Details

sample3.3m (60.7%)

Algorithm
78×intervals
Results
1.9m23266×body10240exit
34.1s44024×body1280valid
11.3s30814×body640valid
6.8s202184×body80valid
4.9s152103×body80nan
4.4s27677×body320valid
2.9s35629×body160valid
2.5s160053×pre80true
766.0ms3187×body2560valid
341.0ms7694×body160nan
338.0ms4104×pre10240exit
89.0ms8222×pre80false
83.0ms266×body5120valid

prune49.8s (15.2%)

series41.6s (12.7%)

Calls

478 calls:

629.0ms
(/ (* (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)))
487.0ms
(* (* 1 (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
486.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
398.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
395.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))

simplify12.3s (3.8%)

rewrite11.8s (3.6%)

Algorithm
145×rewrite-expression-head
Calls

478 calls:

291.0ms
(* (- (/ m (/ v (- 1.0 m))) 1.0) (- 1.0 m))
279.0ms
(* (/ (/ m (/ (fabs (cbrt v)) (- 1.0 m))) (sqrt v)) (/ 1 (sqrt (cbrt v))))
241.0ms
(* (/ m (/ (fabs (cbrt v)) (- 1.0 m))) (/ (/ 1 (sqrt v)) (sqrt (cbrt v))))
229.0ms
(* (- (/ (/ (* m (- 1.0 m)) (sqrt v)) (sqrt v)) 1.0) (- 1.0 m))
202.0ms
(* (- (/ (/ (* m (- 1.0 m)) (sqrt v)) (sqrt v)) 1.0) m)
Rules
9709×times-frac
9167×*-un-lft-identity
8840×add-sqr-sqrt
6531×add-cube-cbrt
2753×add-exp-log
2658×prod-diff
2158×sqrt-prod
1772×add-cbrt-cube
1151×associate-*r*
1028×pow1
906×prod-exp
889×associate-*l*
887×div-exp
760×difference-of-squares
730×associate-/l*
725×add-log-exp
693×distribute-rgt-neg-in
686×distribute-lft-out--
616×unpow-prod-down
614×distribute-lft-out
576×distribute-lft-neg-in
482×expm1-log1p-u
479×log1p-expm1-u
476×associate-/r/
475×associate-/r*
453×div-inv
436×cbrt-unprod
424×cbrt-prod cbrt-undiv
353×fma-neg
310×pow-exp
292×log-prod
285×flip--
284×flip3--
281×unswap-sqr
274×distribute-rgt-in distribute-lft-in
249×fma-def
231×pow-prod-down
227×pow-to-exp
221×cube-prod
202×sqr-pow
192×neg-mul-1
177×flip-+
176×flip3-+
125×unpow2
120×exp-sum
110×clear-num frac-2neg
108×sqrt-div
98×log-pow
96×exp-prod
92×*-commutative
90×associate-/l/
88×associate-*r/
85×sub-neg
74×1-exp
72×diff-log
69×frac-times
65×associate-*l/
58×pow-unpow
57×cos-sum
56×sum-log
52×sqrt-pow1
48×unpow3 cube-mult
47×pow1/3
46×cbrt-div
45×rec-exp
44×div-sub
42×pow1/2
39×+-commutative
37×rem-sqrt-square
33×neg-sub0
32×swap-sqr
28×log-div
27×fma-udef rem-log-exp
25×tan-quot
23×sin-sum
22×neg-log
20×pow-prod-up pow-sqr associate--l+ pow-pow
19×associate-+l-
18×sin-mult
17×sin-diff
15×cos-diff
14×associate--l-
13×distribute-rgt-out cos-mult
12×rem-exp-log sin-cos-mult pow-plus
10×pow2 frac-sub
9×frac-add acos-asin
8×hypot-udef
7×associate-+r+ distribute-frac-neg sum-cubes associate--r+
6×exp-diff pow-flip
5×rem-cube-cbrt un-div-inv distribute-rgt-neg-out expm1-udef
4×sin-neg log1p-udef inv-pow log1p-expm1 associate--r- associate-+r-
3×acos-neg unpow-prod-up associate-+l+ expm1-log1p hypot-def sqrt-undiv rem-cbrt-cube
2×pow-div distribute-lft1-in sqrt-unprod sub-div asin-acos
1×e-exp-1 rem-square-sqrt

regimes9.8s (3.0%)

Accuracy

Total 31.9b remaining (25.4%)

Threshold costs 6.1b (4.8%)

5.6b57.8%Cubic critical, narrow range
4.8b31.1%Cubic critical, medium range
4.3b83.8%Quadratic roots, full range
3.4b70%Quotient of products
3.2b12.3%Cubic critical, wide range

localize2.3s (0.7%)

bsearch580.0ms (0.2%)

end1.0ms (0.0%)