Details

simplify30.2m (47.4%)

series16.5m (25.9%)

Calls

2310 calls:

16.9s
(sqrt (fma b (- (+ y t) 2.0) (fma z (- 1.0 y) (fma a (- 1.0 t) x))))
16.7s
(* (sqrt (sqrt (fma b (- (+ y t) 2.0) (fma z (- 1.0 y) (fma a (- 1.0 t) x))))) (sqrt (sqrt (fma b (- (+ y t) 2.0) (fma z (- 1.0 y) (fma a (- 1.0 t) x))))))
16.0s
(sqrt (fma b (- (+ y t) 2.0) (fma z (- 1.0 y) (fma a (- 1.0 t) x))))
7.9s
(cbrt (fma (/ (- y z) (- a z)) (- t x) x))
1.7s
(+ (* (* 2 (log (cbrt y))) (+ y 0.5)) (* (log (cbrt y)) (+ y 0.5)))

sample8.3m (13.1%)

Algorithm
538×intervals
Results
3.0m2578071×body80valid
1.0m526878×body80nan
40.5s46480×body1280valid
25.0s44410×body640valid
8.7s25052×body320valid
7.9s5559×body2560valid
3.4s13641×body160valid
1.5s1597×body10240exit
230.0ms681×body640nan
229.0ms499×body1280nan
186.0ms44×body5120valid
131.0ms401×body320nan
26.0ms227×body160nan

prune6.0m (9.4%)

rewrite1.5m (2.3%)

Algorithm
869×rewrite-expression-head
Calls

2312 calls:

1.3s
(* a (- (/ y (- (+ t 1.0) z)) (/ z (- (+ t 1.0) z))))
1.2s
(* (- (/ y (- (+ t 1.0) z)) (/ z (- (+ t 1.0) z))) (- x))
1.1s
(* (- (/ y (- (+ t 1.0) z)) (/ z (- (+ t 1.0) z))) (- a x))
962.0ms
(+ x (+ (* a (- (/ y (- (+ t 1.0) z)) (/ z (- (+ t 1.0) z)))) (* (- (/ y (- (+ t 1.0) z)) (/ z (- (+ t 1.0) z))) (- x))))
816.0ms
(- (+ (fma (- x 0.5) (log x) 0.91893853320467) (/ (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x)) (sqrt x))) x)
Rules
52354×times-frac
49721×*-un-lft-identity
47965×add-sqr-sqrt
33950×add-cube-cbrt
13584×prod-diff
9934×add-exp-log
7752×add-cbrt-cube
6194×pow1
6002×cbrt-prod
5898×associate-*r*
5838×sqrt-prod
5296×distribute-lft-out--
5225×difference-of-squares
3494×associate-*l*
3179×associate-/r*
3117×div-inv
3053×add-log-exp
2918×distribute-lft-out
2846×distribute-rgt-in distribute-lft-in
2724×prod-exp
2624×associate-/r/
2354×div-exp
2314×log1p-expm1-u expm1-log1p-u
2190×cbrt-unprod
2148×associate-/l*
1974×unpow-prod-down
1718×pow-prod-down
1688×flip3-- flip--
1586×cbrt-undiv
1245×unswap-sqr
1126×cbrt-div
1038×log-prod
990×fma-def
931×associate-*r/
919×flip-+ flip3-+
880×swap-sqr
828×cube-prod
801×pow1/3 associate-*l/
791×sqrt-pow1
733×fma-neg
682×frac-times
633×*-commutative
561×associate-+r+
512×clear-num frac-2neg
478×associate--l+
405×sub-neg
403×sqr-pow
383×associate-/l/
369×pow1/2
356×pow-prod-up
327×sqrt-div
320×associate-+l+
318×fma-udef
311×1-exp
310×rec-exp
268×log-pow
254×pow-sqr
203×diff-log
200×sum-log
166×distribute-rgt-neg-in
162×associate--r+ pow-exp
161×distribute-lft-neg-in
136×pow-unpow
130×+-commutative
120×frac-sub
119×pow-to-exp
115×unpow2
112×rem-sqrt-square
106×unpow3 cube-mult pow-plus
102×div-sub
99×exp-sum
90×pow-flip
89×pow2
75×frac-add
73×inv-pow distribute-rgt-out
66×distribute-rgt-out-- pow-pow
62×log-div
59×exp-prod
51×tanh-def
50×un-div-inv
44×sinh-def
42×rem-log-exp
36×distribute-rgt-neg-out
29×neg-mul-1
28×sqrt-unprod
25×hypot-def
24×associate-+l-
23×cos-sum
20×sub-div rem-square-sqrt
18×distribute-neg-frac associate-+r-
15×cosh-def
14×exp-to-pow unsub-neg
12×cube-div rem-exp-log sqrt-undiv
11×rem-cube-cbrt distribute-lft-neg-out unpow1/3 distribute-frac-neg
10×pow-neg associate--l-
9×hypot-udef
7×distribute-lft1-in neg-sub0 tan-quot
6×exp-diff sum-cubes
5×distribute-rgt1-in pow-sub count-2 associate--r-
4×log1p-udef log1p-expm1 diff-cos difference-of-sqr-1 sin-mult
3×difference-cubes sqrt-pow2 cos-diff unpow-prod-up expm1-log1p rem-cbrt-cube expm1-udef
1×exp-neg remove-double-div neg-log distribute-neg-in cos-mult

regimes52.6s (1.4%)

Accuracy

Total 192.6b remaining (37.7%)

Threshold costs 29.4b (5.7%)

13.7b45.8%Data.Array.Repa.Algorithms.Pixel:doubleRmsOfRGB8 from repa-algorithms-3.4.0.1
12.3b61.2%Diagrams.TwoD.Arc:arcBetween from diagrams-lib-1.3.0.3
11.1b22.4%AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1
9.5b13%Numeric.Signal:interpolate from hsignal-0.2.7.1
8.2b57.5%FRP.Yampa.Vector3:vector3Rho from Yampa-0.10.2

localize16.4s (0.4%)

bsearch5.7s (0.1%)

end5.0ms (0.0%)