Details

simplify12.1m (39.3%)

prune8.6m (27.9%)

sample5.5m (17.9%)

Algorithm
100×intervals
Results
1.8m16134×body10240exit
1.4m465557×body80valid
47.6s30592×body1280valid
27.0s23666×body640valid
11.9s3191×body1280nan
9.8s70644×body80nan
8.1s2637×body640nan
8.0s11917×body320valid
4.2s9875×body160valid
2.9s1299×body320nan
2.1s49536×pre80true
1.3s1457×body2560valid
1.1s646×body160nan
1.1s595×body5120valid

rewrite2.7m (8.8%)

Algorithm
167×rewrite-expression-head
Calls

517 calls:

42.7s
(log (exp (- 1 (/ (/ (+ (/ (+ (/ (+ (/ (+ (/ 1.061405429 (+ (* (fabs x) 0.3275911) 1)) -1.453152027) (+ (* (fabs x) 0.3275911) 1)) 1.421413741) (+ (* (fabs x) 0.3275911) 1)) -0.284496736) (+ (* (fabs x) 0.3275911) 1)) 0.254829592) (+ (* (fabs x) 0.3275911) 1)) (exp (* (fabs x) (fabs x)))))))
27.4s
(* (/ (* (pow (+ (+ 7 (- z 1)) 0.5) (- z 1)) (* (pow (+ (+ 7 (- z 1)) 0.5) 0.5) (sqrt (* PI 2)))) (exp (+ (+ 7 (- z 1)) 0.5))) (+ (+ (/ -176.6150291621406 (+ (- z 1) 4)) (+ (+ (+ (/ 771.3234287776531 (+ 2 z)) (/ 676.5203681218851 z)) (+ 0.9999999999998099 (/ -1259.1392167224028 (- z -1)))) (/ -0.13857109526572012 (- z -5)))) (/ 12.507343278686905 (+ 4 z))))
22.6s
(* (/ 1 (sqrt 21)) (* (/ 1 (sqrt 21)) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))
10.6s
(- 1 (/ (/ (+ (/ (+ (/ (+ (/ (+ (/ 1.061405429 (+ (* (fabs x) 0.3275911) 1)) -1.453152027) (+ (* (fabs x) 0.3275911) 1)) 1.421413741) (+ (* (fabs x) 0.3275911) 1)) -0.284496736) (+ (* (fabs x) 0.3275911) 1)) 0.254829592) (+ (* (fabs x) 0.3275911) 1)) (exp (* (fabs x) (fabs x)))))
7.7s
(* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
Rules
63168×*-un-lft-identity
62090×times-frac
25135×add-sqr-sqrt
24159×distribute-lft-out
21584×add-cube-cbrt
9571×sqrt-prod
4097×add-exp-log
3471×pow1
2867×add-cbrt-cube
1934×prod-exp
1931×associate-/r/
1474×div-inv
1410×difference-of-squares
1400×flip-+ flip3-+
1227×associate-/l*
1139×cbrt-unprod
1040×associate-/r*
1023×associate-*r*
985×associate-*l*
888×div-exp
882×pow-prod-up
806×add-log-exp
800×pow-prod-down
738×distribute-lft-out--
548×cbrt-undiv
501×associate-*l/
449×pow-plus
421×cbrt-div
418×cbrt-prod
416×frac-times
350×associate-*r/
312×sqrt-div
303×unpow-prod-down
278×log-pow
269×unswap-sqr
236×pow-sqr
234×frac-add
216×sqrt-pow1
178×flip3-- flip--
174×pow2
170×*-commutative
161×unpow-prod-up
143×pow1/2
142×1-exp
136×rec-exp
128×associate-/l/ sub-neg
115×exp-sum
112×sum-log
105×frac-2neg clear-num
103×swap-sqr
101×pow1/3
94×sqr-pow
93×pow-exp
90×log-prod
88×associate--l+
78×distribute-rgt-in distribute-lft-in
70×rem-sqrt-square
58×pow-to-exp
57×+-commutative
55×diff-log
52×pow-pow
43×exp-prod
32×associate--r-
30×pow3
29×pow-flip
26×cube-unmult
20×frac-sub
19×inv-pow
18×pow-unpow div-sub
14×pow-sub
13×exp-diff associate-+r- associate-+r+
11×log-div
10×associate-+l+ associate-+l-
associate--r+
un-div-inv distribute-rgt-out
rem-exp-log
sin-sum rem-log-exp
associate--l- distribute-rgt1-in
difference-of-sqr-1 sum-cubes
rem-cube-cbrt distribute-lft-neg-out sqrt-undiv distribute-rgt-neg-out
pow-div sqrt-unprod rem-square-sqrt
cube-prod unpow3 cube-mult unpow1/3 cos-sum cube-div count-2 rem-cbrt-cube unsub-neg e-exp-1

series1.4m (4.6%)

Calls

517 calls:

2.9s
(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
2.7s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
2.6s
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) -0.284496736)) (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (* (* (/ 1 (- (* 1 1) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (- 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (exp (- (* (fabs x) (fabs x))))))
1.7s
(/ (+ (pow 0.5 3) (pow (* (cos (* u2 (* 2 PI))) (/ (pow (* (log u1) -2) 0.5) 6)) 3)) (+ (* 0.5 0.5) (- (* (* (cos (* u2 (* 2 PI))) (/ (pow (* (log u1) -2) 0.5) 6)) (* (cos (* u2 (* 2 PI))) (/ (pow (* (log u1) -2) 0.5) 6))) (* 0.5 (* (cos (* u2 (* 2 PI))) (/ (pow (* (log u1) -2) 0.5) 6))))))
1.4s
(/ (pow (* (log u1) -2) 0.5) 6)

regimes14.7s (0.8%)

Accuracy

Total 83.4b remaining (31.4%)

Threshold costs 4.9b (1.8%)

9.9b57.8%math.log/2 on complex, real part
9.8b58.8%math.log10 on complex, real part
9.6b59.5%math.log/1 on complex, real part
9.4b68.3%math.sqrt on complex, imaginary part, im greater than 0 branch
9.0b59.4%math.abs on complex

localize7.9s (0.4%)

bsearch3.7s (0.2%)

end1.0ms (0.0%)