Details

sample10.6m (40.0%)

Algorithm
78×intervals
Results
7.5m47769×body10240exit
1.2m44067×body1280valid
26.4s30234×body640valid
18.6s203869×body80valid
13.6s153435×body80nan
13.2s27760×body320valid
8.5s186776×pre80true
8.4s36376×body160valid
2.6s3206×body2560valid
1.3s7956×body160nan
460.0ms4074×pre10240exit
165.0ms216×body5120valid
1.0msbody320nan

prune7.5m (28.1%)

simplify6.3m (23.7%)

series56.9s (3.6%)

Calls

453 calls:

1.4s
(pow (exp (* (cbrt (log (- (fma x x x) (* (/ x 1.0) (/ x 1.0))))) (cbrt (log (- (fma x x x) (* (/ x 1.0) (/ x 1.0))))))) (cbrt (log (- (fma x x x) (* (/ x 1.0) (/ x 1.0))))))
1.0s
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
835.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (* 0.5 c_p) t (fma c_p (log 0.5) 1)) (* (pow (sqrt (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n) (pow (sqrt (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n))))
819.0ms
(/ (* 3.0 a) (fma (sqrt (- (* b b) (* (* 3.0 a) c))) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* b b)))
769.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (* 0.5 c_p) t (fma c_p (log 0.5) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

rewrite45.5s (2.8%)

Algorithm
143×rewrite-expression-head
Calls

453 calls:

18.4s
(* (/ (/ (/ 1 (* (cbrt b1) (cbrt b1))) (cbrt (* (cbrt b2) (cbrt b2)))) (/ (cbrt b2) (/ (/ a1 (cbrt b1)) (cbrt (cbrt b2))))) (/ a2 (cbrt b2)))
739.0ms
(* (* (cbrt (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))) (cbrt (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))) (cbrt (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))))
633.0ms
(* (sqrt (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
587.0ms
(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
490.0ms
(/ (- (* (* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x)))) (log (+ 1.0 (exp x)))) (* (* (* x y) (* x y)) (* x y))) (+ (* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x)))) (+ (* (* x y) (* x y)) (* (log (+ 1.0 (exp x))) (* x y)))))
Rules
216769×times-frac
86711×cbrt-prod
84254×add-sqr-sqrt
84175×*-un-lft-identity
77812×add-cube-cbrt
40074×associate-*l*
8980×div-inv
4114×prod-diff
3786×add-exp-log
1991×add-cbrt-cube
1669×difference-of-squares
1629×distribute-lft-out
1601×sqrt-prod
1459×prod-exp
1416×distribute-lft-out--
1315×pow1
1314×div-exp
847×associate-/r/
766×associate-/l*
751×unpow-prod-down
746×associate-*r*
651×add-log-exp unswap-sqr
616×cube-prod
615×associate-/r*
594×cbrt-unprod
585×cbrt-undiv
517×pow-exp
454×expm1-log1p-u log1p-expm1-u
392×flip--
391×flip3--
389×pow-to-exp
363×flip-+
362×flip3-+
334×fma-neg
306×pow-prod-down
294×sqr-pow
261×distribute-rgt-neg-in
236×frac-times
214×swap-sqr
200×cbrt-div
184×fma-def
183×distribute-rgt-in distribute-lft-in
158×associate-*l/
144×sqrt-div
137×associate-*r/
135×pow-prod-up
114×log-prod
111×distribute-lft-neg-in
104×*-commutative
103×frac-2neg clear-num
93×sub-neg
92×associate-/l/
87×pow-plus
71×sqrt-pow1
65×cos-sum pow1/2 diff-log
63×pow-sqr
55×log-pow
54×frac-add
53×1-exp rec-exp div-sub
45×pow1/3
43×pow2 fma-udef
42×exp-prod
38×frac-sub
37×neg-mul-1
34×pow-unpow
32×difference-cubes
31×associate--l+
30×sum-log rem-sqrt-square
24×log-div
23×pow-flip exp-sum +-commutative
22×sin-sum
18×sin-diff
17×tan-quot
16×pow-pow
15×associate-+l-
14×neg-sub0 rem-log-exp
13×cos-diff
12×pow3
11×tanh-def
10×rem-exp-log sin-mult
sin-cos-mult associate--r+ inv-pow
distribute-frac-neg
cos-mult neg-log acos-asin
exp-diff cube-unmult sqrt-unprod exp-to-pow associate--r-
asin-acos acos-neg rem-square-sqrt
expm1-log1p expm1-udef associate--l- log1p-expm1 log1p-udef sqrt-pow2 rem-cbrt-cube
tanh-undef sqr-sin hypot-udef

regimes21.0s (1.3%)

Accuracy

Total 49.7b remaining (29.3%)

Threshold costs 5.4b (3.2%)

7.5b44.8%Quadratic roots, narrow range
6.1b10.6%Quadratic roots, medium range
5.6b58.5%Cubic critical, narrow range
4.9b40.4%Quotient of products
4.6b30.9%Cubic critical, medium range

localize6.6s (0.4%)

bsearch695.0ms (0.0%)

end1.0ms (0.0%)