Details

Time bar (total: 46.2s)

sample215.0ms

Algorithm
intervals
Results
51.0ms150×body160valid
46.0ms106×body80valid
46.0ms297×body80nan
39.0ms553×pre80true

simplify185.0ms

Counts
1 → 1

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.1b

localize23.0ms

Local error

Found 4 expressions with local error:

29.9b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b
(fma c (* -4 a) (* b b))
0.2b
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
0.1b
(sqrt (fma c (* -4 a) (* b b)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
18×prod-diff
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
6×fma-neg add-log-exp
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×div-sub
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log fma-udef flip-- associate-/l/
Counts
4 → 179
Calls
4 calls:
Slowest
31.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
7.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms
(sqrt (fma c (* -4 a) (* b b)))
0.0ms
(fma c (* -4 a) (* b b))

series341.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
105.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
99.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
84.0ms
(sqrt (fma c (* -4 a) (* b b)))
53.0ms
(fma c (* -4 a) (* b b))

simplify789.0ms

Counts
191 → 191

prune2.1s

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 27.3b

localize85.0ms

Local error

Found 4 expressions with local error:

28.8b
(- (* (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b)))) (* b (* b b)))
0.4b
(/ (- (* (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b)))) (* b (* b b))) (fma b (+ (sqrt (fma (* a -4) c (* b b))) b) (fma (* a -4) c (* b b))))
0.3b
(* (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b))))
0.2b
(* b (* b b))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
23×pow1
17×*-un-lft-identity add-cube-cbrt
13×add-cbrt-cube add-exp-log
12×times-frac
7×associate-*r* pow-prod-up
6×cube-unmult associate-*l* pow3 add-log-exp
5×difference-cubes
4×expm1-log1p-u pow-prod-down prod-exp sqrt-prod cbrt-unprod insert-posit16 log1p-expm1-u associate-/l*
3×associate-/r* unswap-sqr
2×flip3-- *-commutative flip-- associate-/l/
1×pow2 cbrt-undiv clear-num sub-neg frac-2neg sqrt-pow1 pow-plus pow1/2 fma-neg diff-log div-sub div-exp prod-diff pow-sqr div-inv
Counts
4 → 110
Calls
4 calls:
Slowest
63.0ms
(/ (- (* (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b)))) (* b (* b b))) (fma b (+ (sqrt (fma (* a -4) c (* b b))) b) (fma (* a -4) c (* b b))))
23.0ms
(* b (* b b))
20.0ms
(- (* (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b)))) (* b (* b b)))
15.0ms
(* (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b))))

series3.7s

Counts
4 → 12
Calls
4 calls:
Slowest
1.8s
(* (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)))
515.0ms
(/ (- (* (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b)))) (* b (* b b))) (fma b (+ (sqrt (fma (* a -4) c (* b b))) b) (fma (* a -4) c (* b b))))
41.0ms
(* b (* b b))

simplify1.7s

Counts
122 → 122

prune1.8s

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 26.2b

localize61.0ms

Local error

Found 4 expressions with local error:

28.4b
(fma (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b))) (- (* b (* b b))))
0.4b
(/ (fma (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b))) (- (* b (* b b)))) (fma b (+ (sqrt (fma (* a -4) c (* b b))) b) (fma (* a -4) c (* b b))))
0.2b
(* b (* b b))
0.2b
(fma (* a -4) c (* b b))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1
14×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
11×add-cbrt-cube add-exp-log
9×times-frac
5×pow-prod-up
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-*l* pow-prod-down prod-exp cbrt-unprod associate-/l*
2×fma-udef
1×pow2 cbrt-undiv clear-num frac-2neg pow-plus cube-unmult div-exp associate-*r* pow-sqr *-commutative div-inv unswap-sqr
Counts
4 → 79
Calls
4 calls:
Slowest
28.0ms
(* b (* b b))
4.0ms
(/ (fma (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b))) (- (* b (* b b)))) (fma b (+ (sqrt (fma (* a -4) c (* b b))) b) (fma (* a -4) c (* b b))))
0.0ms
(fma (* a -4) c (* b b))
0.0ms
(fma (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b))) (- (* b (* b b))))

series733.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
304.0ms
(/ (fma (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b))) (- (* b (* b b)))) (fma b (+ (sqrt (fma (* a -4) c (* b b))) b) (fma (* a -4) c (* b b))))
278.0ms
(fma (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b))) (- (* b (* b b))))
91.0ms
(fma (* a -4) c (* b b))
59.0ms
(* b (* b b))

simplify947.0ms

Counts
91 → 91

prune1.4s

Pruning

46 alts after pruning (46 fresh and 0 done)

Merged error: 26.1b

localize78.0ms

Local error

Found 4 expressions with local error:

28.4b
(fma (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b))) (- (* b (* b b))))
2.0b
(expm1 (log1p (fma (* a -4) c (* b b))))
0.4b
(/ (fma (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b))) (- (* b (* b b)))) (fma b (+ (sqrt (fma (* a -4) c (* b b))) b) (expm1 (log1p (fma (* a -4) c (* b b))))))
0.2b
(* b (* b b))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1
14×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
11×add-cbrt-cube add-exp-log
9×times-frac
5×pow-prod-up
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-*l* pow-prod-down prod-exp cbrt-unprod associate-/l*
1×pow2 cbrt-undiv expm1-log1p clear-num frac-2neg pow-plus cube-unmult div-exp associate-*r* pow-sqr *-commutative fma-udef div-inv expm1-udef unswap-sqr
Counts
4 → 80
Calls
4 calls:
Slowest
16.0ms
(* b (* b b))
4.0ms
(/ (fma (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b))) (- (* b (* b b)))) (fma b (+ (sqrt (fma (* a -4) c (* b b))) b) (expm1 (log1p (fma (* a -4) c (* b b))))))
0.0ms
(fma (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b))) (- (* b (* b b))))
0.0ms
(expm1 (log1p (fma (* a -4) c (* b b))))

series23.1s

Counts
4 → 12
Calls
4 calls:
Slowest
22.5s
(/ (fma (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b))) (- (* b (* b b)))) (fma b (+ (sqrt (fma (* a -4) c (* b b))) b) (expm1 (log1p (fma (* a -4) c (* b b))))))
267.0ms
(fma (fma (* a -4) c (* b b)) (sqrt (fma (* a -4) c (* b b))) (- (* b (* b b))))
266.0ms
(expm1 (log1p (fma (* a -4) c (* b b))))
48.0ms
(* b (* b b))

simplify1.5s

Counts
92 → 92

prune1.3s

Pruning

50 alts after pruning (50 fresh and 0 done)

Merged error: 26.1b

regimes1.6s

Accuracy

0% (2.8b remaining)

Error of 27.5b against oracle of 24.7b and baseline of 27.5b

bsearch9.0ms

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.4s8567×body80nan
1.2s4519×body160valid
925.0ms16567×pre80true
439.0ms3481×body80valid