Details

simplify10.7m (49.4%)

sample5.4m (25.0%)

Algorithm
77×intervals
Results
1.7m43686×body1280valid
1.0m16967×body10240exit
44.7s30936×body640valid
29.1s202459×body80valid
20.8s152242×body80nan
19.3s27563×body320valid
13.6s35614×body160valid
9.5s153452×pre80true
2.7s3117×body2560valid
2.0s8018×body160nan
923.0ms4122×pre10240exit
303.0ms228×body5120valid

prune4.0m (18.2%)

series53.9s (4.1%)

Calls

437 calls:

1.7s
(/ (fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b))) (fma b (sqrt (fma -3 (* a c) (* b b))) (expm1 (log1p (+ (* b b) (fma -3 (* a c) (* b b)))))))
1.7s
(/ (/ (fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b))) (fma b (sqrt (fma -3 (* a c) (* b b))) (expm1 (log1p (+ (* b b) (fma -3 (* a c) (* b b))))))) (* 3 a))
1.5s
(* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))))
1.4s
(- (* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b)))) (* (* b b) b))
938.0ms
(fma (- (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (sin phi1)) (* (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))) (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (sin phi1))))

regimes20.7s (1.6%)

Accuracy

Total 49.5b remaining (27.4%)

Threshold costs 5.3b (3%)

7.3b48.7%Quadratic roots, narrow range
5.5b43.4%Quotient of products
5.0b29.3%Quadratic roots, medium range
4.8b29.9%Cubic critical, medium range
4.3b84.7%Quadratic roots, full range

rewrite15.0s (1.1%)

Algorithm
140×rewrite-expression-head
Calls

437 calls:

5.2s
(cbrt (* (* (* (* (* (sin lambda1) (* (sin lambda2) (sin phi1))) (cos phi2)) (* (* (sin lambda1) (* (sin lambda2) (sin phi1))) (cos phi2))) (* (sin lambda1) (* (sin lambda2) (sin phi1)))) (cos phi2)))
430.0ms
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)
424.0ms
(* b (/ b a))
390.0ms
(cbrt (* (* (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
263.0ms
(cbrt (* (* (fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
Rules
12964×*-un-lft-identity
11134×times-frac
10433×add-sqr-sqrt
7049×add-cube-cbrt
5093×prod-diff
1830×distribute-lft-out
1497×difference-of-squares
1448×add-exp-log
1310×add-cbrt-cube
1163×sqrt-prod
895×pow1
867×associate-/r/
837×distribute-lft-out--
722×div-inv
696×associate-*r*
608×add-log-exp
576×cbrt-prod
531×difference-of-sqr-1
443×expm1-log1p-u
439×log1p-expm1-u
437×insert-posit16 associate-/r*
399×associate-/l*
357×associate-*l*
354×fma-neg
341×flip-+
340×flip3-+
336×div-exp
335×flip--
334×flip3--
315×prod-exp
296×cbrt-unprod
280×cbrt-undiv
187×fma-def
172×pow-prod-down
163×frac-times
151×unswap-sqr
146×cbrt-div
145×swap-sqr
134×associate-*r/
106×associate-*l/
105×distribute-rgt-in distribute-lft-in
98×log-prod
91×frac-2neg clear-num
86×*-commutative
75×frac-sub
73×sub-neg
59×cos-sum associate-/l/
58×pow1/3
53×diff-log
46×fma-udef
44×log-pow
41×div-sub
39×sin-mult
38×distribute-rgt-neg-in
35×sum-log pow-prod-up
34×sqrt-div
33×exp-prod
32×sqrt-pow1 pow1/2
31×rem-sqrt-square
29×pow-plus
27×pow3 tan-quot
24×+-commutative distribute-lft-neg-in
23×1-exp rec-exp
22×pow-flip sin-sum
21×cos-mult pow-sqr
19×associate--l+
18×sin-diff frac-add log-div
16×pow2
13×exp-sum rem-log-exp cos-diff
12×associate-+l-
11×associate-+l+ neg-sub0 difference-cubes
10×sin-cos-mult acos-asin expm1-def log1p-udef
9×log1p-expm1 inv-pow
8×expm1-log1p expm1-udef neg-log associate--r+ neg-mul-1 asin-acos
7×associate-+r+
6×distribute-rgt-out
5×sqrt-undiv
4×acos-neg
3×exp-diff associate--l- distribute-frac-neg sub-div rem-exp-log
2×distribute-rgt1-in log1p-def hypot-udef sqr-cos associate--r-
1×remove-posit16 sqrt-unprod tanh-def tanh-undef un-div-inv exp-to-pow rem-square-sqrt rem-cbrt-cube

localize5.9s (0.5%)

bsearch1.2s (0.1%)

end1.0ms (0.0%)