Details

simplify31.3m (55.5%)

series14.9m (26.4%)

Calls

2271 calls:

17.1s
(/ (* (* y z) (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3))) (+ (* (tanh (/ t y)) (tanh (/ t y))) (+ (* (tanh (/ x y)) (tanh (/ x y))) (* (tanh (/ t y)) (tanh (/ x y))))))
4.0s
(/ x (* (cbrt (+ 1.0 (sqrt (+ x 1.0)))) (cbrt (+ 1.0 (sqrt (+ x 1.0))))))
3.8s
(pow (pow (log (- 1.0 (/ y x))) 3) 3)
3.3s
(fma (* (* t y) (* z x)) 18.0 (fma c b (- (fma 4.0 (fma t a (* x i)) (* (* j 27.0) k)))))
3.1s
(fma (* (* (* t y) z) x) 18.0 (fma c b (- (fma 4.0 (fma t a (* x i)) (* (* j 27.0) k)))))

prune4.5m (8.0%)

sample3.9m (6.8%)

Algorithm
538×intervals
Results
1.2m2570268×body80valid
19.6s491710×body80nan
17.5s46900×body1280valid
9.7s43539×body640valid
4.0s5623×body2560valid
3.6s24834×body320valid
1.3s13982×body160valid
747.0ms1524×body10240exit
101.0ms40×body5120valid
92.0ms640×body640nan
86.0ms484×body1280nan
47.0ms390×body320nan
15.0ms229×body160nan

rewrite58.4s (1.7%)

Algorithm
856×rewrite-expression-head
Calls

2274 calls:

927.0ms
(* (- (* x 0.5) y) (* (* (exp (/ t (/ 2.0 t))) (sqrt z)) (sqrt 2.0)))
468.0ms
(+ (+ (/ 2.0 t) (/ (sqrt 2.0) (/ (* t z) (sqrt 2.0)))) (- (/ x y) 2.0))
444.0ms
(/ (* (* y z) (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3))) (+ (* (tanh (/ t y)) (tanh (/ t y))) (+ (* (tanh (/ x y)) (tanh (/ x y))) (* (tanh (/ t y)) (tanh (/ x y))))))
430.0ms
(* (/ (* (cbrt y) (cbrt y)) (* (cbrt z) (* (* (cbrt (cbrt z)) (cbrt (cbrt z))) (cbrt (cbrt z))))) (/ x (/ (cbrt z) (cbrt y))))
419.0ms
(+ (- x (+ (* (* 2 (log (cbrt y))) (+ y 0.5)) (* (+ y 0.5) (log (cbrt y))))) y)
Rules
50797×times-frac
47867×*-un-lft-identity
44881×add-sqr-sqrt
33170×add-cube-cbrt
12454×prod-diff
10103×add-exp-log
7432×add-cbrt-cube
6846×frac-add
6845×frac-times
6834×cbrt-prod
5750×associate-/r/
5535×pow1
5477×tanh-def
5442×associate-*r*
4670×distribute-lft-out--
4413×sqrt-prod
4100×difference-of-squares
3429×associate-*l*
3063×associate-/r*
3053×associate-*r/
3018×div-inv
3013×distribute-lft-out
2942×prod-exp
2941×add-log-exp
2841×associate-*l/
2385×div-exp
2321×unpow-prod-down
2282×expm1-log1p-u
2278×log1p-expm1-u
2259×distribute-rgt-in distribute-lft-in
2175×associate-/l*
2133×cbrt-unprod
1670×flip3-- flip--
1638×cbrt-undiv
1288×unswap-sqr
1275×log-prod
1267×pow-prod-down
1112×cbrt-div
858×swap-sqr
840×pow1/3
831×flip-+ flip3-+
797×log-pow
770×cube-prod
713×fma-neg
594×*-commutative
557×associate-+r+
495×clear-num frac-2neg
476×associate-+l+
448×sqrt-pow1
424×fma-def
387×exp-prod
375×sub-neg
370×associate-/l/
354×sqrt-div
347×1-exp
338×exp-sum
335×rec-exp
330×sqr-pow
327×fma-udef
322×pow-exp
279×pow1/2
255×pow-prod-up
203×pow-sqr
201×frac-sub
197×sum-log
176×associate--l+
170×diff-log
168×pow-unpow
152×pow-to-exp
126×+-commutative
101×unpow3 cube-mult
98×unpow-prod-up
92×div-sub
87×pow2
86×pow-plus pow-flip
84×pow-pow
83×distribute-rgt-out--
80×rem-sqrt-square
79×distribute-lft-neg-in distribute-rgt-neg-in
72×inv-pow
71×associate--r+
66×cube-div
49×unpow2
43×log-div
40×rem-log-exp
39×un-div-inv
35×sub-div
33×rem-cube-cbrt
26×sqrt-unprod
25×sinh-def
23×cos-sum
21×neg-mul-1
20×rem-square-sqrt
19×associate-+l- associate-+r-
18×distribute-rgt-out
15×expm1-udef cosh-def
13×expm1-log1p hypot-def rem-cbrt-cube
11×distribute-lft-neg-out
10×unsub-neg
9×rem-exp-log log1p-udef unpow1/3 log1p-expm1 neg-sub0 sum-cubes
8×exp-diff difference-of-sqr-1
7×distribute-rgt-neg-out
6×e-exp-1 tan-quot associate--r-
5×distribute-lft1-in distribute-rgt1-in count-2 hypot-udef
4×exp-neg diff-cos neg-log
3×cos-diff pow-sub exp-to-pow
2×sqrt-pow2 associate--l- distribute-frac-neg sin-mult
1×sqrt-undiv difference-cubes cos-mult distribute-neg-frac

regimes40.3s (1.2%)

Accuracy

Total 207.8b remaining (41.1%)

Threshold costs 30.3b (6%)

18.8b39.6%Data.Array.Repa.Algorithms.Pixel:doubleRmsOfRGB8 from repa-algorithms-3.4.0.1
12.2b60.3%Diagrams.TwoD.Arc:arcBetween from diagrams-lib-1.3.0.3
11.4b48.2%AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1
9.4b8.9%Data.Colour.Matrix:determinant from colour-2.3.3, A
8.8b27.3%Development.Shake.Progress:decay from shake-0.15.5

localize9.5s (0.3%)

bsearch4.3s (0.1%)

end5.0ms (0.0%)