Details

simplify12.1m (45.4%)

sample7.5m (28.0%)

Algorithm
78×intervals
Results
3.1m25814×body10240exit
1.8m44166×body1280valid
41.2s30015×body640valid
28.4s202470×body80valid
20.6s152484×body80nan
18.6s27642×body320valid
13.6s36258×body160valid
11.3s162500×pre80true
3.2s3133×body2560valid
1.8s7984×body160nan
847.0ms4071×pre10240exit
269.0ms246×body5120valid

prune5.6m (20.8%)

series56.9s (3.5%)

Calls

461 calls:

1.5s
(* (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))
1.0s
(- (pow (cos delta) 3) (pow (log1p (expm1 (* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))) (sin phi1)))) 3))
865.0ms
(* (cbrt (fma (pow x 5) 2/15 x)) (cbrt (fma (pow x 5) 2/15 x)))
843.0ms
(cbrt (fma (pow x 5) 2/15 x))

regimes18.3s (1.1%)

Accuracy

Total 49.2b remaining (25.9%)

Threshold costs 5.2b (2.7%)

7.2b46.8%Quadratic roots, narrow range
5.8b48.4%Quotient of products
5.2b19.4%Quadratic roots, medium range
5.0b21.5%Cubic critical, medium range
4.3b84.4%Quadratic roots, full range

rewrite11.1s (0.7%)

Algorithm
147×rewrite-expression-head
Calls

461 calls:

385.0ms
(/ (* (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)))
231.0ms
(* (* (/ -2 b) (/ c 1)) (* (* (/ -2 b) (/ c 1)) (* (/ -2 b) (/ c 1))))
221.0ms
(* (* (* (/ -1/2 b) c) (* (/ -1/2 b) c)) (* (/ -1/2 b) c))
205.0ms
(cbrt (* (* (/ -2 b) (/ c 1)) (* (* (/ -2 b) (/ c 1)) (* (/ -2 b) (/ c 1)))))
193.0ms
(* (+ (sqrt (/ m (/ v m))) (sqrt (fma (/ m (/ v m)) m m))) (- (sqrt (/ m (/ v m))) (sqrt (fma (/ m (/ v m)) m m))))
Rules
35070×times-frac
25843×add-sqr-sqrt
24840×*-un-lft-identity
15018×add-cube-cbrt
5927×add-exp-log
5175×difference-of-squares
5145×prod-diff
2880×prod-exp
2788×add-cbrt-cube
2766×sqrt-prod
2618×distribute-lft-out--
2382×difference-of-sqr-1
2143×div-exp
1622×associate-/r/
1413×pow1
1241×div-inv
1086×cbrt-unprod
1051×distribute-rgt-in distribute-lft-in
1045×distribute-lft-out
736×flip--
735×flip3--
698×associate-*l*
693×pow-exp
684×cbrt-undiv
637×associate-/r*
632×add-log-exp
603×associate-/l*
588×associate-*r*
467×1-exp
465×expm1-log1p-u
464×log1p-expm1-u
461×insert-posit16
444×frac-times
427×distribute-rgt-neg-in
417×distribute-lft-neg-in
347×pow-prod-down
345×pow-to-exp
331×fma-neg
324×flip-+
323×flip3-+
292×associate-*l/
288×unpow-prod-down
280×associate-*r/
267×cbrt-prod
252×cube-prod
219×swap-sqr
213×log-prod
175×unswap-sqr
170×sqrt-div
166×pow-prod-up
141×rec-exp
139×neg-mul-1
116×sqrt-pow1
115×fma-def
111×*-commutative
105×associate-/l/
94×sqr-pow
93×cbrt-div
92×frac-2neg clear-num pow1/2
87×sub-neg
75×cube-mult
74×unpow3
69×pow-plus
63×pow-sqr
62×diff-log
58×cos-sum fma-udef
48×pow1/3 log-pow
44×div-sub
43×rem-sqrt-square associate--l+
30×sum-log
29×pow3 pow2
27×frac-sub
26×associate-+r+ log-div
25×rem-log-exp
24×tan-quot
22×associate-+l+ sin-sum
20×pow-flip
18×sin-diff exp-prod
16×+-commutative
15×sin-cos-mult
14×inv-pow
13×difference-cubes sin-mult
11×sqrt-undiv
10×associate--r+ acos-asin pow-div expm1-def distribute-rgt-out
9×pow-unpow cos-diff log1p-udef
8×associate-+l-
7×neg-sub0 pow-pow
6×log1p-expm1 sqrt-unprod asin-acos log1p-def
4×expm1-log1p expm1-udef cos-mult distribute-frac-neg cube-unmult neg-log acos-neg frac-add
3×distribute-rgt1-in log-rec associate-+r- exp-to-pow hypot-udef rem-exp-log rem-cbrt-cube
2×exp-diff exp-sum rem-square-sqrt associate--r-
1×remove-posit16 associate--l- rem-cube-cbrt tanh-undef tanh-def un-div-inv hypot-def

localize5.9s (0.4%)

bsearch1.5s (0.1%)

end1.0ms (0.0%)