Details

simplify6.9m (44.3%)

sample4.9m (31.5%)

Algorithm
78×intervals
Results
1.6m20426×body10240exit
1.2m43746×body1280valid
30.7s30691×body640valid
22.2s202771×body80valid
15.5s153013×body80nan
12.4s27749×body320valid
9.5s35759×body160valid
7.0s158253×pre80true
1.7s3100×body2560valid
1.3s7869×body160nan
474.0ms4116×pre10240exit
206.0ms8292×pre80false
110.0ms220×body5120valid
2.0ms1×body640nan

prune1.9m (11.9%)

series1.0m (6.7%)

Calls

475 calls:

1.1s
(/ (* 3.0 a) (/ (* c (* 3.0 a)) (cbrt (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
918.0ms
(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)))
875.0ms
(sqrt (/ (* (pow (/ 1.0 (+ (exp (- s)) 1.0)) c_p) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n))) (fma c_p (+ (log 0.5) (* 0.5 t)) 1)))
869.0ms
(sqrt (/ (* (pow (/ 1.0 (+ (exp (- s)) 1.0)) c_p) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n))) (fma c_p (+ (log 0.5) (* 0.5 t)) 1)))
812.0ms
(cbrt (* 2.0 a))

rewrite26.8s (2.9%)

Algorithm
147×rewrite-expression-head
Calls

475 calls:

1.1s
(* (- (/ (+ (* (* 1.0 1.0) m) (- (pow m 3))) (* v (+ 1.0 m))) 1.0) (- 1.0 m))
840.0ms
(* (- (/ (* m (- (* 1.0 1.0) (* m m))) (* (sqrt (* v (+ 1.0 m))) (sqrt (* v (+ 1.0 m))))) 1.0) m)
537.0ms
(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
527.0ms
(- (/ (+ (* (* 1.0 1.0) m) (- (pow m 3))) (* v (+ 1.0 m))) 1.0)
449.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
Rules
42894×times-frac
23842×*-un-lft-identity
21606×add-sqr-sqrt
16656×add-cube-cbrt
4381×prod-diff
3089×add-exp-log
2338×difference-of-squares
2289×distribute-lft-out--
2219×distribute-rgt-neg-in
2058×sqrt-prod
1879×add-cbrt-cube
1633×div-inv
1350×distribute-lft-neg-in
1328×associate-/r/
1260×distribute-lft-out
1145×div-exp
1025×pow1
1009×associate-/r*
939×prod-exp
774×log-prod
764×associate-/l*
710×add-log-exp
678×neg-mul-1
642×associate-*r*
511×exp-sum
498×cbrt-undiv
493×flip--
492×flip3--
478×expm1-log1p-u
476×log1p-expm1-u
443×cbrt-unprod
412×associate-*l*
391×cbrt-prod
386×fma-neg
330×pow-exp
320×unpow-prod-down
316×flip-+
315×flip3-+
278×cube-prod
248×pow-prod-down
233×pow-to-exp
210×fma-def
188×distribute-rgt-in distribute-lft-in
132×unswap-sqr
129×associate-*r/
125×clear-num frac-2neg
113×sqrt-div
105×log-pow sub-neg
104×associate-/l/
100×*-commutative 1-exp
91×sqr-pow
81×diff-log sqrt-pow1
80×unpow3
74×cube-mult
69×associate-*l/
68×associate-+r+
61×rec-exp
60×frac-times
59×div-sub
57×pow1/2
53×exp-prod
50×cos-sum
45×log-div
42×sum-log swap-sqr
37×associate--l+
36×cbrt-div
33×sin-sum rem-sqrt-square
32×fma-udef
31×+-commutative rem-log-exp
26×neg-sub0
21×sin-mult
19×sin-diff
18×pow-prod-up
17×pow1/3
16×associate-+l- neg-log
15×cube-div pow-unpow frac-sub
14×sin-cos-mult associate--l- cos-diff associate-+l+ tan-quot
12×pow-sqr acos-asin
11×distribute-frac-neg cos-mult
9×frac-add distribute-neg-frac associate--r+ pow-pow
8×exp-diff inv-pow pow-flip distribute-rgt-out
7×rem-cube-cbrt associate-+r-
6×acos-neg un-div-inv
5×sqrt-unprod pow2 unsub-neg pow-plus associate--r-
4×rem-cbrt-cube distribute-rgt-neg-out rem-exp-log
3×log1p-udef log1p-expm1 distribute-neg-in log-rec asin-acos
2×e-exp-1 hypot-udef rem-square-sqrt expm1-udef
1×distribute-neg-out distribute-lft-neg-out expm1-log1p tanh-undef exp-to-pow tanh-def

regimes15.7s (1.7%)

Accuracy

Total 28.3b remaining (25.4%)

Threshold costs 6.3b (5.6%)

6.4b10.7%Cubic critical, medium range
6.4b10.7%Quadratic roots, medium range
2.7b75.9%Quotient of products
2.0b0%(- (/ x0 (- 1 x1)) x0)
1.6b92.1%Cubic critical

bsearch5.5s (0.6%)

localize4.3s (0.5%)

end0.0ms (0.0%)