Details

simplify6.9m (43.2%)

sample6.2m (39.0%)

Algorithm
78×intervals
Results
3.1m26914×body10240exit
1.2m43596×body1280valid
28.9s30450×body640valid
19.9s202965×body80valid
13.0s27959×body320valid
12.9s153461×body80nan
9.2s35956×body160valid
6.8s164300×pre80true
2.1s3110×body2560valid
1.3s8154×body160nan
455.0ms4113×pre10240exit
154.0ms8261×pre80false
109.0ms215×body5120valid

prune1.2m (7.6%)

series59.5s (6.2%)

Calls

461 calls:

771.0ms
(/ (* (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)))
766.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
648.0ms
(* (sqrt (log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))) (sqrt (log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))))
645.0ms
(/ (* (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)))
641.0ms
(/ (* (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)))

rewrite22.8s (2.4%)

Algorithm
145×rewrite-expression-head
Calls

461 calls:

839.0ms
(* (sqrt (+ (/ (/ 2.0 x) x) (/ 2.0 (pow x 4)))) (sqrt (+ (/ (/ 2.0 x) x) (/ 2.0 (pow x 4)))))
705.0ms
(- (/ x (+ 1.0 x)) (/ (+ 1.0 x) (pow (cbrt (- x 1.0)) 3)))
481.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
410.0ms
(* (- (/ m (/ v (- 1.0 m))) 1.0) m)
355.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))
Rules
12442×times-frac
12360×*-un-lft-identity
10127×add-sqr-sqrt
7681×add-cube-cbrt
4327×prod-diff
3835×add-exp-log
1919×add-cbrt-cube
1688×sqrt-prod
1479×div-exp
1368×distribute-lft-out
1337×prod-exp
1279×unpow-prod-down
1109×cbrt-prod
1102×difference-of-squares
1096×cube-prod
920×distribute-lft-out--
863×pow1
789×associate-/l*
715×div-inv
692×associate-/r/
665×add-log-exp
652×associate-/r*
617×pow-exp
556×cbrt-undiv
466×associate-*r*
464×associate-*l* log1p-expm1-u
461×expm1-log1p-u
447×cbrt-unprod
438×pow-to-exp
398×distribute-rgt-neg-in
321×fma-neg
307×flip--
306×flip3--
283×sqr-pow
275×flip-+
274×flip3-+
207×fma-def
183×distribute-lft-neg-in
164×unpow3 cube-mult
149×pow-prod-down
139×distribute-rgt-in distribute-lft-in
121×clear-num frac-2neg
118×log-prod
109×1-exp
102×sqrt-div
98×associate-*r/
97×unswap-sqr
93×sub-neg
88×associate-/l/
84×cbrt-div
82×*-commutative
81×frac-times
77×associate-*l/
73×log-pow
69×pow-unpow
68×rec-exp
67×diff-log
61×neg-mul-1
59×cos-sum
56×cube-div
48×pow1/2 sqrt-pow1
44×sin-sum
43×log-div
39×exp-prod
37×pow1/3
36×div-sub sum-log
35×swap-sqr
34×fma-udef
31×pow-pow
29×rem-sqrt-square
26×+-commutative hypot-def exp-sum
25×cos-mult
24×rem-log-exp
22×frac-add
21×neg-sub0 sin-mult
19×rem-cube-cbrt
18×frac-sub sin-diff
15×sin-cos-mult neg-log
14×pow-prod-up
13×associate-+l-
12×tan-quot
11×cos-diff
10×associate--l- pow-sqr pow-flip
9×difference-cubes acos-asin
7×inv-pow rem-cbrt-cube
6×pow-plus pow2 sub-div unpow2 associate--r+
5×expm1-log1p expm1-udef
4×sin-neg associate--r- rem-exp-log associate--l+
3×exp-diff acos-neg un-div-inv sqrt-unprod distribute-frac-neg asin-acos distribute-rgt-neg-out
2×sqrt-undiv sqrt-pow2 log1p-udef log1p-expm1 rem-square-sqrt distribute-rgt-out
1×pow3 distribute-lft-neg-out associate-+l+ tanh-undef sum-cubes cube-neg tanh-def

regimes10.9s (1.1%)

Accuracy

Total 35.3b remaining (28.5%)

Threshold costs 6.5b (5.2%)

7.0b0%Quadratic roots, medium range
7.0b0%Cubic critical, medium range
4.7b83.4%Cubic critical
4.6b83.5%Quadratic roots, full range
2.3b79.1%Quotient of products

localize3.5s (0.4%)

bsearch1.1s (0.1%)

end1.0ms (0.0%)