Details

sample3.3m (59.1%)

Algorithm
78×intervals
Results
1.9m23266×body10240exit
33.7s44024×body1280valid
11.2s30814×body640valid
7.0s202184×body80valid
4.5s152103×body80nan
4.4s27677×body320valid
2.9s35629×body160valid
2.4s160053×pre80true
771.0ms3187×body2560valid
351.0ms4104×pre10240exit
339.0ms7694×body160nan
83.0ms8222×pre80false
80.0ms266×body5120valid

prune57.8s (17.3%)

series40.8s (12.2%)

Calls

479 calls:

613.0ms
(/ (* (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)))
485.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
478.0ms
(* (hypot (* (- lambda1 lambda2) (* 1 (cos (/ (+ phi1 phi2) 2.0)))) (- phi1 phi2)) R)
394.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
389.0ms
(hypot (* (- lambda1 lambda2) (* 1 (cos (/ (+ phi1 phi2) 2.0)))) (- phi1 phi2))

rewrite12.9s (3.9%)

Algorithm
145×rewrite-expression-head
Calls

479 calls:

379.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))
287.0ms
(* (/ (/ m (/ (fabs (cbrt v)) (- 1.0 m))) (sqrt v)) (/ 1 (sqrt (cbrt v))))
275.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
270.0ms
(* (- (/ m (/ v (- 1.0 m))) 1.0) (- 1.0 m))
248.0ms
(* (/ m (/ (fabs (cbrt v)) (- 1.0 m))) (/ (/ 1 (sqrt v)) (sqrt (cbrt v))))
Rules
13854×times-frac
12204×add-sqr-sqrt
12012×*-un-lft-identity
8732×add-cube-cbrt
4637×prod-diff
2790×add-exp-log
2203×sqrt-prod
1809×add-cbrt-cube
1545×unpow-prod-down
1221×distribute-rgt-neg-in
1200×difference-of-squares
1086×associate-*r*
1026×distribute-lft-neg-in
1019×pow1
973×associate--r+
913×div-exp
905×prod-exp
902×distribute-lft-out--
863×associate-*l*
795×associate-/l*
736×add-log-exp
721×distribute-lft-out
702×div-inv
571×sqr-pow
566×associate-/r*
489×associate-/r/
484×fma-neg
483×expm1-log1p-u
480×log1p-expm1-u
460×cube-prod
452×cbrt-undiv
438×cbrt-prod
433×cbrt-unprod
342×neg-mul-1
316×pow-exp
288×flip--
287×flip3--
283×log-prod
282×distribute-rgt-in distribute-lft-in
269×unswap-sqr
255×fma-def
233×pow-prod-down pow-to-exp
187×unpow2
176×flip-+
175×flip3-+
123×unpow3 cube-mult
120×exp-sum
116×clear-num frac-2neg
105×associate-/l/
92×sqrt-div
89×*-commutative
88×sub-neg
86×associate-*r/
85×exp-prod
77×diff-log
72×1-exp
70×log-pow
67×pow-unpow
57×sum-log cos-sum
55×frac-times
53×associate-*l/
46×pow1/3 div-sub
45×rec-exp
40×sqrt-pow1
39×+-commutative pow-pow
38×neg-sub0 cbrt-div
36×pow1/2
33×rem-sqrt-square
29×swap-sqr
28×log-div
26×fma-udef rem-log-exp
23×sin-sum
22×neg-log frac-sub
20×tan-quot
19×pow-prod-up pow-sqr associate-+l- associate--l+
18×sin-mult sin-diff
15×associate--l- cos-diff
13×distribute-rgt-out cos-mult
12×rem-exp-log sin-cos-mult
11×pow-plus frac-add
9×pow2 distribute-frac-neg acos-asin
8×hypot-udef
7×rem-cube-cbrt sum-cubes associate-+r+
6×exp-diff un-div-inv pow-flip associate--r-
5×distribute-rgt-neg-out expm1-udef
4×sin-neg log1p-udef log1p-expm1 inv-pow associate-+r-
3×acos-neg sqrt-undiv unpow-prod-up associate-+l+ expm1-log1p hypot-def
2×pow-div cube-div distribute-lft1-in sqrt-unprod sub-div asin-acos rem-cbrt-cube
1×difference-cubes e-exp-1 exp-neg rem-square-sqrt

simplify12.5s (3.7%)

regimes9.6s (2.9%)

Accuracy

Total 31.3b remaining (24.8%)

Threshold costs 5.5b (4.3%)

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%)

bsearch553.0ms (0.2%)

end1.0ms (0.0%)