Details

sample1.5m (39.7%)

Algorithm
77×intervals
Results
34.9s43745×body1280valid
11.1s30104×body640valid
7.2s202043×body80valid
5.9s13664×body10240exit
4.7s152995×body80nan
4.6s27656×body320valid
3.1s36316×body160valid
2.6s150510×pre80true
794.0ms3110×body2560valid
420.0ms4160×pre10240exit
375.0ms8112×body160nan
98.0ms8388×pre80false
56.0ms210×body5120valid

prune58.0s (26.4%)

series40.1s (18.3%)

Calls

465 calls:

652.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
611.0ms
(/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (pow (- (* b b) (* (* 4.0 a) c)) 1/2))))
513.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (pow (- (* b b) (* (* 4.0 a) c)) 1/2)))) (* 2.0 a))
494.0ms
(/ (+ (pow (/ 1.0 (- x 1.0)) 3) (pow (/ x (+ x 1.0)) 3)) (fma (/ x (+ x 1.0)) (- (/ x (+ x 1.0)) (/ 1.0 (- x 1.0))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))))
452.0ms
(* (pow (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) 1) R)

simplify13.2s (6.0%)

Algorithm
219×egg-herbie

rewrite9.6s (4.4%)

Algorithm
143×rewrite-expression-head
Calls

465 calls:

835.0ms
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))
422.0ms
(* (sqrt (* (- (/ m (/ v (- 1.0 m))) 1.0) (- 1.0 m))) (sqrt (* (- (/ m (/ v (- 1.0 m))) 1.0) (- 1.0 m))))
407.0ms
(/ (+ (pow (/ 1.0 (- x 1.0)) 3) (pow (/ x (+ x 1.0)) 3)) (fma (/ x (+ x 1.0)) (- (/ x (+ x 1.0)) (/ 1.0 (- x 1.0))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))))
208.0ms
(* (- (/ m (/ v (- 1.0 m))) 1.0) (- 1.0 m))
204.0ms
(* (- (/ m (/ v (- 1.0 m))) 1.0) (- 1.0 m))
Rules
13371×times-frac
12473×*-un-lft-identity
11893×add-sqr-sqrt
8737×add-cube-cbrt
5460×prod-diff
2111×add-exp-log
1740×add-cbrt-cube
1646×sqrt-prod
1567×unpow-prod-down
1196×associate-*r*
1164×distribute-rgt-neg-in
1154×difference-of-squares
1127×associate--l+
1010×pow1
987×distribute-lft-neg-in
896×distribute-lft-out
834×distribute-lft-out--
723×div-inv
718×add-log-exp
635×associate-/l*
588×div-exp
549×cube-prod
548×associate-/r/
540×sqr-pow
536×prod-exp
515×associate-*l*
468×expm1-log1p-u
467×fma-neg
466×log1p-expm1-u
428×cbrt-prod
425×associate-/r*
417×flip--
416×flip3--
413×cbrt-undiv
412×cbrt-unprod
389×unpow2
328×neg-mul-1
324×log-prod
288×sqrt-div
262×fma-def frac-times
258×flip-+
257×flip3-+
217×unswap-sqr
199×pow-prod-down
184×associate-*r/
182×distribute-rgt-in distribute-lft-in
153×associate-*l/
144×swap-sqr
114×unpow3 cube-mult
109×clear-num frac-2neg
108×*-commutative
101×associate-/l/
95×sub-neg
92×log-pow
79×diff-log
77×sqrt-pow1
69×associate-+r+
58×cos-sum
56×sum-log
55×frac-add
53×pow1/2
51×pow-unpow
48×1-exp
47×rec-exp
45×sin-sum div-sub
42×cbrt-div
41×pow-exp
40×log-div
39×associate-+l+ pow1/3
38×pow-to-exp
36×+-commutative
33×neg-sub0
32×frac-sub
28×tan-quot rem-log-exp
27×associate-+l-
26×rem-sqrt-square exp-prod pow-prod-up
23×neg-log
22×pow-sqr pow-flip
21×cos-diff
18×sin-diff
17×fma-udef sin-mult
16×associate--l- pow2 pow-plus
15×sin-cos-mult
13×pow-pow
12×distribute-rgt-out
11×associate-+r-
10×cube-div
9×acos-asin
8×rem-cube-cbrt
7×cos-mult
6×inv-pow distribute-frac-neg
5×acos-neg associate--r+
4×sum-cubes log1p-udef log1p-expm1 rem-exp-log distribute-rgt-neg-out
3×sin-neg hypot-udef exp-sum rem-cbrt-cube exp-to-pow
2×un-div-inv distribute-lft1-in sqrt-unprod expm1-udef asin-acos associate--r-
1×distribute-lft-neg-out expm1-log1p rem-square-sqrt hypot-def sub-div

regimes8.8s (4.0%)

Accuracy

Total 34.0b remaining (26.2%)

Threshold costs 5.7b (4.4%)

5.6b58.6%Cubic critical, narrow range
5.5b51.9%Quotient of products
4.7b34.9%Cubic critical, medium range
4.6b84.2%Cubic critical
3.5b0%Cubic critical, wide range

localize2.2s (1.0%)

bsearch579.0ms (0.3%)

end1.0ms (0.0%)