Details

sample7.8m (51.9%)

Algorithm
78×intervals
Results
4.7m34364×body10240exit
1.2m43846×body1280valid
29.3s30562×body640valid
19.6s203326×body80valid
13.9s153094×body80nan
12.9s27510×body320valid
8.6s36242×body160valid
8.1s172374×pre80true
1.8s3009×body2560valid
886.0ms8009×body160nan
525.0ms4182×pre10240exit
227.0ms183×body5120valid
164.0ms8017×pre80false
2.0msbody640nan

simplify3.9m (25.9%)

prune1.3m (8.3%)

series1.1m (7.1%)

Calls

453 calls:

1.9s
(* (hypot (* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
1.1s
(/ (fma (cos delta) (cos delta) (- (pow (cbrt (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))) (* 2 3)))) (fma (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1) (cos delta)))
931.0ms
(* (/ e (sqrt (fma (cos v) e 1.0))) (expm1 (log1p (/ (sin v) (sqrt (fma (cos v) e 1.0))))))
832.0ms
(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
786.0ms
(* (/ e (sqrt (fma (cos v) e 1.0))) (log1p (expm1 (/ (sin v) (sqrt (fma (cos v) e 1.0))))))

rewrite21.6s (2.4%)

Algorithm
141×rewrite-expression-head
Calls

453 calls:

909.0ms
(- (log (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n))) (fma (- (fma t 0.5 (log 0.5)) (* 0.03125 (/ (pow t 2) (pow 0.5 2)))) c_p (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))
907.0ms
(- (log (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n))) (fma (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))
628.0ms
(/ (- (/ 4.0 (pow (+ (exp (* -2.0 x)) 1.0) 2)) 1.0) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
535.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (/ (/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (sqrt (fma b b (* (* 4.0 a) c)))) (sqrt (fma b b (* (* 4.0 a) c))))))) (* 2.0 a))
430.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
Rules
7806×*-un-lft-identity
7507×add-sqr-sqrt
7277×times-frac
5048×add-cube-cbrt
2505×prod-diff
2411×add-exp-log
1982×sqrt-prod
1636×add-cbrt-cube
1104×pow1
843×associate-*r*
829×prod-exp
827×difference-of-squares
671×distribute-lft-out
670×distribute-lft-out--
653×div-exp
650×add-log-exp
637×associate-/l*
495×associate-*l*
476×cbrt-prod
466×associate-/r/
457×log1p-expm1-u
455×expm1-log1p-u
446×unpow-prod-down
439×cbrt-unprod
429×distribute-rgt-neg-in
405×associate-/r*
403×div-inv
345×cbrt-undiv
336×flip--
335×flip3--
318×pow-exp
305×fma-neg
288×pow-prod-down
261×distribute-lft-neg-in
247×fma-def
228×pow-to-exp
207×swap-sqr
203×unswap-sqr
188×distribute-rgt-in distribute-lft-in
183×log-prod
182×cbrt-div
172×flip-+
171×flip3-+
107×clear-num associate-*r/ frac-2neg
103×sqr-pow
102×associate-*l/
99×frac-times
98×sqrt-div
92×*-commutative
90×associate-/l/
87×sub-neg
86×unpow3 neg-mul-1
72×associate-+l+
67×cube-prod distribute-rgt-out
63×log-pow
62×diff-log
55×pow-unpow pow1/3
51×sqrt-pow1
49×pow1/2 rem-log-exp
48×cos-sum
42×unpow2
40×sum-log
37×div-sub
36×rem-sqrt-square
35×pow-prod-up
34×log-div
33×sin-sum pow-sqr
30×+-commutative exp-prod
29×sin-mult
26×fma-udef
23×cos-mult pow-pow
22×neg-sub0 exp-sum
19×sin-diff
15×distribute-rgt1-in frac-add pow-plus rec-exp frac-sub 1-exp
14×neg-log associate-+l-
13×sin-cos-mult distribute-rgt-neg-out
11×pow2 cube-mult
10×cube-div associate--l- cos-diff associate--l+
associate-+r+
sub-div expm1-udef acos-asin associate--r+
rem-exp-log expm1-log1p
sqrt-undiv
sin-neg log1p-udef distribute-lft-neg-out log1p-expm1 sum-cubes distribute-neg-in unsub-neg associate--r-
exp-diff rem-cube-cbrt hypot-udef pow-flip tan-quot
un-div-inv sqrt-unprod distribute-frac-neg hypot-def rem-cbrt-cube
acos-neg asin-acos associate-+r- inv-pow rem-square-sqrt distribute-neg-frac
distribute-neg-out tanh-undef exp-to-pow tanh-def

bsearch20.0s (2.2%)

regimes15.7s (1.7%)

Accuracy

Total 37.5b remaining (28.8%)

Threshold costs 5.0b (3.9%)

7.2b47.9%Quadratic roots, narrow range
7.1b47.2%Cubic critical, narrow range
5.8b12.2%Cubic critical, medium range
3.4b0%Cubic critical, wide range
2.3b79.7%Quotient of products

localize4.3s (0.5%)

end1.0ms (0.0%)