Details

simplify17.3m (49.9%)

prune10.7m (30.9%)

sample4.2m (12.2%)

Algorithm
60×intervals
Results
58.4s240863×body80valid
55.2s29602×body1280valid
37.6s139529×body80nan
27.6s20103×body640valid
22.6s8671×body2560valid
14.3s3391×body5120valid
10.1s10122×body320valid
5.2s8905×body160valid
1.8s818×body10240exit
713.0ms624×body1280nan
485.0ms646×body640nan
297.0ms8256×pre80true
178.0ms348×body320nan
67.0ms202×body160nan

series1.4m (4.1%)

Calls

441 calls:

4.5s
(/ (pow (pow PI (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))
2.5s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
2.3s
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ (* (cbrt Om) (cbrt Om)) 1) (/ (cbrt n) (/ (cbrt Om) l)))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
2.2s
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ Om l) (cbrt n))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
2.0s
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))

rewrite32.6s (1.6%)

Algorithm
116×rewrite-expression-head
Calls

441 calls:

3.0s
(cbrt (* (* (+ (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)) 1) (+ (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)) 1)) (+ (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)) 1)))
1.9s
(* (* (* (* (* M D) (/ 1 (* 2 d))) (cbrt h)) (* (/ (* M D) (* 2 d)) (cbrt h))) (/ (cbrt h) l))
1.6s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.5s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (* (/ c0 w) (/ d D)) (/ (/ d D) h)))
1.1s
(* (/ 1 (* (sin k) (* (/ (* (/ k t) t) l) (/ (* (/ k t) t) l)))) (/ (/ 2 t) (tan k)))
Rules
160386×times-frac
94795×add-sqr-sqrt
94290×*-un-lft-identity
93606×add-cube-cbrt
79967×unpow-prod-up
77133×prod-diff
64704×sqrt-prod
10174×add-exp-log
6632×div-inv
6531×add-cbrt-cube
5111×unpow-prod-down
4830×prod-exp
3315×div-exp
3106×cbrt-unprod
2622×associate-/r*
2273×cbrt-prod
2177×cbrt-undiv
1878×sqr-pow
1591×sub-neg
1404×associate-*r*
1358×pow1
980×associate-*l*
789×associate-/l*
741×frac-times
665×associate-*l/
646×sqrt-div
490×add-log-exp
484×difference-of-squares
463×pow-prod-down associate-*r/
442×expm1-log1p-u
441×insert-posit16 log1p-expm1-u associate-/r/
291×unswap-sqr
250×pow-exp
217×1-exp
213×swap-sqr
205×rec-exp
203×flip3-- flip--
192×distribute-lft-out--
170×pow-sub
142×*-commutative
119×sqrt-pow1
111×pow-to-exp
104×frac-2neg clear-num
102×distribute-rgt-in distribute-lft-in
99×pow-unpow
83×flip-+ flip3-+
81×cbrt-div
79×pow1/3
76×distribute-lft-out
73×pow1/2
54×associate-/l/
53×fma-udef
51×fma-def
48×rem-sqrt-square
44×fma-neg
41×log-pow exp-prod
37×pow-prod-up
31×tan-quot pow-sqr
28×log-prod frac-add
25×pow-pow distribute-rgt-out--
18×pow2 hypot-udef
17×pow-plus
15×cos-sum
12×diff-log
11×sum-log +-commutative div-sub
9×un-div-inv
8×pow-flip inv-pow
7×exp-sum
6×rem-log-exp hypot-def acos-asin
5×unpow2
4×sqrt-unprod rem-exp-log
3×asin-acos rem-square-sqrt cos-diff
2×associate-+r- associate-+r+ associate--l+ sqrt-pow2 associate--r+ rem-cbrt-cube
1×associate-+l+ expm1-log1p expm1-udef frac-sub cube-unmult log1p-expm1 pow3 exp-to-pow e-exp-1 log1p-udef

regimes19.7s (1.0%)

Accuracy

Total 59.7b remaining (33.6%)

Threshold costs 3.9b (2.2%)

9.8b12.1%Toniolo and Linder, Equation (13)
9.3b-19.3%Given's Rotation SVD example
6.8b18.4%Henrywood and Agarwal, Equation (13)
5.9b15.4%Henrywood and Agarwal, Equation (12)
5.4b30.5%Henrywood and Agarwal, Equation (3)

localize5.8s (0.3%)

bsearch1.8s (0.1%)

end1.0ms (0.0%)