Details

sample1.9m (42.7%)

Algorithm
56×intervals
16×halfpoints
Results
25.8s67320×body1280valid
16.8s16999×body2560valid
8.8s42314×body640valid
4.2s12724×body10240exit
3.2s93976×body80valid
2.7s20521×body320valid
1.9s63998×body80nan
918.0ms10597×body160valid
783.0ms47474×pre80true
319.0ms651×body1280nan
239.0ms678×body640nan
152.0ms451×body5120valid
79.0ms374×body320nan
27.0ms211×body160nan

prune1.5m (33.7%)

series32.4s (11.9%)

Calls

388 calls:

804.0ms
(fma (fma (fma (tan x) (tan eps) 1) (* (tan x) (tan eps)) 1) (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (- (tan x)))
629.0ms
(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))
564.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps)) (- (exp (* b eps)) 1.0)))
439.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
429.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

rewrite11.9s (4.4%)

Algorithm
123×rewrite-expression-head
Calls

388 calls:

796.0ms
(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))
731.0ms
(+ (+ (- (* (* (cbrt (exp x)) (cbrt (exp x))) (cbrt (exp x))) 2.0) (fma (- 2.0) 1 2.0)) (exp (- x)))
372.0ms
(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
332.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
316.0ms
(* (sqrt (* (cbrt (/ (+ (exp x) (exp (- x))) 2.0)) (cbrt (/ (+ (exp x) (exp (- x))) 2.0)))) (* (sqrt (cbrt (/ (+ (exp x) (exp (- x))) 2.0))) (* (sqrt (/ (+ (exp x) (exp (- x))) 2.0)) (cos y))))
Rules
10486×*-un-lft-identity
10141×times-frac
9056×add-sqr-sqrt
7409×add-cube-cbrt
4584×prod-diff
2650×sqrt-prod
1302×add-exp-log
909×add-cbrt-cube
889×distribute-lft-out
769×associate-*l*
758×pow1
686×cbrt-prod
649×distribute-lft-out--
637×add-log-exp
636×div-inv
623×difference-of-squares
534×unpow-prod-down
516×distribute-rgt-in distribute-lft-in
491×associate--l+
455×associate-/r/
399×fma-neg
398×associate-/r*
377×distribute-rgt-neg-in
376×log-prod
375×log1p-expm1-u
374×expm1-log1p-u
363×associate-/l*
341×div-exp
329×associate-*r*
294×distribute-lft-neg-in
289×flip-- flip3--
276×associate-+l+ prod-exp
226×cube-prod
222×unswap-sqr
220×flip-+ flip3-+
207×sqr-pow
179×associate-*l/
178×fma-def
176×cbrt-undiv
167×frac-sub
165×log-pow
161×frac-times
159×sqrt-pow1
158×sqrt-div
157×cbrt-unprod
133×swap-sqr
119×associate-*r/
113×exp-sum
107×associate-/l/
103×exp-prod
100×sub-neg
98×neg-mul-1
96×pow-prod-down
95×cbrt-div
94×pow-unpow
91×diff-log
90×pow1/3
85×pow1/2
73×pow-exp
67×rec-exp 1-exp
65×pow-to-exp
62×frac-2neg clear-num
58×*-commutative
56×pow-prod-up
49×unpow2
48×sum-log
42×unpow3 cube-mult
40×associate-+r+
38×tan-quot
36×log-div
32×pow-flip
31×fma-udef
28×pow-sqr div-sub
26×+-commutative
25×cube-div neg-sub0
24×rem-sqrt-square complex-mul-def
23×rem-log-exp
22×pow-pow frac-add
17×exp-diff pow-plus
16×associate-+l-
15×inv-pow
14×neg-log
13×rem-cube-cbrt
11×pow2
10×pow-div
8×associate--l- exp-neg
6×sqrt-unprod *.c-commutative difference-of-sqr-1 distribute-rgt-out--
5×associate-+r- sum-cubes
4×un-div-inv log1p-udef sub-div +.c-commutative expm1-log1p cos-mult expm1-udef complex-add-def associate--r+
3×difference-cubes log1p-expm1 sin-mult
2×associate-+l+.c expm1-def unpow1/3 rem-exp-log unsub-neg associate-*l*.c hypot-def cos-sum tan-sum rem-cbrt-cube sin-sum
1×sin-cos-mult remove-double-div diff-atan distribute-neg-in diff-cos rem-square-sqrt frac-2neg.c diff-sin

simplify11.2s (4.1%)

Algorithm
195×egg-herbie

regimes5.2s (1.9%)

Accuracy

Total 27.4b remaining (14.2%)

Threshold costs 5.9b (3.1%)

4.2b85.3%quadm (p42, negative)
4.0b85.9%quad2m (problem 3.2.1, negative)
3.6b0%expq3 (problem 3.4.2)
3.3b88.7%quadp (p42, positive)
3.2b89.2%quad2p (problem 3.2.1, positive)

localize2.1s (0.8%)

bsearch1.3s (0.5%)

end1.0ms (0.0%)