Details

sample10.0m (57.9%)

Algorithm
78×intervals
Results
5.4m36130×body10240exit
1.8m44174×body1280valid
43.7s30014×body640valid
30.0s203789×body80valid
22.2s152223×body80nan
18.1s27831×body320valid
13.7s36179×body160valid
12.2s174649×pre80true
3.2s2992×body2560valid
1.7s8098×body160nan
1.1s4179×pre10240exit
459.0ms232×body5120valid
4.0ms2×body640nan

simplify3.3m (19.5%)

prune2.1m (12.2%)

series1.0m (5.9%)

Calls

465 calls:

948.0ms
(* (cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))) (cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))))
827.0ms
(* (cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))) (cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))))
792.0ms
(expm1 (log1p (fma (* 1/3 x) x 2)))
717.0ms
(cos (fma 2/3 PI (* (/ (* (cbrt (acos (/ (- g) h))) (cbrt (acos (/ (- g) h)))) (sqrt 3)) (/ (cbrt (acos (/ (- g) h))) (sqrt 3)))))
695.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))

regimes22.4s (2.2%)

Accuracy

Total 51.8b remaining (19.8%)

Threshold costs 5.7b (2.2%)

8.1b41.4%Quadratic roots, narrow range
6.8b0%Quadratic roots, medium range
6.7b38.7%Quotient of products
5.7b57.7%Cubic critical, narrow range
4.1b83.3%Cubic critical

rewrite11.7s (1.1%)

Algorithm
144×rewrite-expression-head
Calls

465 calls:

621.0ms
(* (/ (exp a) (+ (exp (* 3 b)) (exp (* 3 a)))) (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b)))))
405.0ms
(cos (- lambda1 lambda2))
302.0ms
(- (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x)) (/ 1/16 (pow x 5)))
290.0ms
(* (- (+ (/ m v) -1) (/ m (/ v m))) (- 1 m))
215.0ms
(- (/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x))))) 1)
Rules
14299×times-frac
14125×*-un-lft-identity
12526×add-sqr-sqrt
8630×add-cube-cbrt
6103×prod-diff
2861×add-exp-log
1678×distribute-lft-out
1532×difference-of-squares
1508×sqrt-prod
1486×add-cbrt-cube
1094×prod-exp
1027×pow1
971×div-exp
911×associate-/r/
848×div-inv
783×distribute-lft-out--
699×pow-exp
655×associate--l+
654×add-log-exp
623×associate-*l*
547×cbrt-prod
516×associate-*r*
493×fma-neg
473×expm1-log1p-u
469×log1p-expm1-u
465×insert-posit16
461×flip-+
460×flip3-+
434×difference-of-sqr-1
412×associate-/r*
366×associate-/l*
353×cbrt-unprod
349×pow-to-exp
315×cbrt-undiv
270×unpow-prod-down
180×pow-prod-down
171×log-prod
168×flip--
167×flip3--
157×unswap-sqr
153×1-exp
144×rec-exp
129×distribute-rgt-in distribute-lft-in
126×frac-times
120×sqrt-div
115×swap-sqr
110×fma-def
98×*-commutative
97×associate-*r/
96×frac-2neg clear-num
93×associate-*l/
90×difference-of-sqr--1
85×cube-prod
84×sqr-pow
82×distribute-rgt-out--
79×sub-neg
71×diff-log
70×pow-prod-up
68×pow1/3
64×fma-udef
60×cbrt-div
58×associate-/l/
53×pow-plus
48×cos-sum
47×log-pow
46×exp-sum
37×frac-sub
36×sum-log sqrt-pow1 div-sub pow1/2
35×pow-sqr
33×sin-sum
32×distribute-rgt-neg-in
31×distribute-rgt-out
29×pow2 log-div
28×unpow3 rem-sqrt-square cube-mult
26×exp-prod rem-log-exp
25×distribute-lft-neg-in
22×tan-quot
19×+-commutative frac-add
18×pow-pow sin-diff
17×associate--r+
15×pow-flip inv-pow
14×sin-cos-mult sin-mult log1p-udef
12×log1p-expm1
10×cos-diff
9×distribute-rgt1-in pow-unpow pow3 asin-acos acos-asin associate--r-
8×expm1-udef
7×expm1-log1p neg-mul-1
6×neg-sub0 associate-+r+ rem-exp-log
5×remove-posit16 cos-mult distribute-frac-neg associate-+l- expm1-def
4×exp-diff associate--l- log-rec acos-neg
3×neg-log rem-cbrt-cube
2×associate-+l+ cube-unmult sub-div un-div-inv distribute-neg-frac hypot-udef log1p-def
1×associate-+r- sqrt-unprod tanh-def rem-square-sqrt sqr-cos tanh-undef unpow1/3

localize7.0s (0.7%)

bsearch5.4s (0.5%)

end2.0ms (0.0%)