Details

sample2.0m (37.3%)

Algorithm
61×intervals
Results
27.4s248661×body80valid
20.8s30686×body1280valid
19.4s167283×body80nan
10.7s8834×body2560valid
10.3s21165×body640valid
6.4s3493×body5120valid
3.5s10233×body320valid
2.1s9104×body160valid
1.4s2591×body1280nan
960.0ms2319×body640nan
488.0ms599×body10240exit
351.0ms1144×body320nan
146.0ms8256×pre80true
120.0ms644×body160nan
24.0ms220×body80overflowed

series1.7m (31.4%)

Calls

453 calls:

4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
1.7s
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))

prune50.1s (15.8%)

rewrite18.9s (6.0%)

Algorithm
118×rewrite-expression-head
Calls

453 calls:

1.9s
(- (* (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)) (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))) (* 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
739.0ms
(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
562.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
558.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
466.0ms
(/ 1 (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
Rules
32137×add-exp-log
22772×prod-exp
11573×pow-exp
8874×div-exp
5230×pow-to-exp
4029×*-un-lft-identity
3560×add-sqr-sqrt
3205×times-frac
2661×add-cbrt-cube
2651×add-cube-cbrt
1554×sqrt-prod
1497×pow1
1309×rec-exp 1-exp
1165×unpow-prod-down
1132×cbrt-unprod
1038×associate-*r*
814×associate-*l*
619×associate-*r/
593×add-log-exp
562×distribute-lft-out
541×pow-prod-down
464×sqrt-div
406×cbrt-undiv
379×cbrt-prod
369×unswap-sqr
322×associate-/l*
282×frac-times
281×associate-/r*
274×pow-unpow
267×associate-*l/
262×sqr-pow
236×flip3-- flip--
226×distribute-lft-out--
215×div-inv
208×distribute-rgt-neg-in
202×flip-+ flip3-+
164×*-commutative
151×distribute-lft-neg-in
135×associate-/r/
127×sqrt-pow1
112×exp-prod
89×pow1/2 difference-of-squares
85×clear-num unpow2 frac-2neg
76×frac-sub
73×distribute-rgt-in distribute-lft-in
66×tan-quot
65×div-sub
63×exp-diff sub-neg
62×distribute-frac-neg
59×neg-sub0
58×rem-sqrt-square exp-neg
55×pow1/3
54×swap-sqr
52×sum-log
50×pow-pow
39×associate-/l/ cbrt-div pow-prod-up
35×+-commutative
33×pow-sqr
25×un-div-inv frac-add
23×cube-prod
22×diff-log associate--l+
20×log-pow
19×neg-mul-1 log-prod
17×sub-div
16×log-div
12×pow-plus associate-+r+
11×distribute-neg-frac
10×pow-sub
8×rem-cube-cbrt pow-neg pow2 associate--r+
7×neg-log
6×cos-sum
5×associate-+l+ unsub-neg unpow3 cube-mult exp-sum associate-+r-
4×rem-exp-log inv-pow pow-flip
3×sqrt-undiv cos-diff acos-asin asin-acos associate--r- associate-+l- rem-log-exp
2×sqrt-unprod distribute-rgt-out-- associate--l- rem-square-sqrt
1×cube-div sin-mult mul0

simplify12.0s (3.8%)

Algorithm
178×egg-herbie

regimes10.7s (3.4%)

Accuracy

Total 52.7b remaining (25.2%)

Threshold costs 5.4b (2.6%)

8.6b41.1%Henrywood and Agarwal, Equation (3)
7.6b16.3%Toniolo and Linder, Equation (13)
6.9b0.7%Given's Rotation SVD example
6.7b11.9%Toniolo and Linder, Equation (10+)
5.7b3.3%Henrywood and Agarwal, Equation (12)

bsearch5.1s (1.6%)

localize2.3s (0.7%)

end1.0ms (0.0%)