Details

sample1.8m (53.3%)

Algorithm
56×intervals
16×halfpoints
Results
24.9s67332×body1280valid
16.9s17224×body2560valid
8.5s43029×body640valid
3.9s13079×body10240exit
2.9s93199×body80valid
2.6s20577×body320valid
1.7s62973×body80nan
849.0ms10367×body160valid
567.0ms47421×pre80true
295.0ms642×body1280nan
238.0ms707×body640nan
133.0ms425×body5120valid
62.0ms321×body320nan
20.0ms180×body160nan

series36.5s (17.8%)

Calls

387 calls:

811.0ms
(expm1 (log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
729.0ms
(/ (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (sin x))) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
609.0ms
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (/ (* (* (tan x) (tan eps)) (* (tan x) (sin eps))) (cos eps)))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))
560.0ms
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))
525.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))

prune36.3s (17.7%)

simplify10.8s (5.3%)

Algorithm
193×egg-herbie

rewrite5.2s (2.5%)

Algorithm
121×rewrite-expression-head
Calls

387 calls:

228.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
198.0ms
(- (exp (* a x)) 1.0)
104.0ms
(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
82.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
68.0ms
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))
Rules
8445×*-un-lft-identity
7177×add-sqr-sqrt
6166×times-frac
5492×add-cube-cbrt
3846×prod-diff
2237×sqrt-prod
1312×unpow-prod-down
1099×add-exp-log
1067×distribute-lft-out
811×add-cbrt-cube
776×cube-prod
671×associate-*r*
661×pow1
639×add-log-exp
638×difference-of-squares
542×sqr-pow
479×log-prod
477×distribute-lft-out--
440×fma-neg
422×associate-/l*
385×associate-*l*
375×log1p-expm1-u
374×exp-sum
373×expm1-log1p-u
357×cbrt-prod
319×div-inv
289×associate-/r/
288×associate-/r*
265×prod-exp
249×unswap-sqr
248×associate-+l+
236×distribute-rgt-neg-in
210×div-exp
209×flip-- flip3--
188×distribute-lft-neg-in unpow3 cube-mult
171×log-pow
150×flip-+ flip3-+
141×unpow2
137×sqrt-div
133×cbrt-unprod
129×cbrt-undiv
122×pow-unpow
115×exp-prod
111×diff-log
109×sub-neg
94×fma-def
88×pow-to-exp pow-exp
84×pow-prod-down
76×tan-quot
75×associate-*l/
64×neg-mul-1
60×associate-/l/ clear-num frac-2neg
55×*-commutative associate-*r/
52×frac-times
48×pow1/2 sqrt-pow1
46×pow1/3
45×fma-udef
34×distribute-rgt-in rem-sqrt-square distribute-lft-in
31×swap-sqr
29×log-div
27×sum-log
25×div-sub rec-exp 1-exp
24×complex-mul-def cbrt-div
18×+-commutative neg-sub0
17×pow-pow associate-+r+ rem-log-exp
15×associate--l- pow-prod-up
14×difference-cubes associate--l+
13×pow-sqr
12×hypot-def neg-log
11×frac-add pow-flip
9×associate--r+ frac-sub
8×cube-div inv-pow
7×exp-diff associate-+l-
6×rem-cube-cbrt pow-plus *.c-commutative
5×log1p-udef pow2
4×sqrt-unprod log1p-expm1 +.c-commutative expm1-log1p expm1-udef complex-add-def sin-mult
3×sin-cos-mult un-div-inv associate-+r- difference-of-sqr-1 cos-mult
2×rem-exp-log associate-+l+.c expm1-def pow-neg associate--r- exp-neg pow-sub associate-*l*.c cos-sum tan-sum distribute-neg-frac sin-sum
1×rem-cbrt-cube diff-atan sub-div diff-cos rem-square-sqrt distribute-rgt-neg-out frac-2neg.c diff-sin exp-to-pow

regimes3.3s (1.6%)

Accuracy

Total 36.5b remaining (12.8%)

Threshold costs 5.3b (1.8%)

5.7b38.4%expq3 (problem 3.4.2)
5.6b80.3%quad2m (problem 3.2.1, negative)
5.6b80.4%quadm (p42, negative)
4.4b84.9%quadp (p42, positive)
4.4b85%quad2p (problem 3.2.1, positive)

localize1.9s (0.9%)

bsearch1.7s (0.8%)

end1.0ms (0.0%)