Details

sample11.5m (53.4%)

Algorithm
78×intervals
Results
8.2m51433×body10240exit
1.3m44179×body1280valid
27.0s30315×body640valid
20.7s204702×body80valid
14.0s152738×body80nan
11.8s27515×body320valid
9.5s36369×body160valid
9.0s189961×pre80true
1.7s2910×body2560valid
825.0ms7816×body160nan
611.0ms4048×pre10240exit
237.0ms273×body5120valid
205.0ms8075×pre80false
3.0ms3×body640nan

simplify6.6m (30.5%)

prune1.6m (7.6%)

series1.1m (5.0%)

Calls

460 calls:

1.5s
(* (/ (/ (* a (* 3.0 c)) (sqrt 3.0)) (* (cbrt a) (cbrt a))) (/ (/ (/ 1 (- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (sqrt 3.0)) (cbrt a)))
1.1s
(/ (- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))) (fma (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1) (cos delta)))
769.0ms
(* (pow (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) 1) R)
738.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
696.0ms
(cbrt (/ -1 a))

rewrite26.7s (2.1%)

Algorithm
142×rewrite-expression-head
Calls

460 calls:

876.0ms
(* (/ (/ (* a (* 3.0 c)) (sqrt 3.0)) (* (cbrt a) (cbrt a))) (/ (/ (/ 1 (- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (sqrt 3.0)) (cbrt a)))
697.0ms
(- (/ x (+ x 1.0)) (/ (sqrt (+ x 1.0)) (/ (- x 1.0) (sqrt (+ x 1.0)))))
577.0ms
(- (log 2) (- (+ (/ 0.25 (* x x)) (/ 0.09375 (pow x 4))) (log x)))
517.0ms
(/ (* 1.0 (- (- x 1.0) (+ x 1.0))) (* (+ x 1.0) (- x 1.0)))
436.0ms
(- (+ (/ 0.25 (* x x)) (/ 0.09375 (pow x 4))) (log x))
Rules
28861×times-frac
25293×*-un-lft-identity
19987×add-sqr-sqrt
15341×add-cube-cbrt
10428×sqrt-prod
8780×prod-diff
3000×distribute-lft-out
2710×add-exp-log
2073×difference-of-squares
1949×distribute-lft-out--
1742×add-cbrt-cube
1617×associate-*r*
1491×associate-/r/
1300×cbrt-prod
1072×div-inv
1036×pow1
886×div-exp
856×prod-exp
687×add-log-exp
685×associate-/l*
613×flip-+
612×flip3-+
551×associate-/r*
538×fma-neg
514×unpow-prod-down
486×cbrt-undiv
461×log1p-expm1-u expm1-log1p-u
453×distribute-rgt-neg-in
452×cbrt-unprod
434×sqrt-div
397×associate-*l*
376×flip--
375×flip3--
371×cube-prod
300×pow-exp
266×pow-prod-down
215×pow-to-exp
202×distribute-rgt-in distribute-lft-in
198×distribute-lft-neg-in
181×fma-def
176×unswap-sqr
144×sqr-pow
142×exp-prod
128×log-prod
110×associate-/l/ associate-*r/
107×clear-num frac-2neg
97×*-commutative
95×sub-neg
86×unpow3 cube-mult
80×diff-log
76×frac-times
71×pow1/3
66×neg-mul-1
64×associate-*l/
63×pow-unpow
62×log-pow
55×sin-sum
54×cbrt-div
50×cos-sum pow-prod-up pow-sqr swap-sqr
45×div-sub
38×exp-sum
35×sum-log
33×1-exp rec-exp
32×pow1/2 sqrt-pow1
30×distribute-rgt-out log-div
29×fma-udef
28×rem-sqrt-square
27×sin-mult cos-mult
26×frac-sub
25×associate--r+
24×pow-pow
23×+-commutative
22×associate--l+
21×unpow2
19×rem-log-exp
18×tan-quot sin-diff
17×frac-add neg-sub0
16×pow-plus
15×pow2
14×distribute-lft1-in distribute-rgt1-in
13×sin-cos-mult exp-to-pow
12×hypot-def neg-log
11×associate--l-
10×cube-div rem-cube-cbrt cos-diff associate-+l- count-2
8×sub-div distribute-frac-neg acos-asin
7×distribute-rgt-neg-out
6×pow-flip
5×inv-pow rem-cbrt-cube
4×acos-neg sqrt-undiv sin-neg
3×rem-exp-log
2×un-div-inv log1p-udef sqrt-unprod log1p-expm1 expm1-log1p hypot-udef expm1-udef sqr-cos tanh-def
1×unpow1/3 pow3 sqr-sin associate-+l+ tanh-undef asin-acos associate--r- cube-neg

regimes13.1s (1.0%)

Accuracy

Total 36.4b remaining (27.6%)

Threshold costs 6.0b (4.5%)

8.1b40.8%Cubic critical, narrow range
6.2b8.6%Cubic critical, medium range
4.8b82.7%Cubic critical
4.7b83.4%Quadratic roots, full range
1.9b49.8%2-ancestry mixing, positive discriminant

localize4.1s (0.3%)

bsearch817.0ms (0.1%)

end1.0ms (0.0%)