Details

sample13.2m (57.7%)

Algorithm
78×intervals
Results
9.8m58369×body10240exit
1.3m43306×body1280valid
28.2s30587×body640valid
19.7s205068×body80valid
15.9s152559×body80nan
15.2s27969×body320valid
10.0s197689×pre80true
9.1s36128×body160valid
1.7s3124×body2560valid
1.0s7892×body160nan
491.0ms4142×pre10240exit
298.0ms250×body5120valid
204.0ms8365×pre80false
8.0ms1×body640nan

simplify6.9m (30.3%)

prune1.2m (5.4%)

series52.8s (3.9%)

Calls

437 calls:

1.3s
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
1.1s
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
774.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R))
753.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
717.0ms
(- (pow (cos delta) 2) (fma (pow (sin phi1) 4) (pow (cos delta) 2) (* (sin delta) (+ (* (* (cos phi1) (* (cbrt (pow (pow (sin phi1) 3) 3)) (* (cos delta) (cos theta)))) 2) (* (sin delta) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2))))))))

rewrite20.5s (1.5%)

Algorithm
143×rewrite-expression-head
Calls

437 calls:

617.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) (+ x 1.0)) (* (/ (cbrt 1.0) (- x 1.0)) (- (- 1.0) 1.0)))
457.0ms
(cos (- lambda1 lambda2))
426.0ms
(* (/ x (+ x 1.0)) (- (/ x (+ x 1.0)) (/ 1.0 (- x 1.0))))
407.0ms
(* (/ x (+ x 1.0)) (- (/ x (+ x 1.0)) (/ 1.0 (- x 1.0))))
343.0ms
(* (* (- (/ (* m (- 1.0 m)) v) 1.0) (+ (sqrt 1.0) (sqrt m))) (- (sqrt 1.0) (sqrt m)))
Rules
15749×*-un-lft-identity
14708×times-frac
12375×add-sqr-sqrt
9414×add-cube-cbrt
6937×prod-diff
2413×add-exp-log
1908×distribute-lft-out
1577×add-cbrt-cube
1301×difference-of-squares
1213×distribute-lft-out--
1144×distribute-rgt-in distribute-lft-in
1126×associate-/r/
1073×unpow-prod-down
924×cube-prod
915×sqrt-prod
852×div-inv
818×pow1
807×prod-exp
711×div-exp
694×associate-*r*
640×add-log-exp
582×associate-*l*
476×associate-/r*
443×associate-/l*
441×expm1-log1p-u
437×log1p-expm1-u
431×flip-+
430×flip3-+
407×cbrt-unprod
387×distribute-rgt-neg-in
367×flip--
366×flip3--
351×cbrt-undiv
348×fma-neg
321×distribute-lft-neg-in
301×pow-exp
289×cbrt-prod
216×pow-to-exp
213×sqr-pow
156×unpow3 pow-prod-down cube-mult
145×unswap-sqr
132×fma-def
123×associate-*r/ log-prod
115×frac-times
110×sub-neg
97×clear-num frac-2neg
93×*-commutative neg-mul-1 cos-sum
88×associate-*l/
86×sum-cubes
74×diff-log associate-/l/
69×cbrt-div
67×log-pow
59×sqrt-div
57×exp-prod
49×exp-sum
44×sin-sum
39×pow-unpow
37×div-sub
36×1-exp
35×fma-udef pow1/3 rec-exp
34×sin-cos-mult
33×pow1/2 sqrt-pow1
32×associate--l+
31×rem-sqrt-square sum-log
30×log-div
26×swap-sqr cos-mult
23×frac-sub
21×pow-pow
20×+-commutative
18×rem-log-exp sin-diff
16×cos-diff
14×unpow2 sin-mult
13×rem-cube-cbrt neg-sub0
12×frac-add pow-flip
11×associate-+l-
10×associate--r+
9×rem-exp-log associate-+r+ acos-asin
8×tan-quot
7×cube-div inv-pow neg-log
6×exp-diff pow-prod-up pow-sqr distribute-frac-neg
5×pow-plus log1p-udef associate--l- pow2 distribute-neg-in associate-+l+ expm1-log1p expm1-udef
4×log1p-expm1 distribute-rgt-out asin-acos associate--r- rem-cbrt-cube
3×acos-neg
2×un-div-inv distribute-rgt-neg-out distribute-neg-frac
1×expm1-def difference-cubes sqrt-pow2 distribute-lft1-in pow3 associate-+r- sqr-sin difference-of-sqr-1 hypot-udef unsub-neg sub-div tanh-undef sqr-cos exp-to-pow tanh-def

regimes12.6s (0.9%)

Accuracy

Total 39.7b remaining (29.8%)

Threshold costs 5.7b (4.3%)

7.9b43.8%Quadratic roots, narrow range
5.9b14.4%Quadratic roots, medium range
3.9b64.6%Quotient of products
3.5b0%Quadratic roots, wide range
3.5b0%Cubic critical, wide range

localize3.9s (0.3%)

bsearch1.2s (0.1%)

end1.0ms (0.0%)