Details

sample13.1m (58.2%)

Algorithm
78×intervals
Results
9.8m58314×body10240exit
1.3m44249×body1280valid
28.2s30259×body640valid
20.1s205630×body80valid
14.3s151601×body80nan
13.0s27754×body320valid
10.4s198409×pre80true
10.4s35976×body160valid
3.0s3037×body2560valid
978.0ms7845×body160nan
880.0ms4138×pre10240exit
225.0ms205×body5120valid
2.0ms2×body320nan
1.0ms1×body640nan

simplify5.9m (26.5%)

prune1.7m (7.7%)

series1.0m (4.6%)

Calls

466 calls:

1.5s
(* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b)))
1.4s
(* (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)))
1.0s
(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))))))))))

regimes20.6s (1.5%)

Accuracy

Total 53.8b remaining (31.4%)

Threshold costs 5.3b (3.1%)

7.6b45.6%Cubic critical, narrow range
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

rewrite12.9s (1.0%)

Algorithm
144×rewrite-expression-head
Calls

466 calls:

307.0ms
(/ (/ (+ (* (* (* 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))
303.0ms
(* (* (cbrt (+ (/ 1 (- x 1)) (/ x (+ x 1)))) (cbrt (+ (/ 1 (- x 1)) (/ x (+ x 1))))) (cbrt (+ (/ 1 (- x 1)) (/ x (+ x 1)))))
302.0ms
(* (- (- (/ m v) (/ (* m m) v)) 1) (- 1 m))
297.0ms
(/ (/ (+ (* (* (* 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
(/ (+ (* (* (* 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))))
Rules
12568×*-un-lft-identity
12082×times-frac
10293×add-sqr-sqrt
7309×add-cube-cbrt
5076×prod-diff
2785×add-exp-log
1533×distribute-lft-out
1485×add-cbrt-cube
1400×pow1
1334×difference-of-squares
1047×prod-exp
928×div-exp
822×div-inv
773×distribute-lft-out--
724×associate-/r/
693×pow-exp
647×add-log-exp
529×sqrt-prod
493×difference-of-sqr-1
492×associate-*r*
475×associate-/l*
471×expm1-log1p-u
467×log1p-expm1-u
466×insert-posit16
439×associate-*l*
437×cbrt-prod
431×flip-+
430×flip3-+
424×associate-/r*
378×frac-times
349×cbrt-unprod
346×pow-prod-down
345×pow-to-exp
299×cbrt-undiv
293×fma-neg
269×cbrt-div
268×unpow-prod-down
253×flip--
252×flip3--
235×sqrt-pow1
194×distribute-rgt-in distribute-lft-in
191×associate-*l/
186×fma-def
170×log-prod
167×associate-*r/
152×swap-sqr
138×unswap-sqr
136×1-exp
135×rec-exp
113×exp-prod
110×exp-sum *-commutative pow-prod-up
108×log-pow
106×sqrt-div tanh-def
103×frac-2neg clear-num
96×sub-neg
82×sqr-pow
77×pow1/2 associate-/l/
72×diff-log pow-sqr
65×frac-add
59×pow1/3
58×cos-sum
57×pow-plus
50×fma-udef
47×log-div
46×cube-unmult
43×div-sub
34×sin-mult
30×pow2
28×sum-log
26×associate--r+ rem-sqrt-square
24×distribute-rgt-neg-in tan-quot
22×sin-sum difference-cubes rem-log-exp
20×associate--l+ +-commutative
19×frac-sub pow-flip associate--r-
18×sin-diff
12×inv-pow distribute-lft-neg-in
11×cos-diff
9×pow3
8×neg-sub0 associate-+l- acos-asin
7×exp-diff sin-cos-mult expm1-def log1p-udef
6×pow-unpow log1p-expm1 pow-pow rem-exp-log distribute-rgt-out
5×associate--l- distribute-rgt-out--
4×expm1-log1p expm1-udef cos-mult associate-+r- neg-log neg-mul-1 hypot-def rem-cbrt-cube
3×sqrt-unprod log1p-def rem-square-sqrt
2×distribute-rgt1-in distribute-frac-neg hypot-1-def un-div-inv acos-neg
1×remove-posit16 tanh-undef exp-to-pow hypot-udef asin-acos sub-div

localize6.4s (0.5%)

bsearch1.1s (0.1%)

end1.0ms (0.0%)