Details

sample7.2m (74.7%)

Algorithm
78×intervals
Results
5.8m41601×body10240exit
33.9s43992×body1280valid
11.0s30167×body640valid
6.8s204050×body80valid
4.5s27839×body320valid
4.5s153350×body80nan
3.0s36091×body160valid
2.9s181111×pre80true
743.0ms3052×body2560valid
362.0ms7814×body160nan
357.0ms4109×pre10240exit
89.0ms8389×pre80false
72.0ms209×body5120valid

prune59.1s (10.3%)

series41.5s (7.2%)

Calls

467 calls:

1.5s
(/ (- (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))))))
1.3s
(/ (* (- (pow (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) 3) (pow (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) 3)) (- lambda1 lambda2)) (+ (* (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (cos (* phi2 0.5)) (cos (* phi1 0.5)))) (+ (* (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (* (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))))))
1.0s
(* (hypot (* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
634.0ms
(/ (* (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)))
550.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))))))

rewrite18.0s (3.1%)

Algorithm
146×rewrite-expression-head
Calls

467 calls:

1.8s
(* (- (/ (/ m 1) (/ v (/ (- (* 1.0 1.0) (* m m)) (+ 1.0 m)))) 1.0) (- 1.0 m))
1.6s
(* (- (/ (/ (/ (* m (- 1.0 m)) (sqrt v)) (sqrt (sqrt v))) (sqrt (sqrt v))) 1.0) m)
425.0ms
(/ (* (- (pow (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) 3) (pow (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) 3)) (- lambda1 lambda2)) (+ (* (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (cos (* phi2 0.5)) (cos (* phi1 0.5)))) (+ (* (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (* (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))))))
342.0ms
(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
303.0ms
(- (log (exp (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) 1.0)
Rules
16600×times-frac
15614×*-un-lft-identity
12365×add-sqr-sqrt
9648×add-cube-cbrt
5092×prod-diff
4034×sqrt-prod
2910×unpow-prod-down
2833×add-exp-log
2629×cube-prod
1951×distribute-lft-out
1882×add-cbrt-cube
1295×pow1
1282×associate-*r*
1243×difference-of-squares
1137×associate-/r/
1015×distribute-lft-out--
975×prod-exp
868×div-inv
833×div-exp
780×associate-/l*
676×add-log-exp
527×associate-/r*
523×associate-*l*
484×cbrt-unprod
467×log1p-expm1-u expm1-log1p-u
451×distribute-rgt-neg-in
440×cbrt-undiv
430×flip--
429×pow-exp flip3--
423×flip-+
422×flip3-+
365×distribute-lft-neg-in
361×pow-prod-down
341×sqr-pow
316×fma-neg
309×pow-to-exp
292×distribute-rgt-in distribute-lft-in
288×unswap-sqr
240×log-prod
215×log-pow
205×cbrt-prod
201×fma-def
173×associate-*r/
163×neg-mul-1
156×exp-prod frac-times
154×unpow3 cube-mult
126×pow-unpow
125×associate-*l/
115×clear-num frac-2neg
112×associate-/l/
107×*-commutative
99×sub-neg
94×sqrt-div
88×sin-mult
85×cos-mult
75×swap-sqr diff-log
71×frac-add
59×cos-sum
57×div-sub
50×unpow2
46×pow-pow
44×cbrt-div
43×sqrt-pow1
42×pow-prod-up log-div
41×cube-div
40×pow-sqr
39×associate--r+
38×sum-log
34×pow1/2
32×associate--l+
28×rem-log-exp
27×pow1/3 neg-sub0
26×+-commutative
25×associate-+l+
23×rem-sqrt-square fma-udef sin-sum
21×1-exp
20×rem-cube-cbrt
18×pow-plus rec-exp exp-sum sin-diff
17×frac-sub associate-+l-
16×tan-quot
15×cos-diff neg-log
13×distribute-rgt-out
12×associate--l- distribute-frac-neg acos-asin
11×sin-cos-mult pow2
10×sum-cubes distribute-neg-frac
pow-flip associate--r-
associate-+r+
sub-div
acos-neg
rem-exp-log difference-cubes
exp-diff sqrt-undiv inv-pow associate-+r- expm1-udef
sqrt-unprod expm1-log1p
un-div-inv distribute-lft1-in distribute-rgt-out-- distribute-rgt-neg-out
sub0-neg rem-square-sqrt hypot-def asin-acos rem-cbrt-cube

simplify14.1s (2.5%)

Algorithm
224×egg-herbie

regimes10.0s (1.7%)

Accuracy

Total 38.3b remaining (32%)

Threshold costs 5.0b (4.2%)

7.6b44.2%Cubic critical, narrow range
7.3b36.2%Quotient of products
5.1b24.8%Cubic critical, medium range
3.7b86.1%Quadratic roots, full range
3.6b0%Cubic critical, wide range

localize2.5s (0.4%)

bsearch550.0ms (0.1%)

end1.0ms (0.0%)