Details

sample1.9m (53.8%)

Algorithm
56×intervals
16×halfpoints
Results
23.9s66750×body1280valid
16.7s17347×body2560valid
8.3s42645×body640valid
3.9s12758×body10240exit
2.9s93425×body80valid
2.6s20878×body320valid
1.6s63396×body80nan
853.0ms10548×body160valid
526.0ms47348×pre80true
290.0ms622×body1280nan
198.0ms606×body640nan
135.0ms484×body5120valid
67.0ms351×body320nan
19.0ms175×body160nan

prune37.6s (18.1%)

series31.6s (15.2%)

Calls

368 calls:

820.0ms
(expm1 (log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
566.0ms
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))) (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (+ 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (- (tan x)))
509.0ms
(* (cbrt (/ (/ 1 2.0) (sqrt 2.0))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
473.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
471.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

simplify11.0s (5.3%)

Algorithm
192×egg-herbie

rewrite9.2s (4.4%)

Algorithm
120×rewrite-expression-head
Calls

368 calls:

339.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
294.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))
116.0ms
(/ (/ (* (/ a (cbrt (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (/ c (cbrt (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))) (cbrt (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
112.0ms
(/ 1 (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
102.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
Rules
8667×*-un-lft-identity
8026×add-sqr-sqrt
7282×times-frac
6001×add-cube-cbrt
4052×prod-diff
1756×sqrt-prod
1472×add-exp-log
1008×add-cbrt-cube
918×unpow-prod-down
805×difference-of-squares
666×distribute-lft-out
658×distribute-lft-out--
633×pow1
622×add-log-exp
531×fma-neg
474×associate-*l*
449×div-inv
444×associate-*r*
433×associate-/l* prod-exp
407×associate-/r/
392×cube-prod
372×cbrt-prod
361×associate-/r*
355×div-exp
353×sqr-pow expm1-log1p-u
352×log1p-expm1-u
340×distribute-rgt-neg-in
270×distribute-lft-neg-in
254×flip-- flip3--
250×associate-+l+
246×log-prod
238×unswap-sqr
222×cbrt-undiv
218×cbrt-unprod
168×sqrt-div
143×flip-+ flip3-+
135×unpow2
113×diff-log
112×sqrt-pow1
104×pow-exp
102×pow-to-exp
101×sub-neg
88×pow1/2
84×pow-unpow
80×neg-mul-1
78×log-pow
74×unpow3 cube-mult
71×associate-/l/
68×frac-2neg clear-num
67×pow-prod-down
65×fma-def
54×rec-exp associate-*r/ 1-exp
51×associate-*l/
46×*-commutative
43×rem-sqrt-square swap-sqr
40×frac-times
34×fma-udef
33×rem-log-exp
29×tan-quot log-div
26×associate-+r+ sum-log
25×pow-flip cbrt-div
24×complex-mul-def
21×pow-prod-up div-sub frac-sub
19×inv-pow pow1/3
18×neg-sub0 exp-prod
16×+-commutative exp-sum pow-pow
15×associate--l-
13×pow-sqr neg-log
11×distribute-rgt-in distribute-lft-in cos-mult
10×frac-add expm1-udef associate--l+
associate--r- sub-div
sum-cubes sin-mult
cube-div difference-cubes sqrt-unprod hypot-def *.c-commutative associate-+l-
pow2 pow-plus distribute-rgt-out--
rem-cube-cbrt un-div-inv pow-div associate-+r- +.c-commutative associate--r+ complex-add-def log-rec
rem-exp-log exp-diff unpow-prod-up difference-of-sqr-1 rem-square-sqrt
associate-+l+.c expm1-def log1p-udef exp-neg sin-sum log1p-expm1 expm1-log1p associate-*l*.c sqr-cos tan-sum cos-sum frac-2neg.c
sin-cos-mult sqrt-pow2 e-exp-1 diff-atan diff-cos distribute-frac-neg distribute-rgt-out sqrt-undiv diff-sin exp-to-pow rem-cbrt-cube

regimes2.8s (1.4%)

Accuracy

Total 29.1b remaining (10.8%)

Threshold costs 6.7b (2.5%)

4.9b82.6%quad2m (problem 3.2.1, negative)
4.9b82.7%quadm (p42, negative)
4.4b83.5%quad2p (problem 3.2.1, positive)
4.2b50.5%expq3 (problem 3.4.2)
1.6b81.5%2nthrt (problem 3.4.6)

localize2.0s (1.0%)

bsearch1.6s (0.8%)

end1.0ms (0.0%)