Details

sample7.2m (50.2%)

Algorithm
78×intervals
Results
4.0m30960×body10240exit
1.3m43992×body1280valid
27.2s30338×body640valid
18.8s202813×body80valid
13.2s152461×body80nan
13.1s27194×body320valid
9.2s36495×body160valid
7.2s168178×pre80true
1.9s3111×body2560valid
744.0ms8100×body160nan
599.0ms4031×pre10240exit
223.0ms202×body5120valid
181.0ms8350×pre80false
1.0ms1×body640nan

simplify4.4m (31.0%)

prune1.2m (8.4%)

series53.1s (6.2%)

Calls

437 calls:

1.1s
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))) 3))
842.0ms
(/ (* (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 (- (fma 0.25 t 0.5) (* 0.020833333333333336 (pow t 3)))) c_n)))
766.0ms
(/ (* (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)))
759.0ms
(- (pow (cos delta) 3) (pow (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)) 3))
749.0ms
(- (pow (cos delta) 3) (* (* (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) (* (* (sin phi1) (sin phi1)) (sin phi1))))

rewrite17.0s (2.0%)

Algorithm
141×rewrite-expression-head
Calls

437 calls:

304.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))
284.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
272.0ms
(- (/ 1 (/ (+ x 1.0) x)) (/ (+ 1.0 x) (- x 1.0)))
266.0ms
(* (- (/ (+ (* m 1.0) (* m (- m))) v) 1.0) (- 1.0 m))
240.0ms
(* (- (/ (* m (- (* 1.0 1.0) (* m m))) (* v (+ 1.0 m))) 1.0) (- 1.0 m))
Rules
9918×*-un-lft-identity
8721×times-frac
8053×add-sqr-sqrt
6159×add-cube-cbrt
4010×prod-diff
2563×add-exp-log
1499×add-cbrt-cube
1199×distribute-lft-out
894×pow1
874×prod-exp
873×difference-of-squares
803×div-exp
782×sqrt-prod
651×distribute-lft-out--
638×cbrt-prod
615×add-log-exp
538×associate-/r*
537×div-inv
500×associate-/r/
445×expm1-log1p-u
439×log1p-expm1-u
434×unpow-prod-down
425×fma-neg
403×pow-exp
393×associate-/l*
374×associate-*r*
364×associate-*l*
353×cbrt-undiv
345×cbrt-unprod
338×cube-prod
300×flip--
299×flip3--
291×pow-to-exp
222×log-prod
210×distribute-rgt-in distribute-lft-in
181×sqr-pow
174×flip-+
173×flip3-+
169×pow-prod-down
130×distribute-rgt-neg-in
123×unswap-sqr
114×clear-num frac-2neg
109×distribute-lft-neg-in fma-def
105×log-pow
90×sub-neg associate-*r/
78×unpow3 cube-mult
77×*-commutative
75×associate-/l/ frac-times
72×associate-*l/
69×diff-log
68×sqrt-div
57×cos-sum
54×sqrt-pow1
51×cbrt-div exp-prod
50×pow1/2
47×swap-sqr
45×pow-unpow
38×log-div
37×neg-mul-1
35×div-sub
33×associate--l+
32×1-exp
31×pow1/3 rec-exp
30×rem-sqrt-square
24×sum-log
23×pow-pow
22×sin-sum
21×distribute-rgt-out rem-log-exp
20×fma-udef sin-mult
19×pow-sqr pow-prod-up
18×+-commutative
17×sin-diff
16×tan-quot frac-sub
14×sin-cos-mult
13×cos-diff pow-flip
12×rem-cube-cbrt
11×difference-cubes associate--l- pow-plus distribute-rgt-neg-out
10×cube-div associate-+r+ inv-pow pow2
9×log1p-udef expm1-log1p expm1-udef
8×log1p-expm1 frac-add
7×neg-sub0
6×acos-asin cos-mult associate-+l-
5×neg-log asin-acos exp-sum
4×rem-exp-log distribute-lft1-in distribute-rgt1-in tanh-def
3×sin-neg distribute-frac-neg hypot-def rem-cbrt-cube
2×exp-diff acos-neg pow3 associate-+r- count-2 unsub-neg unpow2 associate--r+
1×expm1-def sum-cubes distribute-lft-neg-out sqr-sin hypot-udef difference-of-sqr-1 un-div-inv sub-div tanh-undef cube-neg

regimes14.2s (1.7%)

Accuracy

Total 49.9b remaining (34.5%)

Threshold costs 4.5b (3.1%)

7.5b45.3%Cubic critical, narrow range
6.0b12.3%Cubic critical, medium range
6.0b12.6%Quadratic roots, medium range
4.9b56.7%Quotient of products
4.2b85.1%Quadratic roots, full range

localize4.3s (0.5%)

bsearch527.0ms (0.1%)

end1.0ms (0.0%)