Details

sample3.0m (56.6%)

Algorithm
78×intervals
Results
1.7m21839×body10240exit
34.0s44023×body1280valid
11.1s30181×body640valid
6.9s202959×body80valid
4.6s152248×body80nan
4.6s27697×body320valid
3.0s35752×body160valid
2.7s158684×pre80true
764.0ms3108×body2560valid
382.0ms4122×pre10240exit
373.0ms7923×body160nan
101.0ms8141×pre80false
65.0ms244×body5120valid

prune53.9s (16.8%)

series45.8s (14.3%)

Calls

490 calls:

743.0ms
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
740.0ms
(/ (* (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)))
662.0ms
(fma (pow (cos phi2) 3) (pow (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) 3) (pow (cos phi1) 3))
650.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
607.0ms
(- (pow (cos delta) 3) (expm1 (log1p (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))))

simplify12.6s (3.9%)

Algorithm
224×egg-herbie

regimes9.9s (3.1%)

Accuracy

Total 33.8b remaining (28.5%)

Threshold costs 7.5b (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

rewrite7.8s (2.4%)

Algorithm
146×rewrite-expression-head
Calls

490 calls:

511.0ms
(* (- (/ 1 (/ (/ v (- 1.0 m)) m)) 1.0) m)
235.0ms
(log (+ (/ 1.0 x) (/ (sqrt (sqrt (- 1.0 (* x x)))) (/ x (sqrt (sqrt (- 1.0 (* x x))))))))
204.0ms
(* (- (/ m (/ v (- 1.0 m))) 1.0) (- 1.0 m))
196.0ms
(* (- (/ m (/ v (- 1.0 m))) 1.0) m)
141.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
Rules
11173×times-frac
10437×*-un-lft-identity
9410×add-sqr-sqrt
7385×add-cube-cbrt
3148×prod-diff
3120×add-exp-log
2149×sqrt-prod
1919×add-cbrt-cube
1067×div-exp
1007×prod-exp
910×pow1
909×difference-of-squares
797×associate-*r*
784×distribute-lft-out--
734×distribute-lft-out
718×add-log-exp
680×associate-/l*
654×associate-/r*
649×associate-/r/
625×div-inv
552×unpow-prod-down
507×distribute-rgt-neg-in
505×cbrt-undiv
491×expm1-log1p-u
490×log1p-expm1-u
476×cbrt-unprod fma-neg
468×log-prod
398×distribute-lft-neg-in
392×cbrt-prod
366×associate-*l*
331×flip--
330×flip3--
297×pow-exp
266×cube-prod
257×distribute-rgt-in distribute-lft-in
235×fma-def
225×flip-+
224×flip3-+
214×pow-to-exp
196×sqrt-div
179×sqr-pow
142×unswap-sqr
135×pow-prod-down
129×neg-mul-1
125×clear-num frac-2neg
124×associate-*r/
116×1-exp
103×frac-times
99×associate-*l/
96×associate-/l/
95×swap-sqr
91×rec-exp sub-neg
84×log-pow *-commutative
83×cbrt-div
73×unpow3 cube-mult
69×pow-unpow diff-log
65×pow1/3
58×cos-sum
55×sqrt-pow1
53×associate--l+
50×pow1/2
48×sum-log
41×div-sub
37×sin-mult
36×+-commutative
34×rem-log-exp
30×sin-cos-mult pow-flip log-div
27×rem-sqrt-square fma-udef
26×neg-sub0
25×associate-+l+ exp-prod tan-quot
23×sin-sum exp-sum
22×pow-pow
19×pow-prod-up
18×associate-+l- sin-diff
17×pow-sqr
15×inv-pow cos-diff neg-log
14×frac-add
13×associate-+r+
12×rem-cube-cbrt pow2 pow-plus distribute-rgt-out
10×cube-div distribute-neg-frac
9×associate--l-
7×acos-asin
5×rem-exp-log un-div-inv sum-cubes associate-+r- distribute-frac-neg frac-sub expm1-udef
4×sqrt-unprod asin-acos unpow2
3×acos-neg sqrt-undiv sub0-neg log1p-udef exp-neg hypot-udef cos-mult exp-to-pow rem-cbrt-cube
2×exp-diff distribute-lft1-in log1p-expm1 expm1-log1p distribute-rgt-neg-out
1×difference-cubes rem-square-sqrt hypot-def associate--r- distribute-rgt-out-- associate--r+ log-rec

bsearch6.9s (2.2%)

localize2.2s (0.7%)

end1.0ms (0.0%)