Details

sample14.0m (59.7%)

Algorithm
78×intervals
Results
9.8m57214×body10240exit
1.7m44249×body1280valid
38.2s30259×body640valid
28.7s205535×body80valid
20.5s151601×body80nan
18.8s27753×body320valid
12.4s35976×body160valid
11.3s197212×pre80true
3.2s3036×body2560valid
1.5s7845×body160nan
881.0ms4138×pre10240exit
308.0ms205×body5120valid
2.0msbody320nan
1.0msbody640nan

simplify6.0m (25.6%)

prune1.7m (7.3%)

series1.0m (4.4%)

Calls

468 calls:

1.5s
(* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b)))
1.3s
(sqrt (* (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta)))))) (expm1 (log1p (* (sin phi1) (sin (asin (fma (* (cos phi1) (sin delta)) (cos theta) (* (sin phi1) (cos delta))))))))))
1.3s
(* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b)))
1.3s
(- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b)))
1.1s
(- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b)))

regimes21.0s (1.5%)

Accuracy

Total 48.4b remaining (27.2%)

Threshold costs 5.2b (2.9%)

7.6b-7.1%Cubic critical, medium range
5.6b58.6%Quadratic roots, narrow range
5.4b50.2%Quotient of products
5.2b24%Quadratic roots, medium range
4.6b83.5%Quadratic roots, full range

rewrite13.6s (1.0%)

Algorithm
144×rewrite-expression-head
Calls

468 calls:

377.0ms
(* (cbrt (+ (/ 1 (- x 1)) (/ x (+ x 1)))) (* (cbrt (+ (/ 1 (- x 1)) (/ x (+ x 1)))) (cbrt (+ (/ 1 (- x 1)) (/ x (+ x 1))))))
316.0ms
(* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
275.0ms
(/ (/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (- (* (* b b) (sqrt (fma (* a c) -3 (* b b)))) (* b (* b b)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b)))) (* 3 a))
275.0ms
(/ (+ (* (sqrt (fma (* a c) -3 (* b b))) (* (* a c) -3)) (- (* (sqrt (fma (* a c) -3 (* b b))) (* b b)) (* b (* b b)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b))))
269.0ms
(/ (/ (+ (* (sqrt (fma (* a c) -3 (* b b))) (* (* a c) -3)) (- (* (sqrt (fma (* a c) -3 (* b b))) (* b b)) (* b (* b b)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b)))) (* 3 a))
Rules
11622×*-un-lft-identity
9862×times-frac
9251×add-sqr-sqrt
6553×add-cube-cbrt
4869×prod-diff
2788×add-exp-log
1509×distribute-lft-out
1492×add-cbrt-cube
1396×pow1
1340×exp-sum
1191×difference-of-squares
1047×prod-exp
926×div-exp
791×log-prod
768×associate-/r/
735×distribute-lft-out--
717×div-inv
693×pow-exp
659×add-log-exp
526×sqrt-prod
481×associate-*r*
473×expm1-log1p-u
470×associate-/l*
469×log1p-expm1-u
468×insert-posit16
463×associate-*l*
434×associate-/r*
417×difference-of-sqr-1
410×flip-+
409×flip3-+
407×cbrt-prod
382×frac-times
349×cbrt-unprod
345×pow-prod-down pow-to-exp
301×flip--
300×flip3--
299×cbrt-undiv
294×fma-neg
268×unpow-prod-down
253×cbrt-div
239×distribute-rgt-in distribute-lft-in
235×sqrt-pow1
213×fma-def
185×associate-*r/
175×associate-*l/
151×exp-prod
143×swap-sqr
138×unswap-sqr
135×1-exp rec-exp
129×log-pow
113×*-commutative
107×pow-prod-up
106×sqrt-div tanh-def
105×frac-2neg clear-num
103×sub-neg
82×sqr-pow
80×associate-/l/
77×pow1/2
74×diff-log
69×pow-sqr
66×frac-add
60×cos-sum
52×fma-udef
51×pow-plus
50×pow1/3
48×log-div
47×cube-unmult sin-mult
45×div-sub
33×distribute-rgt-neg-in
30×sum-log
28×pow2
26×associate--r+ rem-sqrt-square
24×rem-log-exp tan-quot
23×frac-sub
22×sin-sum difference-cubes
21×+-commutative
20×associate--l+
19×pow-flip associate--r-
18×sin-diff
12×inv-pow distribute-lft-neg-in
11×cos-mult cos-diff
neg-sub0 exp-diff rem-exp-log acos-asin
associate-+l-
sin-cos-mult pow3 expm1-def log1p-udef
pow-unpow log1p-expm1 pow-pow distribute-rgt-out-- distribute-rgt-out
associate--l- associate-+r- neg-log sub-div
expm1-log1p expm1-udef neg-mul-1 hypot-def
distribute-frac-neg sqrt-unprod acos-neg log1p-def rem-square-sqrt rem-cbrt-cube
distribute-rgt1-in hypot-1-def un-div-inv
remove-posit16 exp-to-pow distribute-neg-frac hypot-udef asin-acos tanh-undef unsub-neg

localize6.4s (0.5%)

bsearch1.1s (0.1%)

end1.0ms (0.0%)