Details

sample11.1m (83.3%)

Algorithm
78×intervals
Results
9.7m61677×body10240exit
34.5s43574×body1280valid
11.5s31381×body640valid
7.1s205134×body80valid
4.6s153420×body80nan
4.5s27679×body320valid
3.5s201527×pre80true
3.0s36062×body160valid
735.0ms3100×body2560valid
408.0ms4138×pre10240exit
340.0ms7746×body160nan
102.0ms8399×pre80false
75.0ms208×body5120valid

prune56.7s (7.1%)

series42.1s (5.3%)

Calls

455 calls:

1.6s
(/ (- (expm1 (log1p (pow (cos delta) 3))) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)) (fma (cos delta) (cos delta) (* (sin phi1) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta))))))
1.6s
(/ (- (* (* (cos delta) (cos delta)) (cos delta)) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)) (fma (cos delta) (cos delta) (* (sin phi1) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta))))))
1.6s
(/ (- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)) (fma (cos delta) (cos delta) (* (sin phi1) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta))))))
1.1s
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3))
565.0ms
(/ (* (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)))

simplify13.5s (1.7%)

Algorithm
220×egg-herbie

regimes9.2s (1.2%)

Accuracy

Total 36.0b remaining (28.2%)

Threshold costs 5.1b (4%)

5.8b57.9%Cubic critical, narrow range
5.8b48.8%Quotient of products
5.1b26.9%Cubic critical, medium range
4.5b84.7%Cubic critical
4.4b85%Quadratic roots, full range

rewrite8.8s (1.1%)

Algorithm
142×rewrite-expression-head
Calls

455 calls:

540.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))
488.0ms
(* (- (/ 1 (/ (/ v (- 1.0 m)) m)) 1.0) m)
412.0ms
(* (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
273.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
218.0ms
(* (- (- (* 1.0 (/ m v)) (/ (pow m 2) v)) 1.0) m)
Rules
15981×*-un-lft-identity
14975×times-frac
13093×add-sqr-sqrt
9409×add-cube-cbrt
7189×prod-diff
2210×add-exp-log
1908×distribute-lft-out
1516×difference-of-squares
1494×add-cbrt-cube
1275×distribute-lft-out--
1206×unpow-prod-down
1034×associate-/r/
975×associate--r+
970×pow1
866×associate-*r*
808×sqrt-prod
799×distribute-rgt-neg-in
788×div-inv
742×distribute-rgt-in distribute-lft-in
704×prod-exp
692×add-log-exp
669×distribute-lft-neg-in
628×div-exp
586×associate-/l*
492×cube-prod
489×associate-/r*
476×sqr-pow
457×log1p-expm1-u
455×expm1-log1p-u
440×flip-+
439×flip3-+
349×cbrt-unprod
339×flip--
338×flip3--
334×associate-*l*
322×fma-neg
317×pow-exp
304×cbrt-undiv
293×cbrt-prod
284×fma-def
237×log-prod
231×pow-to-exp
227×neg-mul-1
212×pow-prod-down
158×unswap-sqr
129×unpow3 cube-mult
108×clear-num frac-2neg
99×pow-unpow
95×sub-neg
94×associate-/l/
93×exp-sum associate-*r/
90×*-commutative
89×associate-*l/
80×frac-times
79×sqrt-div
74×log-pow
72×diff-log
60×cos-sum
55×exp-prod
53×sum-log
51×div-sub
50×pow-pow
45×sin-sum
41×pow1/3
38×+-commutative sqrt-pow1
36×unpow2
35×pow1/2
34×cbrt-div
31×log-div
30×neg-sub0
29×rem-sqrt-square
25×associate-+l+
24×frac-sub associate--l+
21×frac-add swap-sqr sin-mult
20×cube-div rem-cube-cbrt associate-+l-
19×associate-+r+ 1-exp rem-log-exp
18×sin-diff
17×pow-prod-up pow-sqr rec-exp neg-log
16×tan-quot
15×fma-udef cos-diff
14×pow-flip distribute-rgt-neg-out
11×sin-cos-mult distribute-rgt-out
difference-cubes associate--l- pow-plus distribute-frac-neg acos-asin
sin-neg pow2 cos-mult
inv-pow associate--r- expm1-udef
rem-exp-log acos-neg associate-+r- asin-acos rem-cbrt-cube
pow3 expm1-log1p
exp-diff log1p-udef log1p-expm1 hypot-udef hypot-def
unsub-neg distribute-lft1-in sub-div distribute-neg-frac
un-div-inv sum-cubes sqrt-unprod exp-neg distribute-rgt-out-- cube-neg mul-1-neg

localize2.2s (0.3%)

bsearch538.0ms (0.1%)

end1.0ms (0.0%)