Details

rewrite10.6m (71.2%)

Algorithm
151×rewrite-expression-head
Calls

447 calls:

9.2s
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
2.1s
(+ (/ (/ (+ alpha beta) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) 1.0)
1.2s
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
794.0ms
(* (/ 1 (+ (+ (* (* 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))))) (* x (* 1 (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))))
755.0ms
(/ (+ (+ (* (* 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
13676×times-frac
10835×*-un-lft-identity
8240×add-sqr-sqrt
6511×add-cube-cbrt
2577×add-exp-log
2498×fma-def
2002×cbrt-div
1934×add-cbrt-cube
1759×associate-/r/
1674×distribute-lft-out
1552×prod-diff
1459×cbrt-prod
1403×pow1
1251×flip-+ flip3-+
921×prod-exp
808×sqrt-prod
799×associate-*l*
730×associate-*r*
660×associate-/r*
656×frac-times
650×add-log-exp
641×cbrt-unprod
636×div-inv
614×div-exp
604×difference-of-squares
597×distribute-lft-out--
460×associate-*r/
447×expm1-log1p-u
446×log1p-expm1-u
429×associate-/l*
411×associate-*l/
389×cbrt-undiv
383×pow-prod-down
348×unpow-prod-down
278×distribute-rgt-in log-prod distribute-lft-in
270×exp-sum
239×fma-neg
222×log-pow
196×unswap-sqr
169×associate--l+
145×sqrt-pow1
142×cube-prod
130×flip3-- flip--
121×*-commutative
113×1-exp
92×sqr-pow
91×pow-exp
88×sub-neg
85×clear-num swap-sqr frac-2neg
84×pow-unpow sqrt-div
77×diff-log
76×associate-/l/ pow1/3 exp-prod
74×pow1/2
70×rec-exp
69×fma-udef
58×associate-+l+
57×pow-to-exp
53×pow-prod-up
44×associate-+r+
39×distribute-rgt-neg-in distribute-lft-neg-in
38×frac-add
36×sum-log
35×pow-sqr
32×pow-pow
28×pow-flip pow-plus
27×rem-sqrt-square
26×neg-mul-1
24×+-commutative
21×unpow3 inv-pow cube-mult
19×hypot-udef rem-log-exp
18×pow2
17×associate--l-
16×div-sub
14×hypot-def
12×rem-cube-cbrt
11×rem-exp-log
10×distribute-rgt-out
8×log-div unpow2
7×log-rec
6×neg-log associate--r+
5×cube-div exp-diff distribute-lft-neg-out
4×sin-sum unpow-prod-up neg-sub0 frac-sub cos-sum
3×sqrt-unprod unsub-neg rem-square-sqrt associate-+l-
2×distribute-neg-out associate-+r- pow3 distribute-rgt-neg-out
1×sqrt-undiv sqrt-pow2 e-exp-1 un-div-inv log1p-udef exp-neg log1p-expm1 distribute-neg-in pow-sub cube-unmult distribute-frac-neg

sample1.8m (11.9%)

Algorithm
99×intervals
Results
45.3s12412×body10240exit
18.7s457813×body80valid
11.0s27570×body1280valid
4.9s21099×body640valid
2.5s68933×body80nan
1.8s1753×body1280nan
1.6s10672×body320valid
967.0ms9268×body160valid
960.0ms1346×body640nan
725.0ms49536×pre80true
351.0ms669×body320nan
345.0ms1519×body2560valid
136.0ms580×body5120valid
124.0ms359×body160nan

prune1.1m (7.3%)

series1.1m (7.1%)

Calls

446 calls:

8.9s
(log (/ (* 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))))))
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))))
1.8s
(/ (* (* (- (* (+ (+ 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))))
877.0ms
(* (fma (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)) 0.5) (- (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5))
777.0ms
(pow E (log (fma (/ (* (sqrt (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)) (sqrt (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))) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0)))

simplify14.0s (1.6%)

Algorithm
249×egg-herbie

regimes5.0s (0.6%)

Accuracy

Total 42.8b remaining (38.9%)

Threshold costs 4.4b (4%)

8.4b32.2%_divideComplex, imaginary part
7.2b38.5%_divideComplex, real part
5.4b16.9%Octave 3.8, jcobi/2
4.7b22.7%math.sqrt on complex, imaginary part, im greater than 0 branch
4.4b44.4%Octave 3.8, jcobi/4

localize2.7s (0.3%)

bsearch1.0s (0.1%)

end1.0ms (0.0%)