Details

Time bar (total: 10.9s)

sample127.0ms

Algorithm
intervals
Results
64.0ms81×body1280valid
23.0ms45×body640valid
14.0ms21×body2560valid
10.0ms30×body320valid
6.0ms66×body80valid
2.0ms13×body160valid

simplify24.0ms

Calls
1 calls:
Slowest
24.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.0b

localize18.0ms

Local error

Found 3 expressions with local error:

2.4b
(log (+ x (hypot 1 x)))
1.0b
(+ x (hypot 1 x))
0.0b
(hypot 1 x)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
5×add-sqr-sqrt add-cube-cbrt add-log-exp
4×pow1 log-prod add-exp-log
3×expm1-log1p-u fma-def add-cbrt-cube insert-posit16 log1p-expm1-u
2×log-div flip3-+ flip-+ distribute-lft-out
1×+-commutative hypot-udef sum-log rem-log-exp log-pow
Calls
3 calls:
Slowest
8.0ms
(+ x (hypot 1 x))
7.0ms
(log (+ x (hypot 1 x)))
0.0ms
(hypot 1 x)

series341.0ms

Calls
3 calls:
Slowest
181.0ms
(log (+ x (hypot 1 x)))
80.0ms
(hypot 1 x)
80.0ms
(+ x (hypot 1 x))

simplify2.1s

Calls
20 calls:
Slowest
279.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
265.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
236.0ms
(- (+ (* 2 x) (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
226.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
213.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))

prune484.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

13.8b
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
0.4b
(* x -1/6)
0.0b
(fma 3/40 (pow x 5) x)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
2×fma-udef
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Calls
3 calls:
Slowest
6.0ms
(* x -1/6)
0.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
0.0ms
(fma 3/40 (pow x 5) x)

series257.0ms

Calls
3 calls:
Slowest
141.0ms
(fma 3/40 (pow x 5) x)
91.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
25.0ms
(* x -1/6)

simplify1.1s

Calls
18 calls:
Slowest
199.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
175.0ms
(* (* (* x x) x) (* (* -1/6 -1/6) -1/6))
170.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
141.0ms
(+ x (* 3/40 (pow x 5)))
132.0ms
(+ x (* 3/40 (pow x 5)))

prune490.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

2.4b
(log (sqrt (+ x (hypot 1 x))))
2.4b
(log (sqrt (+ x (hypot 1 x))))
1.0b
(+ x (hypot 1 x))
1.0b
(+ x (hypot 1 x))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
14×log-prod
10×add-sqr-sqrt add-cube-cbrt
8×pow1 sqrt-prod add-log-exp
6×fma-def add-exp-log log-pow
4×expm1-log1p-u log-div flip3-+ add-cbrt-cube sqrt-div flip-+ insert-posit16 log1p-expm1-u distribute-lft-out
2×+-commutative sum-log sqrt-pow1 pow1/2 rem-log-exp
Calls
4 calls:
Slowest
8.0ms
(+ x (hypot 1 x))
8.0ms
(+ x (hypot 1 x))
7.0ms
(log (sqrt (+ x (hypot 1 x))))
7.0ms
(log (sqrt (+ x (hypot 1 x))))

series482.0ms

Calls
4 calls:
Slowest
166.0ms
(log (sqrt (+ x (hypot 1 x))))
144.0ms
(log (sqrt (+ x (hypot 1 x))))
89.0ms
(+ x (hypot 1 x))
82.0ms
(+ x (hypot 1 x))

simplify2.9s

Calls
42 calls:
Slowest
379.0ms
(log (sqrt (+ (pow x 3) (pow (hypot 1 x) 3))))
316.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
310.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
304.0ms
(log (sqrt (+ (pow x 3) (pow (hypot 1 x) 3))))
246.0ms
(- (+ (* 2 x) (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))

prune867.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

18.6b
(- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x)))
12.2b
(log (- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x))))
0.1b
(/ (/ 1/8 x) (* x x))
0.1b
(/ 1/16 (pow x 5))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
12469×associate-/r*
10230×*-un-lft-identity
9736×add-sqr-sqrt
9520×frac-sub
9360×frac-add
9107×associate-/l*
9002×add-cube-cbrt
4922×times-frac
4762×log-div
2239×clear-num frac-2neg
2172×unpow-prod-down
2151×associate-/l/
995×prod-diff
994×swap-sqr
992×associate-*l*
990×associate-*r*
724×sqr-pow
404×distribute-lft-out
352×div-inv
334×*-commutative unswap-sqr
199×fma-neg
80×flip3-+ flip-+
22×add-exp-log difference-of-squares
18×log-prod add-cbrt-cube
9×div-exp add-log-exp
8×distribute-lft-out--
7×cbrt-undiv
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
2×flip3-- diff-log prod-exp cbrt-unprod flip-- associate--r+
1×pow-to-exp +-commutative sum-log sub-neg rem-log-exp pow-exp log-pow
Calls
4 calls:
Slowest
209.0ms
(log (- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x))))
145.0ms
(- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x)))
24.0ms
(/ (/ 1/8 x) (* x x))
10.0ms
(/ 1/16 (pow x 5))

series338.0ms

Calls
4 calls:
Slowest
113.0ms
(log (- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x))))
98.0ms
(- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x)))
80.0ms
(/ 1/16 (pow x 5))
46.0ms
(/ (/ 1/8 x) (* x x))