Details

sample2.5m (52.3%)

Algorithm
78×intervals
Results
39.7s44023×body1280valid
34.5s3772×body10240exit
15.5s202959×body80valid
14.6s30181×body640valid
11.5s152248×body80nan
7.7s27697×body320valid
6.3s35752×body160valid
5.1s162806×pre80true
1.8s18067×body80overflowed
1.4s3108×body2560valid
787.0ms7923×body160nan
182.0ms8141×pre80false
138.0ms244×body5120valid

prune56.3s (19.5%)

series44.9s (15.5%)

Calls

486 calls:

1.1s
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3))
759.0ms
(- (pow (cos delta) 3) (expm1 (log1p (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))))
732.0ms
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
570.0ms
(/ (* (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)))
543.0ms
(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)))

simplify12.7s (4.4%)

Algorithm
224×egg-herbie

regimes9.9s (3.4%)

Accuracy

Total 33.7b remaining (28.4%)

Threshold costs 7.4b (6.3%)

6.2b12%Cubic critical, medium range
5.5b60.1%Cubic critical, narrow range
4.7b56.2%Quotient of products
3.7b86.1%Cubic critical
2.9b18.2%Cubic critical, wide range

rewrite9.0s (3.1%)

Algorithm
146×rewrite-expression-head
Calls

486 calls:

503.0ms
(* (- (/ 1 (/ (/ v (- 1.0 m)) m)) 1.0) m)
334.0ms
(* (/ (sqrt 1) (sqrt (sqrt (+ (exp x) (exp (- x)))))) (/ (/ 2.0 (sqrt (+ (exp x) (exp (- x))))) (sqrt (sqrt (+ (exp x) (exp (- x)))))))
275.0ms
(* (cbrt (- (/ m (/ v (- 1.0 m))) 1.0)) (cbrt (- (/ m (/ v (- 1.0 m))) 1.0)))
227.0ms
(log (+ (/ 1.0 x) (/ (sqrt (sqrt (- 1.0 (* x x)))) (/ x (sqrt (sqrt (- 1.0 (* x x))))))))
201.0ms
(* (- (/ m (/ v (- 1.0 m))) 1.0) (- 1.0 m))
Rules
13449×times-frac
12002×*-un-lft-identity
11276×add-sqr-sqrt
8531×add-cube-cbrt
3668×prod-diff
3410×sqrt-prod
3147×add-exp-log
1959×add-cbrt-cube
1175×associate-*r*
1082×div-exp
1013×prod-exp
936×difference-of-squares
894×pow1
887×distribute-lft-out
808×distribute-lft-out--
731×add-log-exp
717×associate-/r/
716×associate-/l*
704×div-inv
684×associate-/r*
555×unpow-prod-down
524×cbrt-undiv
514×distribute-rgt-neg-in
510×fma-neg
487×associate-*l* expm1-log1p-u
486×log1p-expm1-u
485×cbrt-unprod
405×distribute-lft-neg-in
384×cbrt-prod
335×flip--
334×flip3--
300×pow-exp
277×unswap-sqr
269×cube-prod
261×log-prod
255×flip-+
254×flip3-+
247×fma-def
245×sqrt-div
215×pow-to-exp
191×swap-sqr
182×sqr-pow
170×distribute-rgt-in distribute-lft-in
155×sin-sum
136×pow-prod-down neg-mul-1
130×clear-num frac-2neg
119×associate-*r/
114×1-exp
99×cos-sum
94×frac-times
91×associate-/l/ sub-neg
90×rec-exp
89×associate-*l/
85×*-commutative
80×cbrt-div
79×diff-log
76×unpow3 cube-mult
72×pow-unpow
60×log-pow
57×pow1/3
53×sqrt-pow1
50×pow1/2
49×sum-log
43×div-sub
40×sin-mult
37×+-commutative
31×fma-udef
30×sin-cos-mult
29×log-div
27×neg-sub0
26×rem-sqrt-square
25×associate-+l+ pow-flip tan-quot pow-pow
23×exp-prod exp-sum rem-log-exp
22×associate--l+ associate--r+
20×pow-prod-up
19×sin-diff
18×pow-sqr associate-+l-
17×associate-+r+ neg-log
16×cube-div cos-diff
15×rem-cube-cbrt
14×inv-pow frac-add
13×pow2 pow-plus
12×distribute-rgt-out
10×associate--l- acos-asin distribute-neg-frac
8×frac-sub
7×sqrt-undiv
6×un-div-inv sum-cubes
5×rem-exp-log sqrt-unprod associate-+r- distribute-frac-neg cos-mult distribute-rgt-neg-out
4×asin-acos associate--r- expm1-udef rem-cbrt-cube unpow2
3×acos-neg sin-neg sub0-neg exp-neg hypot-udef
2×exp-diff log1p-udef distribute-lft1-in rem-square-sqrt
1×difference-cubes log1p-expm1 expm1-log1p hypot-def sub-div distribute-rgt-out-- cube-neg exp-to-pow mul-1-neg

bsearch2.9s (1.0%)

localize2.2s (0.8%)

end1.0ms (0.0%)