Details

sample13.8m (71.7%)

Algorithm
78×intervals
Results
9.5m54507×body10240exit
1.7m44062×body1280valid
39.1s30354×body640valid
29.1s204603×body80valid
20.8s27595×body320valid
19.1s151935×body80nan
12.9s36134×body160valid
12.2s194406×pre80true
3.1s3128×body2560valid
1.5s7740×body160nan
1.1s4060×pre10240exit
374.0ms243×body5120valid

simplify2.1m (11.1%)

prune1.8m (9.3%)

series50.5s (4.4%)

Calls

472 calls:

924.0ms
(- (* (cos delta) (* (cos delta) (cos delta))) (* (* (* (sin (asin (fma (* (cos phi1) (cos theta)) (sin delta) (* (cos delta) (sin phi1))))) (sin phi1)) (* (sin (asin (fma (* (cos phi1) (cos theta)) (sin delta) (* (cos delta) (sin phi1))))) (sin phi1))) (* (sin (asin (fma (* (cos phi1) (cos theta)) (sin delta) (* (cos delta) (sin phi1))))) (sin phi1))))
705.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
632.0ms
(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))
590.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
559.0ms
(* (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (/ 1/3 a))

regimes20.9s (1.8%)

Accuracy

Total 58.4b remaining (26.3%)

Threshold costs 4.5b (2%)

11.1b-0%Quotient of products
7.5b46.9%Quadratic roots, narrow range
6.2b12.9%Quadratic roots, medium range
5.6b59.5%Cubic critical, narrow range
5.1b27.2%Cubic critical, medium range

rewrite12.0s (1.0%)

Algorithm
149×rewrite-expression-head
Calls

472 calls:

495.0ms
(* (* (- (- (/ m v) (/ m (/ v m))) 1) (+ 1 (sqrt m))) (- 1 (sqrt m)))
388.0ms
(* (- (- (/ m v) (/ m (/ v m))) 1) (- 1 m))
381.0ms
(+ (exp (* -2 x)) 1)
361.0ms
(* (- (- (/ m v) (/ m (/ v m))) 1) (+ 1 (sqrt m)))
299.0ms
(- (* (cos delta) (* (cos delta) (cos delta))) (* (* (* (sin (asin (fma (* (cos phi1) (cos theta)) (sin delta) (* (cos delta) (sin phi1))))) (sin phi1)) (* (sin (asin (fma (* (cos phi1) (cos theta)) (sin delta) (* (cos delta) (sin phi1))))) (sin phi1))) (* (sin (asin (fma (* (cos phi1) (cos theta)) (sin delta) (* (cos delta) (sin phi1))))) (sin phi1))))
Rules
12403×times-frac
11990×*-un-lft-identity
10739×add-sqr-sqrt
8259×add-cube-cbrt
5210×prod-diff
2903×add-exp-log
2029×sqrt-prod
1499×add-cbrt-cube
1315×pow1
1098×distribute-lft-out
1096×prod-exp
1068×difference-of-squares
968×div-exp
788×div-inv
695×pow-exp
673×add-log-exp
672×associate--l+
609×associate-*r*
599×associate-/r/
595×distribute-lft-out--
483×fma-neg
479×expm1-log1p-u
475×associate-/r* log1p-expm1-u
472×insert-posit16
441×associate-*l*
418×associate-/l*
362×cbrt-unprod
346×pow-to-exp
314×associate-+r+
299×cbrt-undiv
278×difference-of-sqr-1
258×flip-+
257×flip3-+
254×log-prod
243×pow-prod-down
238×cbrt-prod
229×flip--
228×flip3--
183×fma-def
163×1-exp rec-exp
143×unswap-sqr
138×pow-prod-up
127×frac-times
124×associate-*r/
120×sqrt-div
114×distribute-rgt-in distribute-lft-in
104×*-commutative
98×associate-*l/
96×frac-2neg clear-num
93×log-pow
92×tan-quot
82×sqrt-pow1 swap-sqr
76×pow-sqr
74×sub-neg
73×pow-plus
70×diff-log
62×pow1/2
58×associate-/l/
54×fma-udef
50×pow2 exp-prod cos-sum
48×rem-log-exp
43×sum-log unpow-prod-down
38×log-div
37×div-sub
35×rem-sqrt-square sin-mult
33×pow-flip sin-sum
30×cbrt-div
28×frac-sub
27×pow1/3
25×exp-sum
24×+-commutative
21×inv-pow
18×distribute-rgt-neg-in sin-diff
15×pow-unpow
14×cos-mult log1p-udef
11×sin-cos-mult frac-add
10×log1p-expm1 associate--r+ acos-asin
9×distribute-lft-neg-in
8×exp-diff cos-diff expm1-def
7×expm1-log1p expm1-udef pow3 log-rec pow-pow
6×neg-sub0 rem-exp-log associate-+l- distribute-rgt-out
5×cube-unmult sqr-pow un-div-inv asin-acos
4×distribute-frac-neg acos-neg associate--r-
3×associate-+r- neg-log sqrt-unprod sub-div neg-mul-1
2×quot-tan remove-posit16 associate--l- distribute-rgt1-in tanh-undef hypot-udef hypot-def rem-square-sqrt sqr-cos rem-cbrt-cube
1×difference-cubes hypot-1-def tanh-def exp-to-pow unpow-prod-up unsub-neg e-exp-1

localize5.7s (0.5%)

bsearch1.9s (0.2%)

end1.0ms (0.0%)