Details

sample9.9m (77.2%)

Algorithm
78×intervals
Results
8.2m53198×body10240exit
36.1s43935×body1280valid
12.5s30504×body640valid
12.3s205708×body80valid
8.7s152819×body80nan
5.8s27636×body320valid
5.6s171899×pre80overflowed
4.4s35726×body160valid
874.0ms2973×body2560valid
626.0ms24768×pre80true
552.0ms8081×body160nan
197.0ms8251×pre80false
153.0ms244×body5120valid

prune1.4m (11.0%)

series43.7s (5.7%)

Calls

500 calls:

1.1s
(* (hypot (* (fma (cos (* phi2 0.5)) (cos (* phi1 0.5)) (- (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))) (- lambda1 lambda2)) (- phi1 phi2)) R)
1.1s
(* (hypot (* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
573.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
506.0ms
(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
491.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

rewrite14.5s (1.9%)

Algorithm
147×rewrite-expression-head
Calls

500 calls:

2.3s
(* (/ (/ a1 (cbrt b2)) (cbrt b2)) (/ (/ (* (cbrt a2) (cbrt a2)) (* (cbrt b1) (cbrt b1))) (/ (cbrt b2) (/ (cbrt a2) (cbrt b1)))))
1.7s
(- (- (/ (- 2.0) (pow x 6)) (/ (/ 2.0 x) x)) (/ 2.0 (pow x 4)))
537.0ms
(+ (+ (log 2) (log (sqrt x))) (- (- (log (sqrt x)) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
397.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
368.0ms
(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
Rules
27965×times-frac
20765×add-sqr-sqrt
20755×*-un-lft-identity
15683×add-cube-cbrt
9220×prod-diff
3685×associate--l+
2913×unpow-prod-down
2700×add-exp-log
2610×cbrt-prod
2225×associate-*r*
1990×sqrt-prod
1699×add-cbrt-cube
1678×distribute-rgt-neg-in
1542×distribute-lft-neg-in
1516×difference-of-squares
1354×distribute-lft-out--
1344×div-inv
1158×distribute-lft-out
1130×pow1
1040×sqr-pow
939×div-exp
886×associate-+r+
762×add-log-exp
759×prod-exp
708×associate-/r/
690×associate-/r*
688×fma-neg
651×associate-*l*
604×associate-/l*
560×cbrt-undiv
514×neg-mul-1
502×log1p-expm1-u expm1-log1p-u
400×cbrt-unprod
388×flip--
387×flip3--
384×fma-def
357×log-pow
350×unswap-sqr
344×pow-exp
332×log-prod
319×cube-prod
317×distribute-rgt-in distribute-lft-in
276×flip-+
275×flip3-+
257×pow-to-exp
171×unpow2
135×frac-times
133×pow-prod-down
120×swap-sqr
115×clear-num frac-2neg
110×cbrt-div sub-neg
106×associate-*r/
105×pow-unpow
93×unpow3 cube-mult
92×associate-*l/ exp-sum
88×*-commutative sqrt-pow1
86×sqrt-div
85×pow1/2
80×diff-log
77×associate-/l/
72×pow1/3
68×sum-log
57×log-div
51×exp-prod
49×cos-sum
46×div-sub
41×+-commutative pow-pow
39×associate-+l+
36×1-exp
35×neg-sub0
34×sin-sum
32×fma-udef sin-mult
31×rem-log-exp
29×rem-sqrt-square frac-sub
25×associate-+l-
24×rec-exp
23×pow-prod-up
22×neg-log
20×pow-flip
19×sin-diff
16×frac-add
15×rem-cube-cbrt pow-sqr
14×distribute-rgt-out
13×sin-cos-mult associate--l- pow-plus
12×cos-diff acos-asin cos-mult
11×inv-pow
10×associate-+r- distribute-frac-neg
9×pow2
8×sin-neg tan-quot distribute-rgt-neg-out
7×rem-exp-log associate--r+
6×acos-neg sub-div asin-acos associate--r-
5×exp-diff expm1-udef
4×cube-div exp-neg expm1-log1p log-rec
3×exp-to-pow
2×unsub-neg log1p-udef distribute-lft1-in log1p-expm1 hypot-udef hypot-def rem-cbrt-cube
1×sqrt-undiv sum-cubes sqrt-unprod pow3 distribute-neg-in rem-square-sqrt

simplify14.2s (1.8%)

Algorithm
225×egg-herbie

regimes11.0s (1.4%)

Accuracy

Total 32.5b remaining (25.5%)

Threshold costs 4.8b (3.8%)

5.8b58.9%Cubic critical, narrow range
5.0b28.8%Cubic critical, medium range
3.7b0%Cubic critical, wide range
3.4b84.8%Cubic critical
3.4b84.8%Quadratic roots, full range

bsearch4.6s (0.6%)

localize2.3s (0.3%)

end1.0ms (0.0%)