Details

sample9.8m (51.7%)

Algorithm
78×intervals
Results
6.5m43146×body10240exit
1.2m43543×body1280valid
30.9s30155×body640valid
19.6s204782×body80valid
13.9s150444×body80nan
12.0s27534×body320valid
9.6s181334×pre80true
7.9s36307×body160valid
2.2s2960×body2560valid
738.0ms7786×body160nan
492.0ms4158×pre10240exit
211.0ms262×body5120valid
151.0ms8146×pre80false

simplify6.5m (34.1%)

prune1.0m (5.5%)

series52.1s (4.6%)

Calls

437 calls:

806.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
779.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
716.0ms
(cbrt (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
656.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
636.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

rewrite21.7s (1.9%)

Algorithm
144×rewrite-expression-head
Calls

437 calls:

808.0ms
(* (/ 2.0 (+ (pow (exp x) 3) (exp (* x -3)))) (+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x))))))
594.0ms
(log (exp (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))))
543.0ms
(* (- (- (* 1.0 (/ m v)) (/ (pow m 2) v)) 1.0) (- 1.0 m))
489.0ms
(* (* (- (/ m (/ v (- 1.0 m))) 1.0) (sqrt m)) (sqrt m))
470.0ms
(* (- (/ m (/ v (- 1.0 m))) 1.0) (- 1.0 m))
Rules
9910×*-un-lft-identity
7886×add-sqr-sqrt
7557×times-frac
5932×add-cube-cbrt
4416×prod-diff
2485×add-exp-log
1594×add-cbrt-cube
1509×unpow-prod-down
1386×cube-prod
1259×distribute-lft-out
1003×sqrt-prod
917×pow1
886×prod-exp
760×difference-of-squares
718×log-prod
712×div-exp
672×exp-prod
660×associate-/r/
636×log-pow
603×add-log-exp
598×distribute-lft-out--
583×associate-*r*
510×exp-sum
488×associate-*l*
477×div-inv
461×cbrt-prod
447×associate-/r*
441×log1p-expm1-u
439×expm1-log1p-u
425×cbrt-unprod
417×fma-neg
349×associate-/l* cbrt-undiv
342×pow-exp
322×flip--
321×flip3--
318×flip-+
317×flip3-+
305×sqr-pow
242×unpow3 pow-to-exp cube-mult
199×pow-prod-down
179×associate-*r/
162×distribute-rgt-in distribute-lft-in
152×fma-def
147×frac-times
143×unswap-sqr
125×cbrt-div
110×associate-*l/
100×swap-sqr
99×clear-num frac-2neg
87×*-commutative
84×frac-sub
79×sub-neg
78×sqrt-div
76×associate-/l/ sqrt-pow1
70×pow1/3
63×exp-neg
60×diff-log
49×distribute-rgt-neg-in
47×cos-sum neg-sub0
46×exp-diff associate--l+
39×pow-unpow
35×fma-udef
33×pow1/2 sin-sum log-div
31×div-sub
30×rem-sqrt-square
28×un-div-inv
27×sum-log distribute-lft-neg-in rem-log-exp
26×pow-prod-up
22×1-exp
21×pow-pow rec-exp
19×sin-diff
18×+-commutative
17×sin-mult
16×pow-sqr sub-div
14×rem-cube-cbrt pow-plus
13×sin-cos-mult
11×cube-div frac-add unpow2
10×cos-diff
9×pow2 neg-mul-1
8×pow-div acos-asin
7×expm1-udef
6×sqrt-undiv rem-cbrt-cube associate--r+
5×associate-+l-
4×log1p-udef log1p-expm1 expm1-log1p tan-quot neg-log asin-acos rem-exp-log
3×difference-cubes inv-pow pow-flip distribute-frac-neg cos-mult associate--l-
2×acos-neg sin-neg pow3 associate-+r+ distribute-rgt-out distribute-rgt-out-- distribute-rgt-neg-out associate-+r-
1×sqrt-unprod hypot-udef rem-square-sqrt hypot-def tanh-undef associate--r- log1p-def cube-neg rgt-mult-inverse tanh-def

regimes16.6s (1.5%)

Accuracy

Total 55.0b remaining (33.6%)

Threshold costs 5.7b (3.5%)

7.7b45.6%Quadratic roots, narrow range
7.6b45.5%Cubic critical, narrow range
6.2b12.4%Cubic critical, medium range
6.2b13.5%Quadratic roots, medium range
4.9b55%Quotient of products

bsearch5.4s (0.5%)

localize3.8s (0.3%)

end1.0ms (0.0%)