Details

rewrite10.2m (69.5%)

Algorithm
153×rewrite-expression-head
Calls

447 calls:

1.7s
(* (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) 1) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ beta (+ alpha (fma 1.0 2.0 1.0)))))
1.2s
(+ (/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
492.0ms
(/ (+ (+ (* (* 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)))))
479.0ms
(/ (+ (+ (* (* 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)))))
476.0ms
(/ (+ (+ (* (* 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)))))
Rules
23256×times-frac
19723×*-un-lft-identity
13754×add-sqr-sqrt
10541×add-cube-cbrt
3658×distribute-lft-out
3399×add-exp-log
1920×sqrt-prod
1905×prod-diff
1767×add-cbrt-cube
1585×fma-def
1447×associate-*r*
1438×prod-exp
1264×pow1
1087×difference-of-squares
1063×distribute-lft-out--
1057×div-exp
874×associate-*l*
862×associate-/l*
851×associate-/r/
748×unpow-prod-down
685×associate-/r*
682×add-log-exp
672×div-inv
556×cube-prod
519×pow-exp
491×flip-+ flip3-+
454×cbrt-unprod
450×log1p-expm1-u
445×expm1-log1p-u
429×cbrt-undiv
315×pow-to-exp
294×unswap-sqr
281×1-exp
272×pow-prod-down
248×cbrt-prod
236×fma-neg
217×distribute-rgt-in distribute-lft-in
195×rec-exp
194×log-pow
183×associate--l+
170×sqr-pow
158×sqrt-pow1
148×associate-*r/
145×flip3-- flip--
142×exp-sum
123×swap-sqr
117×*-commutative
116×log-prod
97×frac-2neg clear-num
91×exp-prod
89×sqrt-div
88×associate-/l/ sub-neg
84×pow1/2
82×diff-log
80×pow-unpow unpow3 cube-mult
71×associate-*l/ associate--r+
62×fma-udef
56×pow-prod-up cbrt-div
54×pow1/3
52×frac-times
49×sum-log
48×pow-pow frac-add
45×distribute-rgt-neg-in distribute-lft-neg-in
44×rem-sqrt-square
38×pow-sqr
32×pow-plus
31×+-commutative
28×neg-mul-1
26×associate-+r+
22×pow2
19×div-sub
18×pow-flip associate--l-
17×associate-+l+
15×inv-pow
14×distribute-rgt1-in distribute-rgt-out hypot-def
13×rem-cube-cbrt
10×rem-exp-log
9×distribute-rgt-neg-out
7×cube-div un-div-inv distribute-neg-in
6×neg-log
5×exp-diff log1p-udef log1p-expm1 expm1-log1p expm1-udef
4×sqrt-unprod sin-sum unsub-neg unpow1/2 neg-sub0 frac-sub unpow2
3×pow3 rem-square-sqrt associate-+l- rem-log-exp log-div
2×sqrt-pow2 distribute-lft-neg-out exp-neg hypot-udef associate--r-
1×difference-cubes unpow-prod-up pow-sub cos-sum distribute-rgt-out-- exp-to-pow

sample1.7m (11.6%)

Algorithm
99×intervals
Results
44.1s11958×body10240exit
20.1s474652×body80valid
11.1s27324×body1280valid
4.9s20939×body640valid
2.7s71279×body80nan
1.7s1610×body1280nan
1.6s10713×body320valid
982.0ms9414×body160valid
912.0ms1289×body640nan
656.0ms49536×pre80true
337.0ms1444×body2560valid
314.0ms628×body320nan
146.0ms578×body5120valid
99.0ms295×body160nan

series1.2m (8.3%)

Calls

445 calls:

7.3s
(/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
7.1s
(/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
2.9s
(pow (exp (* (cbrt (log (fma (sqrt 1.0) (sqrt 1.0) (* (- (* (/ 1 (exp (pow (fabs x) 2))) (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592))))) (cbrt (log (fma (sqrt 1.0) (sqrt 1.0) (* (- (* (/ 1 (exp (pow (fabs x) 2))) (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592))))))) (cbrt (log (fma (sqrt 1.0) (sqrt 1.0) (* (- (* (/ 1 (exp (pow (fabs x) 2))) (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592))))))
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))))
1.1s
(* 6.0 (pow (/ 1 (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0)))) 0.5))

prune1.1m (7.7%)

simplify15.1s (1.7%)

Algorithm
251×egg-herbie

regimes5.7s (0.6%)

Accuracy

Total 41.0b remaining (29.1%)

Threshold costs 5.6b (4%)

7.2b36.4%_divideComplex, real part
6.5b2.3%math.sqrt on complex, real part
5.9b11.5%Octave 3.8, jcobi/2
5.2b11.6%math.sqrt on complex, imaginary part, im greater than 0 branch
4.1b53.4%_divideComplex, imaginary part

localize2.5s (0.3%)

bsearch1.2s (0.1%)

end1.0ms (0.0%)