Details

simplify5.5m (43.4%)

sample4.2m (33.1%)

Algorithm
78×intervals
Results
1.3m43001×body1280valid
1.2m17823×body10240exit
25.6s30567×body640valid
19.1s202128×body80valid
16.2s151378×body80nan
12.3s27992×body320valid
9.1s36071×body160valid
6.6s153687×pre80true
2.0s3023×body2560valid
948.0ms8187×body160nan
900.0ms4066×pre10240exit
189.0ms247×body5120valid
1.0ms1×body640nan

prune1.5m (11.9%)

series48.1s (6.3%)

Calls

453 calls:

862.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)
819.0ms
(fma (- (/ 1 (- x 1))) (+ x 1) (log1p (expm1 (* (/ 1 (- x 1)) (+ x 1)))))
789.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
674.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
665.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R))

regimes19.5s (2.6%)

Accuracy

Total 47.9b remaining (22.5%)

Threshold costs 4.6b (2.1%)

7.6b46%Quadratic roots, narrow range
5.8b57.6%Cubic critical, narrow range
5.3b20.6%Quadratic roots, medium range
5.3b20.2%Cubic critical, medium range
3.6b0%Quadratic roots, wide range

rewrite14.0s (1.8%)

Algorithm
145×rewrite-expression-head
Calls

453 calls:

423.0ms
(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* y x) (* (* y x) (* y x)))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))
410.0ms
(cos (- lambda1 lambda2))
389.0ms
(cos (/ (- phi1 phi2) 2))
375.0ms
(cbrt (* (* (* (sqrt m) (sqrt m)) (* (sqrt m) (sqrt m))) (* (sqrt m) (sqrt m))))
354.0ms
(cbrt (* (* (* (sqrt m) (sqrt m)) (sqrt m)) (* (* (sqrt m) (sqrt m)) (sqrt m))))
Rules
7229×times-frac
7185×*-un-lft-identity
6843×add-sqr-sqrt
4894×add-cube-cbrt
2985×add-exp-log
1749×prod-diff
1588×add-cbrt-cube
1485×pow1
1174×prod-exp
1168×cbrt-prod
977×sqrt-prod
976×div-exp
967×associate-*r*
693×pow-exp
677×difference-of-squares
663×distribute-lft-out
631×add-log-exp associate-*l*
544×associate-/r*
458×log1p-expm1-u
456×expm1-log1p-u
453×insert-posit16
430×cbrt-unprod
399×associate-/r/
356×div-inv
346×distribute-lft-out--
345×pow-to-exp
330×associate-/l*
323×cbrt-undiv
321×pow-prod-down
232×log-prod
228×swap-sqr flip--
227×flip3--
220×unswap-sqr
215×flip-+
214×flip3-+
192×frac-times
190×fma-neg
177×difference-of-sqr-1
172×fma-def
167×pow-prod-up
153×1-exp rec-exp
146×associate-*r/
137×associate-*l/
118×*-commutative
113×distribute-rgt-in distribute-lft-in
105×pow-sqr
102×sqrt-div
101×sqrt-pow1
100×frac-2neg clear-num
96×tan-quot
91×pow-plus
89×pow1/2
75×log-pow
61×pow2
60×cos-sum
59×cbrt-div
58×sub-neg
57×sum-log
55×associate-/l/
54×exp-prod
52×fma-udef
45×diff-log
40×unpow-prod-down
39×div-sub
35×associate--l+
34×distribute-rgt-neg-in
30×+-commutative
29×associate-+l+ rem-log-exp
28×pow-flip pow1/3
27×associate-+r+
22×sin-sum log-div
21×inv-pow cos-diff
18×rem-sqrt-square distribute-lft-neg-in
15×pow3 associate-+l-
14×frac-sub
13×sin-cos-mult sin-mult log1p-udef
11×neg-sub0 acos-asin
10×log-rec sin-diff
8×sqrt-unprod rem-square-sqrt expm1-def
7×expm1-log1p expm1-udef frac-add
6×cos-mult sqrt-undiv pow-unpow neg-log neg-mul-1 pow-pow rem-cbrt-cube
5×distribute-frac-neg cube-unmult associate--r+ acos-neg
4×log1p-expm1 sqr-pow difference-cubes rem-exp-log
3×un-div-inv exp-to-pow hypot-udef distribute-rgt-out
2×distribute-lft-neg-out exp-diff associate-+r- asin-acos unsub-neg
1×associate--l- distribute-rgt1-in tanh-undef tanh-def hypot-def remove-posit16 sqr-cos

localize5.7s (0.8%)

bsearch860.0ms (0.1%)

end1.0ms (0.0%)