Details

sample12.0m (54.1%)

Algorithm
78×intervals
Results
8.6m53096×body10240exit
1.2m43533×body1280valid
30.9s30666×body640valid
20.1s205226×body80valid
13.5s152994×body80nan
11.9s27463×body320valid
9.2s193340×pre80true
9.1s36345×body160valid
2.3s2995×body2560valid
1.4s7986×body160nan
599.0ms4034×pre10240exit
189.0ms214×body5120valid
182.0ms8545×pre80false
1.0ms1×body640nan

simplify6.6m (29.7%)

prune1.4m (6.4%)

series1.1m (5.0%)

Calls

473 calls:

2.0s
(/ (- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 3)) (fma (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) (fma (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1) (cos delta)) (* (cos delta) (cos delta))))
917.0ms
(* (cbrt (fma 2/15 (pow x 5) x)) (cbrt (fma 2/15 (pow x 5) x)))
872.0ms
(cbrt (fma 2/15 (pow x 5) x))
791.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
785.0ms
(/ (* (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)))

rewrite26.0s (2.0%)

Algorithm
150×rewrite-expression-head
Calls

473 calls:

2.4s
(* (- (/ (sqrt m) (/ (/ v (- 1.0 m)) (sqrt m))) 1.0) m)
729.0ms
(log (exp (cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))))
641.0ms
(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
640.0ms
(* (/ 2.0 (+ (pow (exp x) 3) (exp (* x -3)))) (+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x))))))
609.0ms
(* (* x (/ x (log 2.0))) (- 0.25 (+ (/ 0.125 (log 2.0)) (/ 1/2 (pow 2.0 2)))))
Rules
16430×*-un-lft-identity
16381×times-frac
13431×add-sqr-sqrt
9327×add-cube-cbrt
5023×prod-diff
3391×sqrt-prod
2922×add-exp-log
1877×difference-of-squares
1822×distribute-lft-out
1777×add-cbrt-cube
1646×distribute-lft-out--
1104×unpow-prod-down
990×div-exp
973×pow1
971×prod-exp
960×associate-/r/
876×associate-/r*
867×div-inv
812×cube-prod
689×associate-*r*
673×add-log-exp
661×log-prod
655×associate-/l*
532×exp-sum
504×associate-*l*
480×cbrt-prod
475×expm1-log1p-u
474×log1p-expm1-u
464×cbrt-undiv
451×sqr-pow
425×flip--
424×flip3--
396×cbrt-unprod
371×fma-neg
354×pow-exp
329×flip-+
328×flip3-+
260×pow-to-exp
258×distribute-rgt-neg-in
231×distribute-rgt-in distribute-lft-in
226×swap-sqr
204×unswap-sqr log-pow
195×associate--l+
176×associate-*r/
169×fma-def
145×pow-prod-down
127×clear-num frac-2neg
123×associate--r+
112×sqrt-div
106×exp-prod
105×frac-times
94×sub-neg
93×1-exp
91×*-commutative
85×distribute-lft-neg-in
83×associate-*l/
81×associate-/l/
79×diff-log
77×sqrt-pow1
71×pow1/2
64×frac-sub
61×exp-neg
60×cos-sum
50×neg-sub0
49×cbrt-div
48×pow1/3
46×exp-diff unpow3 cube-mult log-div
42×rec-exp
39×pow-unpow unpow2
37×div-sub
34×fma-udef sum-log
33×pow-prod-up
32×difference-cubes
31×rem-sqrt-square
27×neg-mul-1
24×+-commutative
23×rem-log-exp
22×sin-sum un-div-inv pow-pow
17×associate-+r+ pow-sqr
15×sub-div
14×associate-+l+ sin-mult sin-diff
11×frac-add distribute-neg-in pow-flip
10×cos-mult
9×cube-div sin-cos-mult pow-plus pow2 cos-diff
8×acos-asin neg-log associate-+l-
7×rem-cube-cbrt associate--l- sqrt-unprod
6×tan-quot associate--r-
5×rem-exp-log sqrt-undiv associate-+r- inv-pow expm1-log1p expm1-udef rem-cbrt-cube
4×acos-neg rem-square-sqrt distribute-frac-neg distribute-rgt-out
3×log1p-udef log1p-expm1 asin-acos
2×pow3 hypot-def
1×sqrt-pow2 distribute-rgt-out-- rgt-mult-inverse hypot-udef tanh-undef sqr-cos tanh-def

bsearch19.9s (1.5%)

regimes13.1s (1.0%)

Accuracy

Total 42.4b remaining (28.3%)

Threshold costs 5.7b (3.8%)

7.4b46%Cubic critical, narrow range
7.4b46.2%Quadratic roots, narrow range
6.4b10.2%Cubic critical, medium range
3.5b0%Quadratic roots, wide range
3.4b0%Cubic critical, wide range

localize4.2s (0.3%)

end2.0ms (0.0%)