Details

sample2.0m (46.5%)

Algorithm
77×intervals
Results
35.7s3575×body10240exit
35.0s43776×body1280valid
11.5s29556×body640valid
7.3s201956×body80valid
5.0s153026×body80nan
4.9s28060×body320valid
3.3s36530×body160valid
2.7s153149×pre80true
779.0ms3020×body2560valid
393.0ms4122×pre10240exit
380.0ms7891×body160nan
350.0ms13000×body80overflowed
97.0ms8245×pre80false
56.0ms197×body5120valid

prune58.3s (22.8%)

series44.0s (17.2%)

Calls

477 calls:

809.0ms
(/ (fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
577.0ms
(log (expm1 (log1p (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))))
527.0ms
(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
499.0ms
(fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
441.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)

simplify13.8s (5.4%)

Algorithm
221×egg-herbie

regimes9.2s (3.6%)

Accuracy

Total 33.5b remaining (28.5%)

Threshold costs 5.2b (4.5%)

5.7b48.5%Quotient of products
5.7b58%Cubic critical, narrow range
5.2b24.6%Cubic critical, medium range
4.9b82.5%Cubic critical
2.8b16.3%Cubic critical, wide range

rewrite8.6s (3.4%)

Algorithm
145×rewrite-expression-head
Calls

477 calls:

342.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))
264.0ms
(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
250.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
188.0ms
(* (* (- (- (* 1.0 (/ m v)) (/ (* m m) v)) 1.0) (+ (sqrt 1.0) (sqrt m))) (- (sqrt 1.0) (sqrt m)))
153.0ms
(* (- (/ (/ (* m (- 1.0 m)) (sqrt v)) (sqrt v)) 1.0) m)
Rules
15619×*-un-lft-identity
13834×times-frac
13254×add-sqr-sqrt
9493×add-cube-cbrt
7665×prod-diff
3274×unpow-prod-down
2705×cube-prod
1848×add-exp-log
1715×distribute-lft-out
1617×add-cbrt-cube
1467×sqrt-prod
1433×difference-of-squares
1234×distribute-lft-out--
1002×associate-*r*
988×associate-/r/
970×associate--r+
882×div-inv
837×distribute-rgt-neg-in
826×pow1
735×add-log-exp
657×distribute-lft-neg-in
592×associate-/l*
481×div-exp
480×sqr-pow associate-*l*
479×expm1-log1p-u
477×log1p-expm1-u
476×associate-/r*
424×fma-neg
413×prod-exp
398×cbrt-undiv
382×flip--
381×flip3--
365×flip-+
364×flip3-+
363×cbrt-prod
330×cbrt-unprod
316×log-prod
291×fma-def
275×distribute-rgt-in distribute-lft-in
227×unswap-sqr
219×neg-mul-1
191×unpow3 cube-mult
126×associate-*r/
124×clear-num frac-2neg
115×pow-prod-down
106×frac-times
104×associate-/l/
102×sub-neg
94×exp-sum
90×sqrt-div
88×diff-log
87×*-commutative
81×swap-sqr
74×associate-*l/
61×log-pow
60×tan-quot
52×div-sub
51×pow1/3
50×cbrt-div
48×sum-log cos-sum
41×pow1/2 pow-exp sqrt-pow1
38×sin-mult
36×+-commutative distribute-rgt-out frac-sub
34×rem-sqrt-square sin-sum
33×pow-to-exp
30×neg-sub0
27×log-div
26×unpow2
25×pow-unpow exp-prod
24×associate--l+ 1-exp rem-log-exp
22×cos-mult
20×rec-exp neg-log
19×sin-diff
18×fma-udef
17×un-div-inv frac-add
16×associate--l- associate-+l-
14×sin-cos-mult cos-diff
13×hypot-def pow-pow
12×cube-div sub-div
11×pow-prod-up pow-sqr
10×rem-cube-cbrt distribute-frac-neg expm1-udef
9×pow2 acos-asin distribute-rgt-neg-out associate-+r+
8×pow-plus associate-+r-
7×distribute-lft-neg-out pow-flip associate--r-
6×rem-exp-log sin-neg distribute-rgt-out--
5×acos-neg log1p-udef expm1-log1p
3×inv-pow log1p-expm1 associate-+l+ hypot-udef unsub-neg unpow-prod-up asin-acos rem-cbrt-cube
2×exp-neg distribute-lft1-in distribute-neg-frac
1×exp-diff difference-cubes sqrt-pow2 e-exp-1 sqrt-unprod pow3 sqr-sin log-rec exp-to-pow

localize2.3s (0.9%)

bsearch706.0ms (0.3%)

end1.0ms (0.0%)