Details

simplify4.1m (31.0%)

sample3.3m (25.1%)

Algorithm
61×intervals
Results
43.7s254380×body80valid
39.7s29480×body1280valid
29.2s160993×body80nan
21.3s19902×body640valid
17.0s8950×body2560valid
9.9s3339×body5120valid
5.7s9701×body320valid
3.1s8766×body160valid
994.0ms711×body10240exit
350.0ms596×body1280nan
238.0ms8256×pre80true
233.0ms612×body640nan
145.0ms370×body320nan
36.0ms193×body160nan

series2.9m (21.9%)

Calls

443 calls:

16.5s
(- (* (/ (* 1.0 1.0) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)) (/ (* 1.0 1.0) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0))) (* (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)) (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0))))
6.6s
(* (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)) (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)))
4.3s
(- (/ (* 1.0 1.0) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)) (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)))
2.6s
(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))
2.5s
(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))) (* (* 2.0 n) U)))

prune1.9m (14.6%)

rewrite35.0s (4.4%)

Algorithm
117×rewrite-expression-head
Calls

443 calls:

1.7s
(- (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)) 1.0)
1.7s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
1.5s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
953.0ms
(+ (* (* (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
891.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
Rules
50808×add-exp-log
34558×prod-exp
21831×pow-exp
18284×div-exp
11918×times-frac
10336×pow-to-exp
6768×add-sqr-sqrt
6412×*-un-lft-identity
5639×add-cube-cbrt
2654×add-cbrt-cube
2063×1-exp rec-exp
1816×sqrt-prod
1246×unpow-prod-down
1086×pow1
912×cbrt-prod
893×cbrt-unprod
888×associate-/l*
844×div-inv
798×associate-*l*
757×associate-/r/
745×cbrt-undiv
723×associate-*r*
634×prod-diff
525×add-log-exp
509×associate-*r/
487×associate-*l/
456×associate-/r*
444×log1p-expm1-u
443×expm1-log1p-u
336×pow-unpow
309×pow-prod-down
276×sqr-pow
267×difference-of-squares
240×unswap-sqr
230×distribute-lft-out--
196×distribute-lft-out
180×distribute-rgt-neg-in
176×sqrt-div
174×distribute-lft-neg-in
171×frac-times
156×flip3-- flip--
131×*-commutative
106×frac-2neg clear-num
101×sqrt-pow1
97×fma-neg
96×distribute-rgt-in distribute-lft-in
92×cube-prod
77×fma-def
69×pow1/2 flip-+ flip3-+
64×tan-quot
61×pow1/3
55×rem-sqrt-square
54×associate-/l/
53×swap-sqr
47×cos-sum
44×pow-pow
40×sub-neg cbrt-div
34×fma-udef
31×div-sub
27×unpow2
26×pow-sub
24×unpow3 cube-mult
22×diff-log associate--r+
21×sum-log neg-mul-1 log-div
19×exp-diff frac-add log-prod
17×exp-prod
16×+-commutative
15×log-pow
14×pow-prod-up
13×neg-sub0
12×hypot-def
10×pow-sqr frac-sub
9×rem-cube-cbrt pow-flip
8×pow-neg
7×inv-pow neg-log exp-sum
6×un-div-inv sub-div asin-acos
4×pow2 pow-plus
3×associate-+r- distribute-neg-frac hypot-udef associate-+r+ associate--r- distribute-rgt-out-- rem-cbrt-cube associate-+l- rem-log-exp
2×cube-div rem-exp-log associate--l- cos-diff distribute-rgt-neg-out associate--l+
1×sqrt-pow2 associate-+l+ log1p-udef sqrt-unprod log1p-expm1 expm1-log1p expm1-udef rem-square-sqrt acos-asin mul0 exp-to-pow

regimes16.6s (2.1%)

Accuracy

Total 34.2b remaining (16.1%)

Threshold costs 6.6b (3.1%)

7.7b18.6%Toniolo and Linder, Equation (13)
6.9b0%Henrywood and Agarwal, Equation (12)
6.7b72.5%Toniolo and Linder, Equation (7)
4.4b31.7%Toniolo and Linder, Equation (10-)
1.0b0%Henrywood and Agarwal, Equation (3)

localize4.5s (0.6%)

bsearch2.4s (0.3%)

end0.0ms (0.0%)