Details

sample6.6m (75.5%)

Algorithm
78×intervals
Results
5.2m38931×body10240exit
34.3s43788×body1280valid
11.4s30551×body640valid
7.1s204235×body80valid
4.7s153743×body80nan
4.6s28034×body320valid
3.0s177150×pre80true
3.0s35783×body160valid
741.0ms3059×body2560valid
383.0ms4105×pre10240exit
369.0ms7992×body160nan
122.0ms228×body5120valid
101.0ms7991×pre80false
2.0ms3×body640nan

prune52.2s (10.0%)

series41.1s (7.9%)

Calls

469 calls:

911.0ms
(pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)
748.0ms
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
744.0ms
(fma (* (cos delta) (cos delta)) (cos delta) (- (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
730.0ms
(fma (* (cos delta) (cos delta)) (cos delta) (- (cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3))))
713.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

simplify13.5s (2.6%)

Algorithm
224×egg-herbie

regimes9.7s (1.9%)

Accuracy

Total 34.4b remaining (29.5%)

Threshold costs 4.0b (3.5%)

5.7b58.4%Cubic critical, narrow range
5.2b27.5%Cubic critical, medium range
4.2b46.7%Quotient of products
4.0b85.8%Quadratic roots, full range
4.0b86.1%Cubic critical

rewrite8.4s (1.6%)

Algorithm
146×rewrite-expression-head
Calls

469 calls:

523.0ms
(* (- (/ 1 (/ (/ v (- 1.0 m)) m)) 1.0) m)
236.0ms
(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
235.0ms
(* (- (- (* 1.0 (/ m v)) (/ (pow m 2) v)) 1.0) m)
223.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)
207.0ms
(* (- (/ m (/ v (- 1.0 m))) 1.0) m)
Rules
11753×*-un-lft-identity
10679×times-frac
9985×add-sqr-sqrt
7527×add-cube-cbrt
4778×prod-diff
2683×add-exp-log
1738×sqrt-prod
1666×add-cbrt-cube
1219×distribute-lft-out
1079×difference-of-squares
995×pow1
918×unpow-prod-down
903×prod-exp
885×distribute-lft-out--
823×div-exp
797×fma-neg
791×log-prod
765×associate-*r*
729×add-log-exp
728×associate-/r/
622×distribute-rgt-neg-in
583×associate-/r*
562×associate-/l*
539×div-inv
504×distribute-lft-neg-in
490×exp-sum
471×log1p-expm1-u expm1-log1p-u
428×cube-prod
426×cbrt-unprod
425×associate-*l*
395×cbrt-undiv
375×pow-exp
363×sqr-pow
314×flip--
313×flip3--
273×pow-to-exp
272×flip-+
271×flip3-+
232×cbrt-prod
219×fma-def
179×pow-prod-down
176×distribute-rgt-in distribute-lft-in
168×neg-mul-1
164×unswap-sqr
147×sqrt-div unpow2
114×clear-num associate-*r/ frac-2neg
109×associate-+l+
97×sub-neg
92×log-pow
91×*-commutative exp-prod
86×frac-times
84×pow-unpow
83×unpow3 cube-mult
81×diff-log
80×associate-/l/
70×associate-*l/
60×tan-quot
58×cos-sum
53×1-exp
52×pow-prod-up
48×div-sub sum-log associate--l+
42×cbrt-div
39×sqrt-pow1
38×pow-sqr rec-exp pow-pow
36×pow1/3
34×+-commutative log-div
33×pow1/2 rem-sqrt-square neg-sub0 sin-mult
29×fma-udef distribute-rgt-out cos-mult
28×pow-plus swap-sqr
23×sin-sum pow2
21×associate-+l- rem-log-exp
20×neg-log
18×sin-diff
17×associate--l- cos-diff
15×sin-cos-mult
14×difference-cubes frac-sub
13×rem-cube-cbrt exp-to-pow
12×cube-div
10×associate-+r+
9×frac-add distribute-frac-neg
8×pow-flip
7×inv-pow acos-asin sub-div associate--r+
6×rem-exp-log distribute-lft-neg-out distribute-rgt-out-- distribute-rgt-neg-out expm1-udef associate-+r-
4×log1p-udef log1p-expm1 expm1-log1p asin-acos associate--r-
3×exp-diff acos-neg un-div-inv hypot-udef unsub-neg
2×sin-neg distribute-lft1-in hypot-def rem-cbrt-cube
1×sub0-neg

localize2.3s (0.4%)

bsearch798.0ms (0.2%)

end1.0ms (0.0%)