Details

sample1.9m (35.7%)

Algorithm
61×intervals
Results
28.2s253253×body80valid
20.4s29772×body1280valid
18.1s158809×body80nan
10.8s8841×body2560valid
9.7s20314×body640valid
6.6s3475×body5120valid
3.2s9536×body320valid
2.1s9014×body160valid
615.0ms612×body10240exit
279.0ms599×body1280nan
240.0ms647×body640nan
151.0ms8256×pre80true
100.0ms359×body320nan
36.0ms192×body160nan
3.0ms37×body80overflowed

series1.9m (34.9%)

Calls

424 calls:

5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
1.8s
(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

prune55.7s (17.3%)

simplify11.6s (3.6%)

Algorithm
173×egg-herbie

rewrite11.4s (3.5%)

Algorithm
113×rewrite-expression-head
Calls

424 calls:

574.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
457.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
427.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
364.0ms
(/ (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))))
328.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
Rules
25868×add-exp-log
17143×prod-exp
8012×pow-exp
7056×div-exp
4388×add-sqr-sqrt
4242×times-frac
4051×*-un-lft-identity
3458×add-cube-cbrt
2986×pow-to-exp
2642×add-cbrt-cube
1590×sqrt-prod
1111×pow1
1076×cbrt-unprod
928×associate-*r*
912×associate-*l*
830×unpow-prod-down
821×1-exp
813×rec-exp
564×cbrt-prod
542×cbrt-undiv
514×prod-diff
491×add-log-exp
425×expm1-log1p-u
424×log1p-expm1-u
394×associate-/r*
369×associate-*r/
368×associate-/l*
353×pow-prod-down
350×pow-unpow
332×div-inv
276×unswap-sqr
273×sqr-pow
255×sqrt-div
229×frac-times
221×associate-*l/
218×distribute-lft-out
206×distribute-rgt-in distribute-lft-in
187×flip3-- flip--
152×*-commutative
139×difference-of-squares
134×associate-/r/
117×flip-+ flip3-+
111×distribute-rgt-neg-in
110×distribute-lft-out--
100×fma-def
97×frac-2neg clear-num
90×sqrt-pow1
89×distribute-lft-neg-in
78×tan-quot
63×sub-neg
60×pow1/2
55×exp-prod
47×pow1/3 swap-sqr cos-sum
45×rem-sqrt-square
42×associate--l+
38×associate-/l/
37×div-sub
36×fma-udef
35×cbrt-div hypot-def
34×pow-pow
33×fma-neg
32×frac-sub
31×unpow2
30×pow-sub
27×associate-+l+ sum-log
25×log-pow
21×+-commutative
15×pow-prod-up
12×frac-add
11×pow-sqr
10×neg-sub0 neg-mul-1
9×inv-pow pow-flip
7×diff-log
6×associate-+r+ asin-acos
5×pow-neg
4×hypot-udef pow-plus pow2 distribute-neg-frac
3×exp-diff log-prod
2×un-div-inv associate-+r- cos-diff unsub-neg neg-log associate-+l-
1×rem-exp-log log1p-udef sqrt-unprod sin-sum log1p-expm1 expm1-log1p sqrt-undiv rem-square-sqrt distribute-frac-neg acos-asin associate--r- mul0 expm1-udef rem-log-exp

regimes10.0s (3.1%)

Accuracy

Total 42.6b remaining (24.2%)

Threshold costs 5.2b (2.9%)

9.3b3.6%Toniolo and Linder, Equation (13)
6.8b6.8%Toniolo and Linder, Equation (10+)
5.8b-5.1%Henrywood and Agarwal, Equation (12)
5.8b75.5%Toniolo and Linder, Equation (7)
4.0b46%Toniolo and Linder, Equation (10-)

bsearch3.7s (1.2%)

localize2.1s (0.7%)

end1.0ms (0.0%)