Details

sample13.2m (56.6%)

Algorithm
78×intervals
Results
8.9m52262×body10240exit
1.7m43284×body1280valid
43.2s30355×body640valid
27.9s205151×body80valid
20.3s27731×body320valid
19.8s152746×body80nan
13.2s36097×body160valid
13.2s190763×pre80true
2.9s3059×body2560valid
1.9s8254×body160nan
1.5s4142×pre10240exit
733.0ms215×body5120valid
2.0ms1×body640nan
1.0ms1×body320nan

simplify6.2m (26.6%)

prune2.2m (9.4%)

series1.0m (4.4%)

Calls

486 calls:

1.6s
(* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b)))
1.4s
(* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b)))
1.2s
(- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b)))
1.1s
(- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b)))
891.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2))) R)

regimes20.7s (1.5%)

Accuracy

Total 43.2b remaining (20.8%)

Threshold costs 4.5b (2.2%)

7.3b47.6%Quadratic roots, narrow range
6.1b10%Quadratic roots, medium range
4.3b32.6%Quotient of products
4.3b84.5%Quadratic roots, full range
3.7b0%Quadratic roots, wide range

rewrite14.3s (1.0%)

Algorithm
147×rewrite-expression-head
Calls

486 calls:

402.0ms
(cbrt (* (* (* (/ x (+ x 1)) (/ x (+ x 1))) (* (/ x (+ x 1)) (/ x (+ x 1)))) (* (/ x (+ x 1)) (/ x (+ x 1)))))
275.0ms
(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* y x) (* (* y x) (* y x)))) (fma (log1p (exp x)) (log1p (exp x)) (fma (* y x) (log1p (exp x)) (* (* y x) (* y x)))))
273.0ms
(/ (/ (+ (* (sqrt (fma (* a c) -3 (* b b))) (* (* a c) -3)) (- (* (sqrt (fma (* a c) -3 (* b b))) (* b b)) (* b (* b b)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b)))) (* 3 a))
265.0ms
(/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (sqrt (fma (log1p (exp x)) (log1p (exp x)) (fma (* y x) (log1p (exp x)) (* (* y x) (* y x))))))
260.0ms
(* (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b)))) (/ (exp a) (+ (exp (* b 3)) (exp (* 3 a)))))
Rules
14302×times-frac
12704×add-sqr-sqrt
12657×*-un-lft-identity
8717×add-cube-cbrt
5110×add-exp-log
4283×prod-diff
2271×cbrt-prod
2078×add-cbrt-cube
2068×div-exp
1977×prod-exp
1668×pow1
1616×associate-*l*
1434×difference-of-squares
1064×sqrt-prod
921×associate-*r*
884×distribute-lft-out
722×distribute-lft-out--
719×associate-/r/
704×div-inv
695×pow-exp
687×add-log-exp
668×associate-/r*
598×cbrt-undiv
592×cbrt-unprod
491×expm1-log1p-u
487×log1p-expm1-u
486×insert-posit16
485×associate-/l*
457×swap-sqr
420×associate--l+
416×1-exp
407×rec-exp
394×difference-of-sqr-1
363×associate-+l+
347×pow-prod-down pow-to-exp
344×frac-times
336×fma-neg
317×unswap-sqr
308×pow-prod-up
279×flip-+
278×flip3-+
272×flip--
271×flip3--
260×associate-*l/
256×unpow-prod-down
234×associate-*r/
228×log-prod
202×sqrt-pow1
185×pow1/2
159×cbrt-div
151×pow-sqr
131×fma-def
130×sqrt-div
126×*-commutative
114×associate-/l/
111×frac-2neg clear-num
109×pow-plus
85×cube-prod
81×distribute-rgt-out--
80×pow-flip
78×sqr-pow inv-pow
74×sub-neg
73×distribute-rgt-in log-pow distribute-lft-in
71×fma-udef
69×diff-log
66×pow2
59×exp-prod
50×cube-unmult
47×cos-sum
45×div-sub
44×associate-+r+
39×sum-log tan-quot
35×pow1/3
33×sin-sum frac-add
32×rem-sqrt-square
31×frac-sub
29×rem-log-exp
28×unpow3 cube-mult
26×difference-cubes distribute-rgt-neg-in
22×+-commutative
18×sin-diff distribute-lft-neg-in
17×log-div
15×sin-cos-mult
14×pow3 un-div-inv sin-mult
13×cos-mult
10×cos-diff
9×associate-+l-
8×sqrt-unprod associate--r+ expm1-def
7×acos-asin log1p-udef
6×pow-unpow neg-mul-1 pow-pow exp-to-pow
5×expm1-log1p neg-sub0 expm1-udef associate-+r- distribute-rgt-neg-out log1p-expm1 log-rec
4×associate--l- neg-log rem-square-sqrt
3×rem-cbrt-cube
2×distribute-lft-neg-out exp-diff hypot-udef rem-exp-log
1×unsub-neg distribute-frac-neg exp-sum tanh-undef tanh-def asin-acos acos-neg

localize6.6s (0.5%)

bsearch1.2s (0.1%)

end1.0ms (0.0%)