Details

sample9.5m (52.6%)

Algorithm
78×intervals
Results
6.2m41707×body10240exit
1.3m43718×body1280valid
27.2s30409×body640valid
18.1s204361×body80valid
15.8s153009×body80nan
12.4s27727×body320valid
9.3s179917×pre80true
8.4s35925×body160valid
1.7s3019×body2560valid
841.0ms8035×body160nan
585.0ms4132×pre10240exit
253.0ms233×body5120valid
1.0ms1×body640nan

simplify4.5m (24.9%)

prune2.3m (12.9%)

series1.1m (5.9%)

Calls

479 calls:

1.6s
(* (/ c (+ (pow b 3) (pow (sqrt (fma (- (* a c)) 4.0 (* b b))) 3))) (+ (* (sqrt (fma b b (* (- c) (* a 4.0)))) (sqrt (fma b b (* (- c) (* a 4.0))))) (- (* b b) (* (sqrt (fma b b (* (- c) (* a 4.0)))) b))))
904.0ms
(pow (sqrt (fma (- (* a c)) 4.0 (* b b))) 3)
716.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
644.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
637.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))

regimes16.8s (1.6%)

Accuracy

Total 16.8b remaining (14.9%)

Threshold costs 7.9b (7%)

4.9b54.9%Quotient of products
1.6b93.3%Cubic critical
1.2b43.6%(- (/ x0 (- 1 x1)) x0)
1.2b66.1%2-ancestry mixing, positive discriminant
0.9b94.4%Quadratic roots, full range

rewrite15.7s (1.5%)

Algorithm
144×rewrite-expression-head
Calls

479 calls:

730.0ms
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))
418.0ms
(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))
370.0ms
(- (/ (- 2.0) (pow x 4)) (+ (/ 2.0 (pow x 6)) (/ (/ 2.0 x) x)))
365.0ms
(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
317.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
Rules
18960×times-frac
17093×*-un-lft-identity
15037×add-sqr-sqrt
11512×add-cube-cbrt
6750×prod-diff
2900×add-exp-log
2551×sqrt-prod
1892×unpow-prod-down
1805×distribute-lft-out
1656×add-cbrt-cube
1543×difference-of-squares
1453×distribute-rgt-neg-in
1370×distribute-lft-neg-in
1290×log-prod
1217×cube-prod
1093×div-exp
1069×associate--l+
1065×associate-/l*
1012×exp-sum
939×distribute-lft-out--
935×div-inv
851×prod-exp
847×pow1
713×associate-/r/
702×sqr-pow
696×add-log-exp
674×associate-/r*
617×fma-neg
512×associate-*r*
479×expm1-log1p-u log1p-expm1-u
461×cbrt-undiv
442×associate-*l*
381×neg-mul-1
329×distribute-rgt-in distribute-lft-in
324×cbrt-unprod
303×pow-exp
300×flip-+
299×flip3-+
288×cbrt-prod
241×flip--
240×flip3--
218×pow-to-exp
187×fma-def
151×unpow3 cube-mult
131×pow-prod-down unswap-sqr
127×1-exp
121×frac-2neg clear-num
86×sqrt-div
75×sub-neg
74×rec-exp
72×*-commutative
69×associate-*r/
68×diff-log
65×sqrt-pow1
64×associate-/l/
63×pow-unpow
62×pow1/2 fma-udef associate-*l/
61×frac-times
54×log-pow
49×cos-sum
47×exp-prod div-sub
45×sum-log
37×pow1/3
35×+-commutative
34×cbrt-div
33×sin-sum rem-sqrt-square
32×log-div
29×frac-sub pow-pow
26×rem-log-exp
22×swap-sqr
21×pow-prod-up
20×neg-sub0 distribute-neg-frac
19×sin-diff
18×frac-add
16×pow-flip
15×sin-cos-mult hypot-def
13×associate--r+
12×rem-cube-cbrt neg-log
11×distribute-frac-neg pow-sqr
10×associate--l- pow-plus sin-mult distribute-rgt-out
9×unpow2
8×difference-cubes distribute-rgt-neg-out cube-div cos-diff tan-quot
7×inv-pow associate-+l- acos-asin
6×distribute-lft-neg-out pow2
5×cos-mult rem-cbrt-cube associate--r-
4×exp-diff sqrt-unprod rem-exp-log
3×distribute-rgt-out-- sum-cubes acos-neg
2×expm1-udef associate-+r- unsub-neg asin-acos rem-square-sqrt
1×expm1-log1p sqrt-undiv log1p-expm1 log1p-udef pow3 tanh-undef sqrt-pow2 tanh-def hypot-udef distribute-neg-in un-div-inv

localize6.5s (0.6%)

bsearch1.4s (0.1%)

end1.0ms (0.0%)