Details

simplify48.6m (73.0%)

series6.2m (9.4%)

Calls

2568 calls:

2.7s
(* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))
2.3s
(* (/ (/ (cbrt (- y z)) (cbrt (- a z))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
1.5s
(+ (* (pow (/ x (sqrt 1.0)) 3) (/ 1/8 (pow (+ (sqrt 1.0) 1.0) 2))) (+ (* 1/4 (/ (/ (pow x 3) 1.0) (pow (+ (sqrt 1.0) 1.0) 3))) (* (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) -1/2)))
1.3s
(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
1.2s
(* (cbrt (+ x (* (- y x) (* (- (/ 2.0 3.0) z) 6.0)))) (cbrt (+ x (* (- y x) (* (- (/ 2.0 3.0) z) 6.0)))))

prune6.0m (8.9%)

rewrite2.7m (4.1%)

Algorithm
903×rewrite-expression-head
Calls

2568 calls:

4.0s
(* (sqrt (sqrt x)) (* (sqrt (sqrt x)) (* (sqrt x) (+ (+ (+ (+ y z) z) y) t))))
3.3s
(+ (+ (+ (+ (+ x y) y) x) z) x)
3.3s
(/ (+ (* (+ (* (+ (* (* (* (* (cbrt (cbrt (* (+ (* x y) z) y))) (cbrt (cbrt (* (+ (* x y) z) y)))) (cbrt (cbrt (* (+ (* x y) z) y)))) (cbrt (* (+ (* x y) z) y))) (cbrt (* (+ (* x y) z) y))) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
2.4s
(+ (+ (* (pow (/ x (sqrt 1.0)) 3) (/ 1/8 (pow (+ (sqrt 1.0) 1.0) 2))) (+ (* 1/4 (/ (/ (pow x 3) 1.0) (pow (+ (sqrt 1.0) 1.0) 3))) (* (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) -1/2))) (/ x (+ (sqrt 1.0) 1.0)))
2.4s
(/ (- (+ x (/ (/ z (- (* t z) x)) (/ 1 y))) (/ x (- (* t z) x))) (+ x 1.0))
Rules
52421×times-frac
49400×*-un-lft-identity
39402×add-sqr-sqrt
27998×add-cube-cbrt
26737×sqrt-prod
12269×add-exp-log
9359×add-cbrt-cube
8342×distribute-lft-out
6844×pow1
6057×associate-*r*
5573×cbrt-prod
5028×associate-*l*
4046×add-log-exp
3871×prod-exp
3699×difference-of-squares
3470×associate-/r*
3199×distribute-lft-out--
3109×cbrt-unprod
2919×associate-/l*
2853×div-exp
2185×div-inv
2054×cbrt-undiv
2040×associate-/r/
2014×associate-*r/
1907×flip-+ flip3-+
1896×pow-prod-down
1844×flip3-- flip--
1594×sqrt-div
1523×unswap-sqr
1478×cbrt-div
1464×frac-times
1457×associate-*l/
1107×unpow-prod-down
883×log-prod
869×distribute-rgt-in distribute-lft-in
816×*-commutative
744×pow1/3
742×swap-sqr
689×sub-neg
653×sqrt-pow1
579×associate-/l/
552×clear-num frac-2neg
527×sum-log
503×cube-prod
482×frac-sub
403×pow1/2
381×pow-prod-up
342×sqr-pow
311×diff-log
300×+-commutative
292×1-exp
277×frac-add
266×associate--l+
259×pow-sqr
257×rec-exp
235×pow-exp
232×associate-+r+
219×associate-+l+
211×pow-to-exp
154×log-pow
153×pow-unpow
131×rem-sqrt-square
130×pow-plus
112×div-sub
108×pow2
95×distribute-rgt-neg-in distribute-lft-neg-in
90×exp-sum
82×pow-flip
80×tanh-def
76×inv-pow
67×log-div
56×pow-pow
55×unpow2
54×exp-prod
48×difference-of-sqr--1
47×associate--r+
46×distribute-rgt-out-- rem-log-exp
45×sum-cubes
44×un-div-inv
40×associate-+l-
39×cube-div sinh-def
32×distribute-lft-neg-out sqrt-unprod
22×associate-+r- rem-square-sqrt distribute-rgt-out
21×sub-div neg-mul-1
20×unpow-prod-up
19×distribute-rgt-neg-out
18×difference-of-sqr-1 unsub-neg unpow3 cube-mult
17×cosh-def
16×rem-cube-cbrt
15×rem-exp-log
14×difference-cubes sin-mult
12×associate--l-
9×exp-diff pow-sub
8×unpow1/3
7×associate--r-
6×distribute-rgt1-in
5×distribute-lft1-in count-2 distribute-neg-frac
4×sqrt-pow2 diff-cos neg-sub0 rem-cbrt-cube
3×cos-diff
2×neg-log exp-to-pow exp-neg cos-sum tan-quot
1×pow-div sqrt-undiv sin-cos-mult pow3 remove-double-div distribute-frac-neg

sample2.3m (3.4%)

Algorithm
353×intervals
Results
56.4s817117×body80valid
21.3s18581×body1280valid
10.3s85865×body80nan
9.9s16452×body640valid
4.0s9247×body320valid
1.1s5038×body160valid
578.0ms1555×body2560valid
50.0ms41×body10240exit
6.0ms2×body5120valid
6.0ms20×body640nan
3.0ms16×body320nan
3.0ms9×body1280nan
0.0ms4×body160nan

regimes24.8s (0.6%)

Accuracy

Total 14.8b remaining (28.1%)

Threshold costs 4.9b (9.3%)

2.2b0%Numeric.Histogram:binBounds from Chart-1.5.3
2.1b0%Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, A
2.0b0%Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, A
1.3b0%SynthBasics:moogVCF from YampaSynth-0.2
1.3b0%Numeric.AD.Rank1.Halley:findZero from ad-4.2.4

localize19.4s (0.5%)

bsearch48.0ms (0.0%)

end1.0ms (0.0%)