Details

rewrite15.6m (51.6%)

Algorithm
160×rewrite-expression-head
Calls

495 calls:

2.1m
(+ (/ -176.6150291621406 (+ 4.0 (- z))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ 9.984369578019572e-06 (+ 7.0 (- z))))))
1.6m
(+ (/ -176.6150291621406 (+ 4.0 (- z))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ 9.984369578019572e-06 (+ 7.0 (- z))))))
1.5m
(+ (/ -176.6150291621406 (+ 4.0 (- z))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ 9.984369578019572e-06 (+ 7.0 (- z))))))
1.2m
(* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5))) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))))))
1.1m
(+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ 9.984369578019572e-06 (+ 7.0 (- z)))))
Rules
8383×frac-add
7863×*-un-lft-identity
7434×times-frac
5937×add-sqr-sqrt
4583×add-cube-cbrt
3301×add-exp-log
2984×flip-+ flip3-+
2718×add-cbrt-cube
2380×sqrt-prod
2286×pow1
2149×frac-times
1751×distribute-lft-out
1606×prod-exp
1463×associate-*r/
1286×cbrt-unprod
1282×associate-*r*
1273×associate-*l/
1175×add-log-exp
1088×associate-*l*
1044×pow-prod-down
813×exp-neg
729×unpow-prod-down
609×associate-/l*
582×associate-/r/
538×associate-/l/
525×div-exp
516×exp-diff
495×neg-sub0
494×pow-sub
455×cbrt-prod
444×associate-/r*
429×sum-log
365×cbrt-undiv
352×div-inv
332×un-div-inv
324×difference-of-squares
282×unswap-sqr
275×sqrt-div
256×associate-+l-
250×cbrt-div
247×distribute-lft-out--
219×log-pow
212×sqrt-pow1
209×cube-prod
205×swap-sqr
187×flip-- flip3--
173×sqr-pow
170×pow-unpow
154×exp-sum
149×pow1/2
148×pow-exp
140×*-commutative log-prod
105×exp-prod
102×pow-to-exp
94×frac-sub
90×frac-2neg clear-num
81×pow1/3
80×sub-neg
71×rem-sqrt-square
67×distribute-rgt-in distribute-lft-in
60×unpow-prod-up
58×+-commutative
54×diff-log
47×pow-prod-up
45×1-exp
43×rec-exp
42×pow-pow
37×pow-sqr
31×distribute-rgt-neg-in
28×rem-cube-cbrt
26×div-sub
24×cube-div
23×rem-exp-log
22×unpow3 cube-mult
21×distribute-lft-neg-in
19×log-div
17×associate-+l+ pow-plus
15×pow2 associate-+r+
13×associate-+r-
12×neg-log
10×sum-cubes
associate--r+ rem-log-exp
sin-sum
e-exp-1 inv-pow unpow2 pow-flip associate--l+
sqrt-undiv neg-mul-1
difference-cubes sqrt-unprod distribute-neg-in rem-square-sqrt rem-cbrt-cube
cos-sum sqrt-pow2 unsub-neg pow-neg
distribute-rgt-out-- distribute-rgt-out associate--r- associate--l-

simplify7.6m (25.2%)

sample2.7m (8.9%)

Algorithm
99×intervals
Results
49.2s435510×body80valid
29.6s30468×body1280valid
16.4s23370×body640valid
15.8s11871×body10240exit
7.6s70314×body80nan
6.1s11701×body320valid
3.5s10264×body160valid
2.1s1573×body1280nan
1.8s1322×body640nan
1.8s49536×pre80true
947.0ms1547×body2560valid
940.0ms570×body5120valid
519.0ms647×body320nan
145.0ms340×body160nan

prune2.1m (7.1%)

series1.9m (6.2%)

Calls

493 calls:

4.7s
(- (pow 1.0 3) (* (sqrt (pow (/ (* 1.0 (/ (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (exp (pow (fabs x) 2)))) (+ (* 0.3275911 (fabs x)) 1.0)) 3)) (sqrt (pow (/ (* 1.0 (/ (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (exp (pow (fabs x) 2)))) (+ (* 0.3275911 (fabs x)) 1.0)) 3))))
4.7s
(- (pow 1.0 3) (* (sqrt (pow (/ (* 1.0 (/ (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (exp (pow (fabs x) 2)))) (+ (* 0.3275911 (fabs x)) 1.0)) 3)) (sqrt (pow (/ (* 1.0 (/ (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (exp (pow (fabs x) 2)))) (+ (* 0.3275911 (fabs x)) 1.0)) 3))))
4.6s
(- (pow 1.0 3) (pow (/ (* 1.0 (/ (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (exp (pow (fabs x) 2)))) (+ (* 0.3275911 (fabs x)) 1.0)) 3))
3.1s
(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
2.9s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))

regimes11.9s (0.7%)

Accuracy

Total 94.1b remaining (33.9%)

Threshold costs 5.1b (1.8%)

11.1b56.2%math.log/2 on complex, real part
10.2b59%math.log10 on complex, real part
10.1b59.3%math.log/1 on complex, real part
9.9b63.9%math.sqrt on complex, imaginary part, im greater than 0 branch
9.9b58.9%math.abs on complex

localize5.3s (0.3%)

bsearch3.2s (0.2%)

end1.0ms (0.0%)