Details

sample1.8m (45.0%)

Algorithm
56×intervals
16×halfpoints
Results
24.5s66903×body1280valid
16.8s17179×body2560valid
8.4s41935×body640valid
3.7s12406×body10240exit
3.0s94243×body80valid
2.6s20497×body320valid
1.7s63467×body80nan
898.0ms10833×body160valid
568.0ms47419×pre80true
327.0ms693×body1280nan
218.0ms668×body640nan
139.0ms439×body5120valid
69.0ms369×body320nan
18.0ms170×body160nan

prune1.1m (28.2%)

series36.5s (15.2%)

Calls

382 calls:

889.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b))))
606.0ms
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))
551.0ms
(* (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)))
500.0ms
(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
493.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

simplify13.6s (5.7%)

Algorithm
192×egg-herbie

rewrite7.9s (3.3%)

Algorithm
120×rewrite-expression-head
Calls

382 calls:

234.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
228.0ms
(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))
203.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
191.0ms
(- (/ (- b_2) a) (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))))
123.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (tan x))
Rules
31887×times-frac
22369×*-un-lft-identity
21292×add-sqr-sqrt
17314×add-cube-cbrt
7634×prod-diff
4022×sqrt-prod
3397×cbrt-prod
1815×difference-of-squares
1750×distribute-rgt-neg-in
1662×distribute-lft-out--
1357×add-exp-log
1336×unpow-prod-down
1224×associate-/l*
1166×distribute-lft-neg-in
987×add-cbrt-cube
981×div-inv
918×distribute-lft-out
713×pow1
670×associate-/r/
654×add-log-exp
621×fma-neg
606×cube-prod
600×log-prod
517×sqr-pow
513×associate-*r*
501×associate-*l*
394×div-exp
390×neg-mul-1
377×associate-/r*
367×log1p-expm1-u expm1-log1p-u
351×sqrt-div
330×flip-- flip3--
279×associate-+l+
277×prod-exp
231×cbrt-undiv
220×exp-sum
194×unswap-sqr
193×flip-+ flip3-+
178×pow-unpow
171×cbrt-unprod
166×associate-*l/
164×log-pow
144×sqrt-pow1
139×unpow3 cube-mult
120×diff-log
119×sub-neg
109×swap-sqr
94×exp-prod
92×unpow2
87×fma-def
76×pow-prod-down
74×frac-2neg clear-num
71×associate-/l/
70×pow1/2
62×distribute-rgt-in distribute-lft-in
58×cbrt-div
55×pow1/3
53×pow-to-exp pow-exp
52×frac-times
48×*-commutative
46×rec-exp 1-exp
44×associate-*r/
40×rem-sqrt-square log-div
33×pow-prod-up
31×rem-log-exp
28×frac-sub
27×div-sub
26×sum-log tan-quot
25×associate-+r+
24×fma-udef complex-mul-def
21×pow-sqr associate--r+
20×neg-sub0 pow-pow
19×associate--l+
18×cube-div associate--l-
17×+-commutative
15×pow-flip
13×difference-cubes neg-log cos-mult
12×pow-plus
11×frac-add
9×exp-diff rem-cube-cbrt sin-mult associate-+l-
8×inv-pow pow2
6×rem-exp-log *.c-commutative
5×un-div-inv sub-div
4×pow-div +.c-commutative complex-add-def
3×difference-of-sqr-1 rem-cbrt-cube exp-to-pow
2×associate-+l+.c expm1-def sin-sum distribute-rgt-out-- sqrt-unprod exp-neg rem-square-sqrt associate-*l*.c cos-sum tan-sum distribute-neg-frac
1×sin-cos-mult sqrt-pow2 associate-+r- pow3 associate--r- diff-atan diff-cos frac-2neg.c diff-sin log-rec

regimes2.9s (1.2%)

Accuracy

Total 25.6b remaining (11.2%)

Threshold costs 6.7b (2.9%)

4.9b83.1%quadm (p42, negative)
4.8b83.5%quad2m (problem 3.2.1, negative)
3.2b0%expq3 (problem 3.4.2)
1.7b83.8%2cos (problem 3.3.5)
1.6b93.9%quad2p (problem 3.2.1, positive)

localize2.0s (0.8%)

bsearch1.4s (0.6%)

end1.0ms (0.0%)