Details

sample1.7m (36.1%)

Algorithm
98×intervals
Results
43.5s8571×body10240exit
18.4s437321×body80valid
11.3s27266×body1280valid
5.0s20392×body640valid
2.6s69400×body80nan
1.8s1759×body1280nan
1.7s10675×body320valid
1.1s9854×body160valid
928.0ms1324×body640nan
657.0ms49536×pre80true
386.0ms1529×body2560valid
383.0ms740×body320nan
258.0ms5092×body80overflowed
148.0ms584×body5120valid
144.0ms410×body160nan

prune1.0m (22.4%)

series59.4s (21.4%)

Calls

431 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))))
1.2s
(pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)
967.0ms
(* (/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
940.0ms
(* 0.16666666666666666 (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5))
792.0ms
(log (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0))

rewrite34.0s (12.2%)

Algorithm
148×rewrite-expression-head
Calls

431 calls:

7.0s
(* (/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (* (* x x) (* x x)))) (* 0.0072644182 (* (* (* x x) (* x x)) (* x x)))) (* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (+ (+ (+ (+ (+ (+ 1.0 (* 0.7715471019 (* x x))) (* 0.2909738639 (* (* x x) (* x x)))) (* 0.0694555761 (* (* (* x x) (* x x)) (* x x)))) (* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0008327945 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (* 2.0 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x))))) x)
5.1s
(* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))
4.9s
(* 0.0008327945 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))
4.1s
(/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (* (* x x) (* x x)))) (* 0.0072644182 (* (* (* x x) (* x x)) (* x x)))) (* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (+ (+ (+ (+ (+ (+ 1.0 (* 0.7715471019 (* x x))) (* 0.2909738639 (* (* x x) (* x x)))) (* 0.0694555761 (* (* (* x x) (* x x)) (* x x)))) (* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0008327945 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (* 2.0 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x)))))
1.0s
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
Rules
16415×times-frac
13671×*-un-lft-identity
10579×add-sqr-sqrt
8015×add-cube-cbrt
2971×add-exp-log
2189×pow1
2145×add-cbrt-cube
1977×distribute-lft-out
1421×prod-exp
1370×prod-diff
1291×fma-def
979×pow-prod-down
972×cbrt-unprod
943×difference-of-squares
930×distribute-lft-out--
897×associate-*r*
837×associate-/r/
771×associate-/l*
727×sqrt-prod
674×associate-*l*
637×associate-/r*
625×add-log-exp
576×div-exp
521×cbrt-prod
511×div-inv
478×flip-+ flip3-+
432×log1p-expm1-u
431×expm1-log1p-u
284×cbrt-undiv
278×distribute-rgt-in distribute-lft-in
247×unswap-sqr
234×sqrt-pow1
217×log-pow
213×fma-neg
202×associate-*r/
191×log-prod
179×1-exp flip3-- flip--
158×exp-sum
156×pow-exp
141×associate--l+
135×cbrt-div
129×unpow-prod-down
125×*-commutative
121×sqrt-div
116×rec-exp swap-sqr
113×pow1/3
108×pow-prod-up
88×pow-to-exp
85×clear-num frac-2neg
84×sub-neg
80×cube-prod
77×pow1/2
76×exp-prod
75×associate-*l/ diff-log
73×associate--r+
70×frac-times
67×associate-/l/
58×pow-sqr
50×fma-udef
49×pow-plus
47×sqr-pow
46×pow-unpow
40×distribute-rgt-neg-in distribute-lft-neg-in frac-add
34×sum-log
32×rem-sqrt-square
28×pow2 neg-mul-1
26×pow-pow
21×pow-flip +-commutative rem-log-exp
18×unpow3 cube-mult
16×inv-pow frac-sub log-div
15×associate--l-
14×div-sub
13×pow3
12×hypot-def
11×cube-div
9×exp-diff un-div-inv
7×rem-exp-log
6×neg-sub0
5×rem-cube-cbrt associate-+l+ exp-neg
4×sin-sum expm1-udef unpow2
3×neg-log distribute-rgt-neg-out associate-+l-
2×sqrt-pow2 distribute-neg-in expm1-log1p rem-cbrt-cube
1×log1p-udef sqrt-unprod log1p-expm1 hypot-udef rem-square-sqrt distribute-frac-neg cos-sum associate--r- distribute-rgt-out--

simplify13.7s (4.9%)

Algorithm
244×egg-herbie

regimes5.2s (1.9%)

Accuracy

Total 47.8b remaining (31.8%)

Threshold costs 5.2b (3.5%)

9.9b16%_divideComplex, imaginary part
7.8b31.5%_divideComplex, real part
6.3b-8.3%math.sqrt on complex, real part
5.8b-4%math.sqrt on complex, imaginary part, im greater than 0 branch
5.6b18.3%Octave 3.8, jcobi/2

localize2.2s (0.8%)

bsearch1.1s (0.4%)

end1.0ms (0.0%)