
intervals
Results
5.7s6500×body10240exit
2.2s12678×body80nan
1.0s7406×body80valid
157.0ms717×body160valid