Details

sample2.2m (53.2%)

Algorithm
56×intervals
16×halfpoints
Results
32.0s66323×body1280valid
20.1s17425×body2560valid
12.2s42039×body640valid
7.0s94005×body80valid
4.2s20637×body320valid
4.0s63065×body80nan
1.5s10916×body160valid
1.0s12736×body80overflowed
857.0ms47526×pre80true
395.0ms621×body1280nan
301.0ms667×body640nan
250.0ms427×body5120valid
103.0ms345×body320nan
42.0ms226×body160nan

series48.8s (19.9%)

Calls

373 calls:

3.1s
(/ (expm1 (log1p (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
2.3s
(/ (* 1.0 (- (* (hypot (sqrt x) (sqrt 1.0)) (hypot (sqrt x) (sqrt 1.0))) (* (sqrt x) (sqrt x)))) (* (fma (sqrt x) (hypot (sqrt x) (sqrt 1.0)) x) (hypot (sqrt x) (sqrt 1.0))))
1.8s
(expm1 (log1p (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
1.7s
(/ (* 1.0 (- (hypot (sqrt x) (sqrt 1.0)) (sqrt x))) (* (sqrt x) (hypot (sqrt x) (sqrt 1.0))))
1.3s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b)))))

prune42.1s (17.2%)

simplify10.9s (4.5%)

Algorithm
192×egg-herbie

rewrite6.1s (2.5%)

Algorithm
120×rewrite-expression-head
Calls

373 calls:

277.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
246.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* (* (cbrt (/ 1.0 (- x 1.0))) (cbrt (/ 1.0 (- x 1.0)))) (cbrt (/ 1.0 (- x 1.0)))))
217.0ms
(- (/ 1 (pow x 3)) (+ (/ 1 (pow x 2)) (/ 1 (pow x 4))))
201.0ms
(cbrt (pow (- (exp (* a x)) 1.0) 3))
110.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
Rules
13396×times-frac
12883×*-un-lft-identity
10935×add-sqr-sqrt
8543×add-cube-cbrt
4274×prod-diff
3913×sqrt-prod
1463×distribute-lft-out
1207×add-exp-log
954×difference-of-squares
890×add-cbrt-cube
863×distribute-lft-out--
804×unpow-prod-down
751×associate-/l*
741×pow1
723×cbrt-prod
716×div-inv
611×add-log-exp
584×associate-*l*
553×associate-*r*
484×associate-+l+
472×fma-neg
431×associate-/r*
425×distribute-rgt-neg-in
414×associate-/r/
362×log1p-expm1-u
360×expm1-log1p-u
353×cube-prod
310×div-exp
274×sqr-pow
260×log-prod
248×prod-exp
243×distribute-lft-neg-in
223×flip3-- flip--
184×unswap-sqr
183×cbrt-undiv
179×flip-+ flip3-+
166×log-pow
143×cbrt-unprod
138×unpow2
137×sqrt-div
119×pow-unpow
108×diff-log
102×associate-*l/
96×sub-neg
88×exp-sum
81×neg-mul-1
79×tan-quot
77×pow-prod-down frac-2neg clear-num
76×unpow3 cube-mult
75×fma-def
74×frac-times
71×pow-exp
69×associate-/l/ pow-to-exp
62×pow1/3
61×associate-*r/
59×cbrt-div
58×sqrt-pow1
54×swap-sqr
48×pow1/2
45×*-commutative
40×rec-exp 1-exp
33×distribute-rgt-in fma-udef distribute-lft-in
32×frac-add
31×pow-flip
30×rem-sqrt-square
27×log-div
26×pow-pow exp-prod
24×complex-mul-def
23×div-sub
22×rem-log-exp
20×frac-sub
19×sum-log
18×pow-prod-up neg-sub0
17×associate--l-
16×pow-sqr
15×hypot-def
14×neg-log associate--l+
13×inv-pow
11×+-commutative
10×pow-div
8×pow-plus
7×pow2 hypot-udef expm1-udef associate-+l-
6×cube-div *.c-commutative expm1-log1p exp-to-pow
5×rem-exp-log rem-cube-cbrt associate--r+
4×exp-diff un-div-inv log1p-udef +.c-commutative sin-mult rem-cbrt-cube complex-add-def
3×sqrt-unprod cos-mult
2×associate-+l+.c expm1-def exp-neg log1p-expm1 difference-of-sqr-1 rem-square-sqrt associate-*l*.c cos-sum tan-sum sin-sum
1×sin-cos-mult difference-cubes diff-atan sub-div diff-cos log-rec quot-tan diff-sin

regimes3.3s (1.4%)

Accuracy

Total 31.0b remaining (12.1%)

Threshold costs 5.4b (2.1%)

4.6b84%quadm (p42, negative)
4.5b83.2%quad2p (problem 3.2.1, positive)
4.5b84.3%quad2m (problem 3.2.1, negative)
4.4b83.4%quadp (p42, positive)
3.4b0%expq3 (problem 3.4.2)

localize1.8s (0.7%)

bsearch1.6s (0.6%)

end1.0ms (0.0%)