Details

sample7.3m (43.1%)

Algorithm
78×intervals
Results
3.0m25797×body10240exit
1.7m43626×body1280valid
40.8s31115×body640valid
27.8s202594×body80valid
20.3s27857×body320valid
20.3s153103×body80nan
12.6s35981×body160valid
11.5s163544×pre80true
3.3s3039×body2560valid
1.4s7926×body160nan
949.0ms4152×pre10240exit
407.0ms289×body5120valid

simplify5.3m (31.4%)

prune2.0m (11.6%)

series1.6m (9.6%)

Calls

493 calls:

22.4s
(/ (fma (fma (* -4 a) c (* b b)) (sqrt (fma (* -4 a) c (* b b))) (- (* b (* b b)))) (fma b (+ b (sqrt (fma (* -4 a) c (* b b)))) (expm1 (log1p (fma (* -4 a) c (* b b))))))
1.4s
(* (fma (* -4 a) c (* b b)) (sqrt (fma (* -4 a) c (* b b))))
1.3s
(- (* (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b)))) (* b (* b b)))
1.3s
(* (fma (* c -3) a (* b b)) (sqrt (fma (* c -3) a (* b b))))
1.3s
(- (* (fma (* -4 a) c (* b b)) (sqrt (fma (* -4 a) c (* b b)))) (* b (* b b)))

regimes21.0s (2.1%)

Accuracy

Total 36.0b remaining (9.7%)

Threshold costs 5.3b (1.4%)

5.5b33.5%Quotient of products
4.2b84.3%Quadratic roots, full range
3.2b0%Cubic critical, medium range
3.2b0%Quadratic roots, wide range
3.1b0%Quadratic roots, medium range

rewrite10.6s (1.0%)

Algorithm
145×rewrite-expression-head
Calls

493 calls:

441.0ms
(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))
378.0ms
(cbrt (* (* (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
369.0ms
(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (* (* (cbrt (log1p (exp x))) (cbrt (log1p (exp x)))) (cbrt (log1p (exp x)))) (* y x)))))
331.0ms
(+ (/ 1 (- x 1)) (/ 1 (/ (+ x 1) x)))
227.0ms
(* (- (/ (* (* m (+ 1 (sqrt m))) (- 1 (sqrt m))) v) 1) (- 1 m))
Rules
15040×*-un-lft-identity
12717×times-frac
12100×add-sqr-sqrt
8464×add-cube-cbrt
6747×prod-diff
2607×add-exp-log
2059×distribute-lft-out
1879×sqrt-prod
1633×difference-of-squares
1286×pow1
1251×add-cbrt-cube
986×associate-/r/
980×prod-exp
883×distribute-lft-out--
856×div-exp
771×div-inv
697×pow-exp
679×add-log-exp
570×associate-*l*
568×fma-neg
564×difference-of-sqr-1
498×expm1-log1p-u
494×log1p-expm1-u
493×insert-posit16
466×associate-/l*
441×flip-+
440×flip3-+
431×associate-*r*
360×flip--
359×flip3--
351×associate-/r*
348×pow-to-exp
342×associate--r+
258×cbrt-unprod
219×pow-prod-down
215×frac-times
203×cbrt-undiv
201×cbrt-prod
186×unpow-prod-down
184×sqrt-div
165×distribute-rgt-in distribute-lft-in
152×log-prod
150×1-exp
147×rec-exp
142×pow-prod-up
133×unswap-sqr
132×fma-def
125×associate-*l/
122×associate-*r/
119×fma-udef
106×swap-sqr
96×*-commutative
90×frac-2neg clear-num
86×sub-neg
83×cbrt-div
76×associate-/l/ pow-sqr
73×frac-sub
72×log-pow
68×sqrt-pow1
65×pow-plus diff-log
62×sqr-pow
60×pow1/2
58×tan-quot
57×cos-sum
51×pow2
47×div-sub
43×distribute-rgt-neg-in
41×exp-sum
40×pow3
35×pow1/3
31×sum-log exp-prod log-div
27×rem-log-exp distribute-lft-neg-in
26×rem-sqrt-square
24×pow-flip difference-cubes
22×sin-sum cube-unmult distribute-rgt-out--
20×+-commutative
18×inv-pow
17×sin-diff
15×pow-unpow
14×pow-pow sin-mult
13×expm1-def
11×sin-cos-mult
10×acos-asin
9×neg-mul-1 cos-diff
8×log1p-udef
7×rem-exp-log
6×log1p-expm1 distribute-rgt-out
5×rem-cbrt-cube
4×expm1-log1p expm1-udef exp-diff cube-prod cos-mult distribute-frac-neg associate--l+ neg-sub0 exp-to-pow acos-neg frac-add
3×rem-cube-cbrt log-rec neg-log un-div-inv associate-+l- associate--r-
2×distribute-rgt1-in unpow3 sqrt-unprod sub-div associate--l- hypot-udef asin-acos log1p-def hypot-def rem-square-sqrt cube-mult
1×hypot-1-def tanh-def tanh-undef unpow1/3

localize6.6s (0.6%)

bsearch4.8s (0.5%)

end1.0ms (0.0%)