Details

sample13.5m (41.4%)

Algorithm
78×intervals
Results
9.3m53187×body10240exit
1.7m43348×body1280valid
40.7s30046×body640valid
27.8s204660×body80valid
19.7s27977×body320valid
18.1s151476×body80nan
13.1s193131×pre80true
12.1s36418×body160valid
2.8s3030×body2560valid
2.0s7980×body160nan
886.0ms4130×pre10240exit
360.0ms213×body5120valid
2.0ms1×body640nan

simplify8.7m (26.7%)

prune7.8m (23.8%)

rewrite1.2m (3.7%)

Algorithm
145×rewrite-expression-head
Calls

464 calls:

3.4s
(* (cbrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (cbrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))
2.2s
(* (- (* (* m (- 1 m)) (/ 1 v)) 1) m)
2.2s
(+ (- (/ (- m (* m m)) v) 1) (* (- (/ (- m (* m m)) v) 1) (- m)))
2.1s
(log (+ (/ -1/2 x) (- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))))
1.8s
(/ (* (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)))
Rules
157875×add-sqr-sqrt
130904×associate-/l*
121422×frac-add
117623×*-un-lft-identity
112868×cbrt-div
70030×add-cube-cbrt
66664×sqrt-prod
64656×associate-/r*
57917×frac-times
46552×difference-of-squares
43809×times-frac
19364×clear-num
19336×frac-2neg
18951×unswap-sqr
18897×associate-*l*
14924×swap-sqr
13301×associate-*r*
12800×*-commutative
12084×associate-/l/
11198×prod-diff
10518×frac-sub
10255×distribute-lft-out--
9236×log-div
8701×unpow-prod-down
8644×sqrt-div
4710×flip--
4709×flip3--
3311×pow1
3235×add-exp-log
2501×distribute-lft-out
2393×sqr-pow
1902×cbrt-prod
1708×add-cbrt-cube
1397×div-inv
1333×prod-exp
1184×associate-/r/
1077×flip-+
1076×flip3-+
1024×div-exp
827×pow-prod-up
803×associate-*r/
698×pow-exp
690×associate-*l/
654×add-log-exp
606×fma-neg
602×pow-prod-down
539×log-pow
493×cbrt-unprod
472×expm1-log1p-u
470×log1p-expm1-u
466×distribute-rgt-out--
464×insert-posit16
403×pow-flip
352×pow-plus
350×pow-to-exp
348×cbrt-undiv
345×pow-sqr
283×log-prod
274×distribute-rgt-neg-in
273×difference-of-sqr-1
220×pow2
215×distribute-lft-neg-in
209×distribute-lft-in distribute-rgt-in
200×associate--l+
175×1-exp rec-exp
173×associate-+l+
169×fma-def
83×sqrt-pow1 sub-neg
74×exp-sum fma-udef
64×cos-sum
63×pow1/3
62×diff-log
60×un-div-inv
57×pow1/2
50×+-commutative
45×neg-mul-1 div-sub
40×sum-log
33×pow3 distribute-rgt-out
32×rem-log-exp
30×rem-sqrt-square
26×exp-prod associate--r+
24×tan-quot
22×sin-sum
17×sin-diff
16×inv-pow
14×associate-+r+
13×cos-diff
12×log-rec
11×exp-diff log1p-expm1
10×neg-sub0 distribute-rgt1-in cube-unmult asin-acos associate-+l-
9×expm1-log1p pow-unpow acos-asin log1p-udef
8×associate--r- sin-mult
7×pow-pow rem-exp-log log1p-def rem-cbrt-cube
6×expm1-udef sin-cos-mult
5×distribute-frac-neg
4×cos-mult neg-log distribute-neg-frac expm1-def
3×distribute-rgt-neg-out hypot-udef acos-neg
2×remove-double-div sqrt-unprod associate--l- rem-square-sqrt
1×associate-+r- unsub-neg tanh-undef tanh-def

series52.5s (2.7%)

Calls

464 calls:

1.0s
(fma (cos phi1) (* (cos phi1) (cos phi1)) (* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (* (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))) (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1)))))))
766.0ms
(hypot (* (cos (/ (+ phi2 phi1) 2)) (- lambda1 lambda2)) (- phi1 phi2))
706.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
635.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
583.0ms
(expm1 (log1p (cbrt (* 3 a))))

regimes22.1s (1.1%)

Accuracy

Total 50.1b remaining (23.2%)

Threshold costs 4.7b (2.2%)

7.5b45.5%Quadratic roots, narrow range
5.8b57.2%Cubic critical, narrow range
5.3b80.8%Cubic critical
5.2b80.9%Quadratic roots, full range
4.8b27.9%Cubic critical, medium range

localize6.1s (0.3%)

bsearch4.5s (0.2%)

end1.0ms (0.0%)