Details

sample3.7m (63.0%)

Algorithm
78×intervals
Results
1.7m11206×body10240exit
40.1s43523×body1280valid
16.2s203931×body80valid
15.0s30398×body640valid
11.6s153118×body80nan
7.8s27475×body320valid
6.4s36066×body160valid
5.5s180253×pre80true
3.6s25757×body80overflowed
1.4s2989×body2560valid
852.0ms7980×body160nan
192.0ms8316×pre80false
134.0ms198×body5120valid
1.0ms1×body640nan

prune51.4s (14.6%)

series45.9s (13.0%)

Calls

477 calls:

3.1s
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (/ (+ (pow b (/ 6 2)) (pow (* (* 4.0 a) c) (/ 3 2))) (sqrt (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))) (/ (- (pow b (/ 6 2)) (pow (* (* 4.0 a) c) (/ 3 2))) (sqrt (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4))))))))
568.0ms
(/ (* (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)))
549.0ms
(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
533.0ms
(+ (log (/ 1 (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
513.0ms
(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)))

simplify12.7s (3.6%)

Algorithm
225×egg-herbie

regimes9.5s (2.7%)

Accuracy

Total 34.4b remaining (26.3%)

Threshold costs 5.1b (3.9%)

6.7b38.3%Quotient of products
5.7b59.3%Cubic critical, narrow range
5.1b27.6%Cubic critical, medium range
4.4b83.4%Quadratic roots, full range
2.9b13.1%Cubic critical, wide range

rewrite7.7s (2.2%)

Algorithm
147×rewrite-expression-head
Calls

477 calls:

563.0ms
(* (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (/ (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
271.0ms
(/ (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
132.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
130.0ms
(exp (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))
109.0ms
(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
Rules
11403×*-un-lft-identity
8787×times-frac
7534×add-sqr-sqrt
5446×add-cube-cbrt
2759×prod-diff
2637×add-exp-log
1790×add-cbrt-cube
1679×distribute-lft-out
1446×pow1
1158×distribute-lft-out--
1020×associate-*r*
887×difference-of-squares
881×prod-exp
808×unpow-prod-down
773×div-exp
770×sqrt-prod
688×add-log-exp
615×associate-/l*
566×associate-/r/
536×associate-/r*
503×distribute-rgt-neg-in
484×cbrt-unprod
482×log1p-expm1-u expm1-log1p-u
466×pow-prod-down
441×flip--
440×flip3--
427×div-inv
425×associate-*l*
403×fma-neg
390×distribute-lft-neg-in
384×cbrt-undiv
319×pow-exp
300×sqr-pow
253×frac-times log-prod
239×cbrt-prod
231×pow-to-exp
225×flip-+
224×flip3-+
206×fma-def
197×cbrt-div
191×associate-*r/
164×cube-prod
157×unswap-sqr
133×associate-*l/
131×associate-/l/
130×neg-mul-1
123×cos-sum clear-num frac-2neg
114×log-pow
108×distribute-rgt-in distribute-lft-in
106×sub-neg
95×pow-unpow
93×swap-sqr
88×*-commutative
87×exp-prod
81×sqrt-div
69×diff-log
58×sqrt-pow1
57×div-sub
56×sin-sum
53×pow-sqr pow-prod-up
50×log-div
47×associate-+l+ 1-exp
45×exp-sum
44×sum-log
40×pow1/2
38×unpow3 pow1/3 cube-mult rec-exp frac-sub
36×unpow2
30×+-commutative
29×rem-sqrt-square fma-udef associate-+r+
28×neg-sub0
27×associate--l+ pow-pow
25×cos-diff cos-mult
24×rem-log-exp
22×pow-plus
20×pow-flip sin-mult
18×exp-diff associate-+l- associate--r+ sin-diff
16×tan-quot neg-log
15×sin-cos-mult
14×associate--l-
13×distribute-rgt-out
12×pow2 frac-add acos-asin
11×expm1-udef
9×distribute-frac-neg inv-pow expm1-log1p
8×rem-exp-log associate-+r-
7×log1p-udef log1p-expm1 associate--r-
6×acos-neg sub-div
4×rem-cube-cbrt hypot-def rem-cbrt-cube
3×un-div-inv sub0-neg distribute-rgt-neg-out
2×distribute-lft1-in hypot-udef asin-acos
1×sqrt-undiv sin-neg distribute-lft-neg-out unsub-neg sqrt-unprod

localize2.3s (0.6%)

bsearch1.1s (0.3%)

end1.0ms (0.0%)