Details

simplify5.5m (31.2%)

prune4.8m (27.4%)

sample3.4m (19.2%)

Algorithm
59×intervals
Results
41.7s243618×body80valid
41.0s29317×body1280valid
29.5s157721×body80nan
20.3s20690×body640valid
18.0s8872×body2560valid
10.8s3487×body5120valid
6.8s9713×body320valid
3.2s9130×body160valid
997.0ms829×body10240exit
391.0ms617×body1280nan
245.0ms646×body640nan
165.0ms8256×pre80true
100.0ms346×body320nan
80.0ms197×body160nan

series2.4m (13.8%)

Calls

421 calls:

6.4s
(- (* (* (* 1.0 (* 1.0 1.0)) (* 1.0 1.0)) (* (* 1.0 1.0) (* 1.0 1.0))) (* (* (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))) (* (* (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))) (* (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))))
4.9s
(sqrt (* (* 2.0 n) (* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))))
4.8s
(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))
4.4s
(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0)))))
4.3s
(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))

rewrite49.6s (4.7%)

Algorithm
112×rewrite-expression-head
Calls

421 calls:

7.8s
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
2.5s
(+ (sqrt (- (* (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (* M M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))
2.3s
(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
2.3s
(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
2.2s
(+ (sqrt (- (* (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (* M M))) (* (/ (/ d D) 1) (* (/ (/ d D) h) (/ c0 w))))
Rules
91615×add-exp-log
46493×div-exp
46056×prod-exp
23795×times-frac
18342×pow-exp
13329×add-sqr-sqrt
12269×*-un-lft-identity
11399×add-cube-cbrt
8263×pow-to-exp
5931×1-exp rec-exp
5914×sqrt-prod
4635×unpow-prod-down
4440×add-cbrt-cube
4079×associate-*l*
3384×cbrt-prod
2046×cbrt-undiv
1788×cbrt-unprod
1407×pow1
1403×sqrt-div
1183×frac-times
1181×sqr-pow
1036×associate-*r*
755×prod-diff
665×associate-*r/
633×div-inv
555×flip3-- flip--
501×add-log-exp
489×pow-prod-down
475×associate-*l/
458×associate-/l*
443×difference-of-squares
423×associate-/r*
421×expm1-log1p-u log1p-expm1-u
370×exp-sum
346×distribute-lft-out--
325×unswap-sqr
316×pow-unpow
294×distribute-rgt-neg-in
288×distribute-lft-neg-in
176×associate-/r/
160×sqrt-pow1
157×flip-+ flip3-+
148×exp-prod
143×*-commutative
128×distribute-lft-out
110×pow1/2
101×distribute-rgt-in distribute-lft-in
86×fma-def
78×frac-2neg clear-num
73×rem-sqrt-square
70×pow-prod-up
61×fma-neg
58×pow1/3
57×swap-sqr
50×div-sub
47×neg-mul-1
45×sub-neg
42×tan-quot
40×pow-sqr
39×fma-udef
35×associate-/l/
34×pow-pow
33×pow-sub
27×diff-log
26×cos-sum
20×frac-add
18×cbrt-div
15×rem-exp-log
13×pow3
12×sum-log pow-plus +-commutative hypot-def
11×associate--r+ log-pow
10×log-prod sqrt-unprod
9×exp-diff pow2
8×hypot-udef
7×cube-unmult difference-cubes
6×neg-sub0 neg-log
5×pow-flip distribute-frac-neg inv-pow rem-square-sqrt
4×associate-+r- associate-+r+ associate-+l- associate--r-
3×sqrt-undiv pow-neg acos-asin rem-log-exp
2×sin-sum frac-sub associate--l+ un-div-inv
1×mul0 sub-div associate--l- exp-to-pow asin-acos cos-diff log-div

regimes27.4s (2.6%)

Accuracy

Total 40.2b remaining (21.6%)

Threshold costs 5.1b (2.7%)

9.8b21.2%Toniolo and Linder, Equation (13)
7.4b16.1%Henrywood and Agarwal, Equation (13)
7.4b0%Henrywood and Agarwal, Equation (12)
5.4b77.4%Toniolo and Linder, Equation (7)
2.7b0%Toniolo and Linder, Equation (10-)

localize8.6s (0.8%)

bsearch1.9s (0.2%)

end1.0ms (0.0%)