Details

sample8.2m (79.6%)

Algorithm
78×intervals
Results
6.3m41053×body10240exit
38.4s43618×body1280valid
14.3s204311×body80valid
13.6s30288×body640valid
10.1s151719×body80nan
6.9s27597×body320valid
5.8s36482×body160valid
5.6s186459×pre80true
1.2s3047×body2560valid
693.0ms7966×body160nan
195.0ms8423×pre80false
135.0ms2811×body80overflowed
134.0ms206×body5120valid

prune52.9s (8.6%)

series39.0s (6.3%)

Calls

483 calls:

684.0ms
(/ (* (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)))
568.0ms
(/ (* (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)))
512.0ms
(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
505.0ms
(cbrt (/ (* (cbrt g) (cbrt g)) 2.0))
440.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)

simplify12.3s (2.0%)

Algorithm
225×egg-herbie

regimes10.0s (1.6%)

Accuracy

Total 35.8b remaining (30.1%)

Threshold costs 5.7b (4.8%)

5.7b57.6%Cubic critical, narrow range
5.6b48.5%Quotient of products
5.0b79%Quadratic roots, full range
4.8b29.7%Cubic critical, medium range
3.4b0%Cubic critical, wide range

rewrite8.0s (1.3%)

Algorithm
147×rewrite-expression-head
Calls

483 calls:

527.0ms
(* (- (/ 1 (/ (/ v (- 1.0 m)) m)) 1.0) (- 1.0 m))
238.0ms
(* (- (- (* 1.0 (/ m v)) (/ (pow m 2) v)) 1.0) (- 1.0 m))
224.0ms
(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
208.0ms
(* (- (/ m (/ v (- 1.0 m))) 1.0) (- 1.0 m))
136.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
Rules
9585×*-un-lft-identity
8861×times-frac
8104×add-sqr-sqrt
6242×add-cube-cbrt
3027×prod-diff
2922×add-exp-log
2189×sqrt-prod
1798×add-cbrt-cube
1326×cbrt-prod
1156×pow1
1034×distribute-lft-out
1007×associate-/r/
966×prod-exp
941×associate-*r*
937×div-exp
725×cbrt-div
719×add-log-exp
700×associate-/l*
695×difference-of-squares
630×flip-+
629×flip3-+
619×distribute-lft-out--
564×associate-/r*
521×div-inv
486×log1p-expm1-u
483×expm1-log1p-u
472×unpow-prod-down
465×associate-*l*
447×distribute-rgt-neg-in
438×cbrt-undiv
436×cbrt-unprod
399×distribute-rgt-in distribute-lft-in
359×pow-exp
340×frac-times
327×distribute-lft-neg-in
317×flip--
316×flip3--
310×fma-neg
270×associate-*r/
260×pow-to-exp
250×cube-prod pow-prod-down
223×fma-def
207×unswap-sqr
193×associate-*l/
191×sqr-pow
156×sqrt-div
144×cos-sum
139×swap-sqr
134×sqrt-pow1
129×log-prod
125×clear-num frac-2neg
120×associate-/l/
119×log-pow
109×neg-mul-1
102×pow1/2 *-commutative
99×sub-neg
77×diff-log
70×unpow3 cube-mult
63×1-exp
56×pow-prod-up
51×log-div
49×frac-sub
48×associate--l+
47×div-sub
46×pow-unpow sum-log
43×rec-exp
42×rem-sqrt-square exp-prod
40×pow-sqr
36×unpow2
34×fma-udef
32×pow1/3
31×+-commutative
29×neg-sub0
23×sin-sum pow-pow
22×tan-quot sin-mult
21×exp-sum rem-log-exp
20×neg-log
18×associate-+l- sin-diff
17×cos-diff pow-plus associate--r+
15×associate--l- pow2 acos-asin
13×cos-mult
12×rem-cube-cbrt sin-cos-mult distribute-rgt-out
11×associate--r-
10×cube-div
9×rem-exp-log pow-flip
8×inv-pow frac-add distribute-frac-neg
7×associate-+r+
6×expm1-udef
5×exp-diff sqrt-unprod expm1-log1p sub-div distribute-rgt-neg-out
4×associate-+r- rem-square-sqrt hypot-def
3×acos-neg associate-+l+ hypot-udef unpow-prod-up rem-cbrt-cube
2×un-div-inv distribute-lft1-in distribute-neg-frac exp-to-pow
1×sub0-neg difference-cubes e-exp-1 sin-neg asin-acos distribute-rgt-out--

localize2.3s (0.4%)

bsearch981.0ms (0.2%)

end1.0ms (0.0%)