Details

sample28.9m (75.2%)

Algorithm
72×intervals
Results
7.8m81227×body10240exit
52.5s33195×body1280valid
24.9s198039×body80valid
23.7s24057×body640valid
19.5s152615×body80nan
15.2s25414×body320valid
11.6s34974×body160valid
9.7s153862×pre80true
3.3s3052×body2560valid
1.8s7875×body160nan
906.0ms4165×pre10240exit
245.0ms224×body5120valid

prune4.3m (11.2%)

simplify3.6m (9.2%)

series58.6s (2.5%)

Calls

404 calls:

Slowest
1.5s
(* (sqrt (fma (* a -4) c (* b b))) (fma (* a -4) c (* b b)))
1.5s
(* (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b))))
1.3s
(- (* (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b)))) (* b (* b b)))
1.3s
(- (* (sqrt (fma (* a -4) c (* b b))) (fma (* a -4) c (* b b))) (* (* b b) b))
835.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

regimes16.5s (0.7%)

Accuracy

Total 31.2b remaining (9.4%)

Threshold costs 4.8b (1.4%)

5.7b58%Cubic critical, narrow range
5.3b53%Quotient of products
3.1b0%Cubic critical, medium range
3.1b0%Quadratic roots, medium range
2.6b0%Quadratic roots, wide range

bsearch10.6s (0.5%)

rewrite10.5s (0.5%)

Algorithm
127×rewrite-expression-head
Calls

404 calls:

Slowest
1.3s
(/ (+ (+ (* (* (* a -4) c) (sqrt (fma (* a -4) c (* b b)))) (- (* (* b b) (sqrt (fma (* a -4) c (* b b)))) (* (* b b) b))) (fma (- (* b b)) b (* (* b b) b))) (fma b (+ (sqrt (fma (* a -4) c (* b b))) b) (fma (* a -4) c (* b b))))
349.0ms
(- (exp x) (exp (- x)))
322.0ms
(* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
314.0ms
(/ (- (- (- x 1) x) 1) (* (+ x 1) (- x 1)))
306.0ms
(* (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (/ 1 (- x 1)) (/ x (+ x 1))))
Rules
18295×times-frac
14997×*-un-lft-identity
13581×add-sqr-sqrt
10673×add-cube-cbrt
6294×prod-diff
2554×add-exp-log
1944×sqrt-prod
1345×difference-of-squares
1217×add-cbrt-cube
1184×distribute-lft-out
1028×prod-exp
941×div-inv
897×pow1
863×div-exp
788×associate-*r*
702×distribute-lft-out--
692×pow-exp
685×log-prod
682×associate-*l*
614×exp-sum
583×associate-/r/
531×add-log-exp
472×associate-/l*
411×expm1-log1p-u
405×log1p-expm1-u
404×insert-posit16
391×fma-neg
346×difference-of-sqr-1
345×pow-to-exp
322×associate-/r*
281×cbrt-unprod
259×cbrt-prod
254×flip--
253×flip3--
227×cbrt-undiv
220×flip-+
219×flip3-+
178×pow-prod-down
167×unpow-prod-down
153×unswap-sqr
145×1-exp
144×cube-prod
139×exp-prod
137×rec-exp
114×fma-def
106×associate-*r/
100×*-commutative
98×associate-*l/
97×frac-times
95×fma-udef
87×distribute-rgt-in distribute-lft-in
86×swap-sqr
84×sqr-pow
81×frac-2neg clear-num
67×pow-prod-up
64×sub-neg
58×associate-/l/
57×log-pow
50×difference-cubes
49×pow3
46×diff-log
45×cube-unmult
42×pow-plus distribute-rgt-neg-in
41×cbrt-div
39×sqrt-pow1 pow-sqr
35×pow1/2 distribute-lft-neg-in
34×rem-sqrt-square
33×sin-sum
28×pow1/3
26×cos-sum div-sub
24×pow2 tan-quot
20×sqrt-div
17×sum-log sin-mult
16×associate--l+ +-commutative
15×pow-pow frac-add
14×pow-flip
13×expm1-def
12×neg-mul-1
10×cos-mult inv-pow rem-log-exp log-div
exp-diff log1p-udef
neg-sub0 frac-sub log1p-expm1 cube-mult acos-asin
exp-neg
pow-unpow un-div-inv distribute-rgt-out
distribute-rgt-neg-out sub-div
expm1-log1p expm1-udef distribute-rgt-out-- associate-+l-
associate-+r+ hypot-udef
distribute-rgt1-in distribute-frac-neg associate--r+ exp-to-pow rem-exp-log acos-neg rem-cbrt-cube cos-diff
associate-+l+ remove-posit16 associate--l- associate-+r- unsub-neg neg-log tanh-def sqr-sin tanh-undef asin-acos unpow1/3 sqr-cos sin-diff

localize5.7s (0.2%)

end1.0ms (0.0%)