Details

rewrite10.2m (71.8%)

Algorithm
151×rewrite-expression-head
Calls

436 calls:

478.0ms
(/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))
401.0ms
(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))
340.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
306.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
298.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
Rules
11418×times-frac
9811×*-un-lft-identity
7370×add-sqr-sqrt
6374×add-cube-cbrt
2276×add-exp-log
1697×distribute-lft-out
1572×add-cbrt-cube
1513×sqrt-prod
1392×pow1
1272×prod-diff
730×associate-/l*
726×prod-exp
675×associate-/r/
670×associate-*r*
634×add-log-exp
621×div-exp
607×associate-*l*
586×div-inv
508×associate-/r*
467×flip-+ flip3-+
435×log1p-expm1-u
433×expm1-log1p-u
419×cbrt-unprod
355×pow-prod-down
331×cbrt-undiv
323×associate-*r/
316×cbrt-prod
276×unpow-prod-down
232×sqrt-div
225×difference-of-squares
223×log-pow
217×distribute-lft-out--
205×unswap-sqr
198×fma-neg
191×sqrt-pow1
165×exp-sum
163×fma-def
157×distribute-rgt-in distribute-lft-in
146×1-exp
142×log-prod
139×associate--l+
136×frac-add
119×flip3-- flip--
114×*-commutative cube-prod
100×pow1/3
95×clear-num frac-2neg
92×frac-times
88×sqr-pow
87×swap-sqr pow-exp
83×associate-*l/ rec-exp
76×associate-/l/ sub-neg
72×cbrt-div diff-log
71×pow-prod-up
70×pow-to-exp
69×associate--r+
67×pow-unpow
65×exp-prod
61×pow1/2
51×fma-udef
47×pow-sqr
40×distribute-rgt-neg-in distribute-lft-neg-in pow-plus sum-log
29×rem-sqrt-square
27×+-commutative
23×unpow3 cube-mult pow2
22×pow-pow neg-mul-1
21×div-sub log-div
18×hypot-def
17×unpow2
16×pow-flip
14×inv-pow
13×associate--l-
12×frac-sub
11×rem-log-exp
10×exp-diff rem-cube-cbrt
7×rem-exp-log associate-+l+
6×expm1-udef
4×cube-div pow3 sin-sum expm1-log1p distribute-rgt-neg-out
3×un-div-inv associate-+l-
2×sqrt-undiv cos-diff associate-+r+ distribute-frac-neg neg-sub0
1×sqrt-pow2 log1p-udef sqrt-unprod log1p-expm1 hypot-udef unsub-neg rem-square-sqrt cos-sum associate--r- rem-cbrt-cube

sample1.7m (12.2%)

Algorithm
99×intervals
Results
43.8s12092×body10240exit
22.2s500333×body80valid
11.1s27438×body1280valid
4.8s20626×body640valid
2.5s69552×body80nan
1.6s1566×body1280nan
1.6s10745×body320valid
948.0ms9367×body160valid
927.0ms1311×body640nan
633.0ms49536×pre80true
345.0ms663×body320nan
343.0ms1516×body2560valid
140.0ms582×body5120valid
109.0ms327×body160nan

prune1.0m (7.3%)

series51.3s (6.0%)

Calls

433 calls:

1.8s
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))
780.0ms
(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
759.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
727.0ms
(pow (fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3)
720.0ms
(/ 1.0 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))

simplify13.9s (1.6%)

Algorithm
249×egg-herbie

regimes5.3s (0.6%)

Accuracy

Total 46.6b remaining (39.7%)

Threshold costs 5.1b (4.3%)

10.2b17.4%_divideComplex, imaginary part
7.2b-7%Octave 3.8, jcobi/2
7.1b38%_divideComplex, real part
6.8b-8.5%math.sqrt on complex, real part
4.1b27.2%math.sqrt on complex, imaginary part, im greater than 0 branch

localize2.3s (0.3%)

bsearch939.0ms (0.1%)

end1.0ms (0.0%)