Details

simplify10.4m (43.3%)

sample8.6m (35.8%)

Algorithm
78×intervals
Results
4.3m31346×body10240exit
1.7m43446×body1280valid
42.5s31146×body640valid
27.8s203438×body80valid
20.6s27563×body320valid
19.8s152791×body80nan
12.6s36001×body160valid
9.7s169407×pre80true
3.1s2959×body2560valid
1.5s7967×body160nan
877.0ms4105×pre10240exit
270.0ms227×body5120valid
3.0ms1×body640nan
2.0ms1×body320nan

prune3.5m (14.5%)

series55.1s (3.8%)

Calls

446 calls:

1.6s
(* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))))
1.3s
(- (* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b)))) (* (* b b) b))
962.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
748.0ms
(/ (fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b))) (sqrt (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b))))))
703.0ms
(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)))

regimes18.0s (1.2%)

Accuracy

Total 54.2b remaining (25.4%)

Threshold costs 4.8b (2.3%)

7.3b47.3%Quadratic roots, narrow range
6.3b10.7%Quadratic roots, medium range
6.1b23.1%Cubic critical, narrow range
5.7b49.7%Quotient of products
4.7b31.2%Cubic critical, medium range

rewrite9.1s (0.6%)

Algorithm
142×rewrite-expression-head
Calls

446 calls:

331.0ms
(* (cbrt (+ (/ 1 (- x 1)) (/ x (+ x 1)))) (cbrt (+ (/ 1 (- x 1)) (/ x (+ x 1)))))
280.0ms
(/ (- (* (fma x (fma 1/8 x 1/2) (log 2)) (* (fma x (fma 1/8 x 1/2) (log 2)) (fma x (fma 1/8 x 1/2) (log 2)))) (* (* (* y x) (* y x)) (* y x))) (fma (* y x) (fma x (fma 1/8 x 1/2) (log 2)) (fma (fma x (fma 1/8 x 1/2) (log 2)) (fma x (fma 1/8 x 1/2) (log 2)) (* (* y x) (* y x)))))
194.0ms
(- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))
147.0ms
(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))
145.0ms
(* (* (/ 1 (sqrt a)) (/ 1 (sqrt a))) (* (/ b (sqrt a)) (/ b (sqrt a))))
Rules
7201×*-un-lft-identity
6687×add-sqr-sqrt
6302×times-frac
4711×add-cube-cbrt
3238×add-exp-log
2407×prod-diff
1473×add-cbrt-cube
1305×prod-exp
1185×sqrt-prod
1139×div-exp
1090×pow1
700×distribute-lft-out
693×pow-exp
652×associate-*l*
649×associate-*r*
645×difference-of-squares
603×add-log-exp
543×cbrt-prod
453×div-inv
450×log1p-expm1-u
448×expm1-log1p-u
446×insert-posit16
375×distribute-lft-out--
361×cbrt-unprod
345×pow-to-exp
342×associate-/l*
341×associate-/r* associate-/r/
319×cbrt-undiv
317×fma-neg
288×swap-sqr
252×unswap-sqr
236×frac-times
217×1-exp
211×rec-exp
187×pow-prod-down
166×difference-of-sqr-1
157×flip-+
156×flip3-+
152×flip--
151×flip3--
143×cbrt-div
127×associate-*l/
108×pow-prod-up
107×associate-*r/
106×tanh-def
100×log-prod
98×*-commutative
95×unpow-prod-down
94×fma-def
87×frac-2neg clear-num
82×pow1/3
73×sqrt-pow1
72×fma-udef
69×pow-flip
67×pow-plus pow1/2
63×sub-neg
60×pow-sqr
58×diff-log
55×distribute-rgt-in distribute-lft-in
52×cos-sum
50×associate-/l/
41×pow2
37×pow3
36×sqrt-div rem-sqrt-square
35×div-sub
33×sin-sum
32×inv-pow
26×sum-log
23×sqr-pow log-pow
22×frac-sub associate--l+
19×sin-diff
18×exp-prod tan-quot
16×+-commutative difference-cubes rem-log-exp frac-add
15×distribute-rgt-neg-in log-div
14×sin-mult
11×un-div-inv distribute-rgt-out
9×sin-cos-mult distribute-rgt-out-- distribute-lft-neg-in
8×pow-div cos-diff
7×cube-unmult acos-asin
6×pow-unpow pow-pow log1p-udef
5×cos-mult associate--r+ expm1-def
4×expm1-log1p neg-sub0 expm1-udef remove-posit16 log1p-expm1 asin-acos associate-+l-
3×distribute-rgt-neg-out neg-mul-1 hypot-udef rem-cbrt-cube
2×exp-diff associate--l- distribute-frac-neg exp-sum log-rec neg-log rem-exp-log acos-neg sqrt-unprod rem-square-sqrt
1×distribute-rgt1-in sin-asin unsub-neg tanh-undef sqr-sin sub-div sqr-cos

localize5.9s (0.4%)

bsearch4.3s (0.3%)

end2.0ms (0.0%)