Details

sample8.1m (59.0%)

Algorithm
78×intervals
Results
4.0m30335×body10240exit
1.6m43701×body1280valid
39.5s30705×body640valid
29.7s203130×body80valid
19.7s151125×body80nan
15.9s27262×body320valid
15.0s36157×body160valid
9.9s167372×pre80true
3.2s3107×body2560valid
1.2s7849×body160nan
1.1s4077×pre10240exit
323.0ms252×body5120valid
3.0ms2×body640nan
2.0ms1×body320nan

simplify2.6m (19.2%)

prune1.5m (10.9%)

series53.4s (6.5%)

Calls

425 calls:

1.7s
(- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b)))
1.5s
(* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b)))
754.0ms
(/ (sqrt m) (/ v (cbrt (- 1 m))))
703.0ms
(/ (/ (- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (* b b) (fma (* a c) -3 (* b b))))) (* 3 a))
614.0ms
(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

regimes19.2s (2.3%)

Accuracy

Total 47.3b remaining (25.4%)

Threshold costs 3.9b (2.1%)

7.3b45.5%Quadratic roots, narrow range
6.2b11.9%Quadratic roots, medium range
4.9b50.9%Quotient of products
4.7b31.9%Cubic critical, medium range
4.5b83.4%Quadratic roots, full range

rewrite10.6s (1.3%)

Algorithm
137×rewrite-expression-head
Calls

425 calls:

441.0ms
(cbrt (* (* (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
347.0ms
(* (/ 2 (+ (exp (fma x 2 x)) (exp (- (fma x 2 x))))) (+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x))))))
313.0ms
(/ (/ (+ (* (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 (+ (* b b) (fma (* a c) -3 (* b b))))) (* 3 a))
288.0ms
(* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
230.0ms
(* (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (/ 1 (- x 1)) (/ x (+ x 1))))
Rules
10809×*-un-lft-identity
9082×times-frac
8781×add-sqr-sqrt
5853×add-cube-cbrt
3906×prod-diff
2775×add-exp-log
1405×difference-of-squares
1390×add-cbrt-cube
1379×distribute-lft-out
1106×prod-exp
1005×pow1
922×div-exp
773×distribute-lft-out--
725×associate-/r/
721×sqrt-prod
714×cbrt-prod
695×pow-exp
616×add-log-exp
611×associate-*l*
530×div-inv
433×expm1-log1p-u
430×associate-*r*
428×log1p-expm1-u
425×insert-posit16
421×difference-of-sqr-1
380×cbrt-unprod
364×associate-/r*
358×fma-neg
346×pow-to-exp
334×associate-/l*
311×flip--
310×flip3--
279×cbrt-undiv
276×flip-+
275×flip3-+
236×pow-prod-down
204×fma-def
197×exp-prod
167×frac-times
160×log-prod
156×cbrt-div
145×1-exp
144×rec-exp
131×associate-*r/ unswap-sqr
112×associate-*l/
110×log-pow
102×*-commutative
96×frac-sub
86×swap-sqr
78×frac-2neg clear-num
74×sub-neg
72×distribute-rgt-in distribute-lft-in
68×exp-neg
65×pow-prod-up
64×diff-log
60×cos-sum
55×distribute-rgt-neg-in
54×neg-sub0
53×pow1/3
52×associate-/l/
48×exp-diff
43×unpow-prod-down
42×sqrt-pow1 div-sub
41×distribute-lft-neg-in
40×fma-udef
39×sum-log pow1/2
37×pow-sqr
35×pow-plus
27×rem-sqrt-square log-div
26×sqrt-div sin-mult
25×cube-unmult cos-diff
24×pow-flip rem-log-exp tan-quot
23×un-div-inv
22×sin-sum
21×pow2 +-commutative
19×sub-div
17×inv-pow
16×unpow-prod-up exp-sum associate--l+ frac-add
15×neg-mul-1
13×log1p-udef
12×cos-mult pow-unpow sin-cos-mult
11×difference-cubes log1p-expm1 associate--r+
10×acos-asin expm1-def
9×associate-+l-
8×associate--r-
7×expm1-log1p expm1-udef pow-pow
6×associate-+r+ neg-log sin-diff
5×pow3 log-rec sqr-pow
4×distribute-frac-neg rem-exp-log acos-neg
3×asin-acos
2×distribute-lft-neg-out hypot-udef distribute-rgt-out-- rem-cbrt-cube distribute-rgt-out
1×associate-+l+ associate--l- rgt-mult-inverse associate-+r- sqrt-unprod tanh-def tanh-undef rem-square-sqrt remove-posit16 e-exp-1 pow-sub

localize6.0s (0.7%)

bsearch918.0ms (0.1%)

end1.0ms (0.0%)