Details

sample2.1m (57.0%)

Algorithm
56×intervals
16×halfpoints
Results
30.7s66896×body1280valid
19.5s17490×body2560valid
11.6s42127×body640valid
5.3s94042×body80valid
4.0s20518×body320valid
3.0s64302×body80nan
1.3s10471×body160valid
746.0ms12805×body80overflowed
735.0ms47289×pre80true
362.0ms614×body1280nan
267.0ms586×body640nan
214.0ms469×body5120valid
108.0ms383×body320nan
35.0ms213×body160nan

series36.7s (16.8%)

Calls

402 calls:

1.1s
(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
1.1s
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
990.0ms
(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
903.0ms
(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
891.0ms
(+ (* 1 (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (* (tan x) (- (* (tan eps) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) 1)))

prune33.6s (15.4%)

simplify10.3s (4.7%)

Algorithm
195×egg-herbie

rewrite7.1s (3.2%)

Algorithm
123×rewrite-expression-head
Calls

402 calls:

290.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ (sqrt 1.0) (/ (- x 1.0) (sqrt 1.0))))
263.0ms
(- (/ (- (pow (* (cos x) (cos eps)) 3) (pow (* (sin x) (sin eps)) 3)) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))) (cos x))
194.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
192.0ms
(* (/ 1 (* 2.0 a)) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))))
189.0ms
(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
Rules
6269×times-frac
6238×add-sqr-sqrt
5777×*-un-lft-identity
3587×add-cube-cbrt
1704×add-exp-log
1153×add-cbrt-cube
1142×sqrt-prod
1101×associate-*r*
947×difference-of-squares
872×pow1
756×distribute-lft-out--
723×add-log-exp
704×unpow-prod-down associate-*l*
584×associate-/l*
509×prod-exp
408×div-exp
392×associate-/r*
388×unswap-sqr
355×distribute-lft-out
336×sqr-pow
301×log-prod
274×flip-- flip3--
271×cbrt-prod
256×cbrt-unprod
237×flip-+ flip3-+
226×associate-*l/
218×cbrt-undiv
217×div-inv
216×associate-/r/
215×cube-prod
181×frac-times
179×associate-*r/
168×pow-prod-down
158×unpow2
152×cbrt-div
134×sqrt-div sub-neg
133×frac-add
128×tan-quot
124×diff-log
115×distribute-rgt-neg-in
110×pow-exp
109×pow-to-exp
103×*-commutative log-div
100×sqrt-pow1
94×log-pow
85×associate-/l/
73×1-exp
70×rec-exp
69×frac-2neg exp-sum clear-num
68×pow1/2
55×sum-log swap-sqr
45×distribute-rgt-in distribute-lft-in cos-mult associate--l+
39×exp-prod
38×rem-sqrt-square pow1/3
37×unpow3 cube-mult
36×pow-prod-up
35×pow-unpow
33×frac-sub
30×pow-sqr +-commutative
28×associate-+l+
25×associate--r+ rem-log-exp
24×complex-mul-def sin-mult
22×associate--r- associate-+r+
21×div-sub
19×neg-sub0
18×associate--l-
13×pow-plus
12×exp-diff neg-log
10×distribute-rgt-out-- pow-flip associate-+l-
9×cube-div pow2
8×inv-pow exp-to-pow
7×pow-pow
6×difference-cubes associate-+r- *.c-commutative
5×rem-exp-log sqrt-unprod
4×rem-cube-cbrt un-div-inv difference-of-sqr-1 +.c-commutative complex-add-def
3×sin-cos-mult
2×associate-+l+.c exp-neg pow-sub unsub-neg rem-square-sqrt associate-*l*.c sqrt-undiv sub-div cos-sum tan-sum pow-neg sin-sum
1×diff-atan diff-cos +-inverses rem-cbrt-cube diff-sin

regimes2.7s (1.2%)

Accuracy

Total 22.5b remaining (11%)

Threshold costs 6.5b (3.2%)

4.3b83.9%quadp (p42, positive)
3.3b0%expq3 (problem 3.4.2)
2.6b90.3%quad2m (problem 3.2.1, negative)
1.6b83.4%2cos (problem 3.3.5)
1.5b82.3%2nthrt (problem 3.4.6)

localize1.8s (0.8%)

bsearch1.6s (0.7%)

end1.0ms (0.0%)