Details

simplify46.6m

Calls

25047 calls:

Slowest
1.3s
(* (- a b) (fma (- (sqrt (* a b))) (sqrt (* a b)) (* (sqrt (* a b)) (sqrt (* a b)))))
1.2s
(* (* (* (- (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1)) 3) (- (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1)) 3)) (- (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1)) 3)) (* (* (* (* x1 2) (* x1 2)) (* x1 2)) (/ (* (* (- (fma x2 2 (* (* 3 x1) x1)) x1) (- (fma x2 2 (* (* 3 x1) x1)) x1)) (- (fma x2 2 (* (* 3 x1) x1)) x1)) (* (* (fma x1 x1 1) (fma x1 x1 1)) (fma x1 x1 1)))))
1.2s
(* (- (pow (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1)) 3) (pow 3 3)) (* x1 2))
1.1s
(* (fma (- (sqrt (* a b))) (sqrt (* a b)) (* (sqrt (* a b)) (sqrt (* a b)))) (- a b))
1.1s
(* (+ (pow (fma 1 (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1)) (- (* (sqrt 3) (sqrt 3)))) 3) (pow 0 3)) (* x1 2))

prune4.1m

sample1.2m

Algorithm
60×intervals
Results
31.0s239196×body80valid
11.9s12868×body1280valid
5.3s8894×body640valid
4.6s2818×body2560valid
4.3s67605×pre80true
4.2s2036×body10240exit
2.4s6544×body320valid
2.3s8865×body160valid
2.1s16873×body80nan
201.0ms110×body5120valid

series24.9s

Calls

246 calls:

Slowest
625.0ms
(fma (fma (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1)) 4 -6) (* x1 x1) (* (+ (fma 1 (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1)) (- (* (sqrt 3) (sqrt 3)))) 0) (* (* x1 2) (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1)))))
572.0ms
(* (+ (fma 1 (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1)) (- (* (sqrt 3) (sqrt 3)))) 0) (* (* x1 2) (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1))))
502.0ms
(fma 3 (/ (- (* (* 3 x1) x1) (fma 2 x2 x1)) (fma x1 x1 1)) (+ (fma x1 (* x1 x1) (fma (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1)) (* (* 3 x1) x1) (* (fma x1 x1 1) (fma (fma (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1)) 4 -6) (* x1 x1) (* (- (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1)) 3) (* (* x1 2) (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1)))))))) x1))
489.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
462.0ms
(fma (* (+ (/ (fma 2 x2 (- (* x1 (* x1 3)) x1)) (fma x1 x1 1)) -3) x1) (* (/ (fma 2 x2 (- (* x1 (* x1 3)) x1)) (fma x1 x1 1)) 2) (* (* (cbrt x1) (cbrt x1)) (* (* (cbrt x1) x1) (fma 4 (/ (fma 2 x2 (- (* x1 (* x1 3)) x1)) (fma x1 x1 1)) -6))))

rewrite16.3s

Algorithm
87×rewrite-expression-head
Calls

246 calls:

Slowest
2.1s
(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
1.1s
(exp (+ (+ (+ (+ c e) d) a) b))
880.0ms
(cbrt (* (* (* (/ (fma -2 v 3) (- 1 v)) 0.125) (* (/ (fma -2 v 3) (- 1 v)) 0.125)) (* (/ (fma -2 v 3) (- 1 v)) 0.125)))
585.0ms
(+ (+ (+ (+ c e) d) a) b)
528.0ms
(/ (fma (fma b (* b b) (* a (* a a))) (* a a) (* (fma b (* b b) (* a (* a a))) (- (* b b)))) (* (- a b) (+ (* a a) (- (* b b) (* a b)))))
Rules
24061×add-sqr-sqrt
23449×*-un-lft-identity
21960×times-frac
16700×add-cube-cbrt
11068×prod-diff
6520×associate-*l/
4619×associate-/r*
4570×frac-times
4364×associate-/l*
3920×sqrt-prod
3640×associate-*l*
3492×exp-sum
2662×associate-*r*
2534×difference-of-squares
2196×cbrt-div
1989×associate--r+
1904×distribute-rgt-in distribute-lft-in
1876×unswap-sqr
1576×distribute-lft-out
1379×swap-sqr
1347×distribute-lft-out--
1124×frac-sub
1012×associate-/l/
963×pow1
904×div-inv
873×clear-num
868×add-exp-log
859×frac-2neg
829×add-cbrt-cube
805×*-commutative
719×distribute-rgt-neg-in
703×distribute-lft-neg-in
495×add-log-exp
449×associate-/r/
444×associate-*r/
390×associate-+r+
347×sub-neg
313×pow-prod-down
295×cbrt-prod
293×sqrt-div
277×fma-neg
252×flip-+ flip3-+
249×expm1-log1p-u
246×log1p-expm1-u
245×insert-posit16
217×prod-exp
215×cbrt-unprod
179×fma-def
173×div-exp
150×cbrt-undiv
132×sqrt-pow1
121×flip3-- flip--
120×neg-mul-1
117×sum-log
107×unpow-prod-down
92×sqr-pow
90×pow-prod-up
88×+-commutative
87×difference-of-sqr-1
85×hypot-def
83×associate-+l+
60×pow1/2
50×log-prod
49×distribute-rgt-out
46×pow-sqr
41×rem-sqrt-square
40×distribute-neg-frac
38×fma-udef
37×diff-log
36×un-div-inv
32×log-div
31×pow-plus
26×div-sub
25×exp-prod
24×log-pow
15×sub-div
14×pow-flip exp-diff pow2
11×rem-log-exp associate--r-
8×1-exp rec-exp exp-lft-sqr
7×expm1-udef
6×neg-sub0 cube-unmult pow3
5×remove-double-div distribute-rgt-out-- rem-exp-log distribute-frac-neg
4×distribute-lft1-in associate--l- log1p-expm1 log-rec sqrt-unprod inv-pow pow-div rem-cbrt-cube frac-add log1p-udef
3×distribute-lft-neg-out pow-unpow rem-square-sqrt expm1-def
2×expm1-log1p pow-exp pow1/3 associate--l+ neg-log pow-to-exp log1p-def remove-posit16
1×distribute-rgt-neg-out pow-pow

regimes3.9s

Accuracy

Total 31.0b remaining (57.9%)

8.6b57.3%Compound Interest
7.8b31%Complex division, imag part
7.0b35.5%Complex division, real part
4.5b84.6%The quadratic formula (r2)
1.4b0%Rosa's DopplerBench

localize2.9s

bsearch1.9s

end1.0ms