Details

sample4.9m (39.2%)

Algorithm
56×intervals
16×halfpoints
Results
1.0m66759×body1280valid
38.3s17648×body2560valid
25.2s41715×body640valid
13.2s12438×body10240exit
12.4s94099×body80valid
9.0s20948×body320valid
7.0s63993×body80nan
2.6s10800×body160valid
2.2s47361×pre80true
694.0ms670×body1280nan
521.0ms706×body640nan
488.0ms434×body5120valid
222.0ms366×body320nan
57.0ms220×body160nan

prune4.0m (32.1%)

simplify2.6m (20.9%)

series38.3s (5.2%)

Calls

369 calls:

611.0ms
(/ 1 (+ (hypot (sqrt x) 1) (sqrt x)))
566.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
558.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))
531.0ms
(- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
521.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite9.2s (1.2%)

Algorithm
118×rewrite-expression-head
Calls

369 calls:

162.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
146.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
145.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))
136.0ms
(* (- (* (cos (* eps 1/2)) (cos x)) (* (sin (/ eps 2)) (sin x))) (sin (/ eps 2)))
134.0ms
(cbrt (* (* (* (sin x) (sin x)) (sin x)) (* (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))) (/ (sin eps) (cos eps)))))
Rules
15166×times-frac
13903×*-un-lft-identity
13449×add-sqr-sqrt
9510×add-cube-cbrt
5907×prod-diff
3280×sqrt-prod
1757×difference-of-squares
1345×pow1
1287×add-exp-log
1078×add-cbrt-cube
1036×distribute-lft-out
953×distribute-lft-out--
903×div-inv
885×associate-*r*
834×associate-*l*
601×fma-neg
559×add-log-exp
550×cbrt-prod
435×unpow-prod-down
432×associate-/r/
414×associate-/l*
411×associate-/r*
366×log1p-expm1-u
365×expm1-log1p-u
362×insert-posit16
313×prod-exp
301×pow-prod-down
294×div-exp
269×associate-+l+
265×cbrt-unprod
231×pow-prod-up
228×distribute-rgt-neg-in
220×flip3-- flip--
217×flip-+ flip3-+
199×cbrt-undiv
169×unswap-sqr
152×distribute-rgt-out
151×associate-*l/
147×distribute-lft-neg-in
143×sqr-pow
121×swap-sqr
104×log-prod
103×pow-sqr
97×frac-times
95×sqrt-div
81×diff-log
78×pow-plus sub-neg
74×sqrt-pow1 associate-*r/
73×frac-2neg clear-num *-commutative fma-def
71×cbrt-div
67×log-pow
64×pow1/3
61×pow1/2
56×pow2
49×1-exp rec-exp neg-mul-1 associate-/l/
43×exp-prod
40×distribute-rgt-in distribute-lft-in
39×pow-flip pow-unpow
34×frac-add
33×rem-sqrt-square
29×tan-quot
25×div-sub
23×fma-udef
21×sum-log
20×log-div
18×difference-of-sqr-1 inv-pow
17×sin-mult
16×cube-unmult
15×+-commutative
14×frac-sub hypot-def
12×distribute-rgt1-in distribute-lft1-in
10×associate--l- pow-div rem-log-exp
9×neg-sub0
8×exp-sum associate--l+
7×neg-log
6×expm1-udef
5×expm1-log1p exp-diff cos-mult
4×log1p-def log1p-expm1 pow-exp log1p-udef pow3 associate--r+ sqr-sin un-div-inv pow-to-exp count-2
3×sqrt-unprod sub-div pow-pow distribute-rgt-out-- cos-sum
2×sin-sum +.c-commutative tan-sum hypot-udef exp-neg rem-exp-log associate-+l- rem-cbrt-cube
1×diff-atan frac-2neg.c sin-cos-mult remove-double-div hypot-1-def rem-square-sqrt diff-sin diff-cos expm1-def

localize4.3s (0.6%)

regimes4.2s (0.6%)

Accuracy

Total 22.8b remaining (15.9%)

Threshold costs 4.7b (3.3%)

4.9b82.2%quad2p (problem 3.2.1, positive)
4.6b83.4%quadm (p42, negative)
4.6b83.6%quad2m (problem 3.2.1, negative)
2.8b11%expq3 (problem 3.4.2)
1.1b90%2nthrt (problem 3.4.6)

bsearch1.5s (0.2%)

end1.0ms (0.0%)