Details

sample29.2m (65.3%)

Algorithm
72×intervals
Results
8.1m80199×body10240exit
52.8s33308×body1280valid
25.7s197506×body80valid
22.5s24182×body640valid
20.0s151768×body80nan
14.6s25099×body320valid
12.2s35307×body160valid
9.4s153484×pre80true
2.9s3105×body2560valid
1.8s7981×body160nan
1.1s4125×pre10240exit
248.0ms238×body5120valid

prune6.1m (13.7%)

simplify6.0m (13.5%)

bsearch2.1m (4.8%)

series42.3s (1.6%)

Calls

370 calls:

Slowest
952.0ms
(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (fma 1/2 (* t c_p) (fma c_p (log 1/2) 1)) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))
758.0ms
(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)))
628.0ms
(/ (fma (sqrt (sqrt (fma c (* -3 a) (* b b)))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b)) (* 3 a))
614.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
557.0ms
(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))

regimes15.0s (0.6%)

Accuracy

Total 50.4b remaining (25.4%)

Threshold costs 3.2b (1.6%)

7.6b44.9%Quadratic roots, narrow range
6.3b11.5%Quadratic roots, medium range
5.8b57.1%Cubic critical, narrow range
5.3b31.1%Quotient of products
4.8b27.5%Cubic critical, medium range

rewrite9.6s (0.4%)

Algorithm
125×rewrite-expression-head
Calls

370 calls:

Slowest
633.0ms
(* (/ (/ (cbrt a1) (/ b1 (cbrt a1))) (* (cbrt b2) (cbrt b2))) (/ (/ (cbrt a1) (/ 1 (* (cbrt a2) (cbrt a2)))) (/ (cbrt b2) (cbrt a2))))
456.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
170.0ms
(* (- (/ m (/ v (- 1 m))) 1) m)
141.0ms
(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))
128.0ms
(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (fma 1/2 (* t c_p) (fma c_p (log 1/2) 1)) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))
Rules
57303×times-frac
27291×add-sqr-sqrt
26512×*-un-lft-identity
23553×add-cube-cbrt
11956×cbrt-prod
3855×add-exp-log
3047×div-inv
2712×prod-diff
2356×associate-*r*
1731×div-exp
1594×add-cbrt-cube
1359×pow1
1330×prod-exp
1050×sqrt-prod
983×associate-/r/
804×difference-of-squares
795×distribute-lft-out
787×pow-exp
668×cbrt-undiv
667×associate-*l*
618×associate-/r*
589×associate-/l*
510×add-log-exp
457×unswap-sqr
430×distribute-lft-out--
400×pow-to-exp
395×cbrt-unprod
384×swap-sqr
373×associate-+r+
372×expm1-log1p-u
370×insert-posit16 log1p-expm1-u
309×flip--
308×flip3--
234×pow-prod-up
230×pow-prod-down
229×difference-of-sqr-1
223×fma-neg
190×1-exp
187×rec-exp
185×flip-+
184×flip3-+
175×frac-times
163×fma-def
160×distribute-lft-in distribute-rgt-in
152×log-prod
147×associate-*r/
142×associate-*l/ pow-sqr
119×pow-plus
96×frac-2neg clear-num tan-quot
90×pow2
80×*-commutative
74×sqrt-div distribute-rgt-neg-in
63×unpow-prod-down
62×distribute-rgt-out
60×distribute-lft-neg-in
59×sub-neg
57×associate-/l/
56×pow1/3
51×distribute-rgt1-in sqrt-pow1 pow1/2
46×associate-+l+
42×log-pow
40×fma-udef
39×rem-sqrt-square
38×diff-log
35×sum-log
33×sin-sum
31×log-div
30×cbrt-div
24×cos-sum
23×associate--l+
21×+-commutative
20×neg-mul-1 div-sub
19×frac-sub rem-log-exp
18×hypot-def frac-add
16×exp-sum
15×exp-prod
14×pow-flip inv-pow
12×sqrt-undiv
11×neg-sub0 associate-+l-
9×pow-unpow pow-pow
8×neg-log
6×sqr-pow associate--r+ acos-asin
5×cube-unmult associate--r-
4×distribute-lft-neg-out cos-diff expm1-def
3×exp-diff log1p-expm1 log-rec sqrt-unprod hypot-udef rem-exp-log rem-square-sqrt log1p-udef
2×pow3 sub-div sin-mult rem-cbrt-cube
1×expm1-log1p expm1-udef cos-mult associate-+r- unsub-neg distribute-rgt-out-- distribute-frac-neg tanh-def tanh-undef asin-acos acos-neg sin-diff

localize4.5s (0.2%)

end1.0ms (0.0%)