Details

Time bar (total: 21.1s)

sample95.0ms

Algorithm
intervals
Results
18.0ms135×body160valid
16.0ms256×body80nan
14.0ms512×pre80true
9.0ms48×body320valid
5.0ms73×body80valid

simplify89.0ms

Counts
1 → 1
Iterations
IterNodes
done128
5128
4119
386
246
125
014

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (fma (- a) (* 4.0 c) (* b b)))
0.2b
(fma (- a) (* 4.0 c) (* b b))
0.2b
(/ (- (sqrt (fma (- a) (* 4.0 c) (* b b))) b) a)
34.7b
(- (sqrt (fma (- a) (* 4.0 c) (* b b))) b)

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
18×times-frac prod-diff
10×difference-of-squares
6×add-cbrt-cube fma-neg add-exp-log associate-/l* add-log-exp
5×pow1 distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u
3×associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp fma-udef div-inv
Counts
4 → 110
Calls
4 calls:
2.0ms
(sqrt (fma (- a) (* 4.0 c) (* b b)))
0.0ms
(fma (- a) (* 4.0 c) (* b b))
22.0ms
(/ (- (sqrt (fma (- a) (* 4.0 c) (* b b))) b) a)
12.0ms
(- (sqrt (fma (- a) (* 4.0 c) (* b b))) b)

series483.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(sqrt (fma (- a) (* 4.0 c) (* b b)))
71.0ms
(fma (- a) (* 4.0 c) (* b b))
183.0ms
(/ (- (sqrt (fma (- a) (* 4.0 c) (* b b))) b) a)
129.0ms
(- (sqrt (fma (- a) (* 4.0 c) (* b b))) b)

simplify744.0ms

Counts
122 → 122
Iterations
IterNodes
done5001
21064
1336
0152

prune568.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ b (sqrt (fma 4.0 (* c (- a)) (* b b))))
0.2b
(fma 4.0 (* c (- a)) (* b b))
0.2b
(/ (/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma 4.0 (* c (- a)) (* b b))))) a)
0.3b
(/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma 4.0 (* c (- a)) (* b b)))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
99×*-un-lft-identity
65×add-sqr-sqrt add-cube-cbrt
21×associate-/l*
17×distribute-lft-out
11×add-cbrt-cube add-exp-log
10×associate-/r/
7×associate-/r*
6×flip3-+ flip-+ div-inv add-log-exp
4×expm1-log1p-u pow1 cbrt-undiv div-exp log1p-expm1-u
3×fma-def
2×clear-num frac-2neg
1×+-commutative sum-log fma-udef associate-/l/
Counts
4 → 154
Calls
4 calls:
10.0ms
(+ b (sqrt (fma 4.0 (* c (- a)) (* b b))))
0.0ms
(fma 4.0 (* c (- a)) (* b b))
39.0ms
(/ (/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma 4.0 (* c (- a)) (* b b))))) a)
12.0ms
(/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma 4.0 (* c (- a)) (* b b)))))

series842.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(+ b (sqrt (fma 4.0 (* c (- a)) (* b b))))
81.0ms
(fma 4.0 (* c (- a)) (* b b))
351.0ms
(/ (/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma 4.0 (* c (- a)) (* b b))))) a)
292.0ms
(/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma 4.0 (* c (- a)) (* b b)))))

simplify1.1s

Counts
166 → 166
Iterations
IterNodes
done5000
22541
1605
0251

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (cbrt (pow (fma 4.0 (* (- c) a) (pow b 2)) 3))))) a)
0.3b
(/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (cbrt (pow (fma 4.0 (* (- c) a) (pow b 2)) 3)))))
0.5b
(cbrt (pow (fma 4.0 (* (- c) a) (pow b 2)) 3))
0.7b
(pow (fma 4.0 (* (- c) a) (pow b 2)) 3)

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
102×*-un-lft-identity
70×add-sqr-sqrt add-cube-cbrt
21×associate-/l*
16×distribute-lft-out
12×cbrt-prod add-cbrt-cube add-exp-log
10×associate-/r/
7×associate-/r*
6×unpow-prod-down cube-prod div-inv
5×pow1 flip3-+ flip-+
4×expm1-log1p-u cbrt-undiv div-exp log1p-expm1-u add-log-exp
3×pow-unpow
2×cube-mult clear-num frac-2neg unpow3 sqr-pow
1×pow-to-exp pow-pow pow1/3 pow-exp rem-cbrt-cube rem-cube-cbrt associate-/l/
Counts
4 → 175
Calls
4 calls:
58.0ms
(/ (/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (cbrt (pow (fma 4.0 (* (- c) a) (pow b 2)) 3))))) a)
24.0ms
(/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (cbrt (pow (fma 4.0 (* (- c) a) (pow b 2)) 3)))))
2.0ms
(cbrt (pow (fma 4.0 (* (- c) a) (pow b 2)) 3))
2.0ms
(pow (fma 4.0 (* (- c) a) (pow b 2)) 3)

series977.0ms

Counts
4 → 12
Calls
4 calls:
359.0ms
(/ (/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (cbrt (pow (fma 4.0 (* (- c) a) (pow b 2)) 3))))) a)
304.0ms
(/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (cbrt (pow (fma 4.0 (* (- c) a) (pow b 2)) 3)))))
85.0ms
(cbrt (pow (fma 4.0 (* (- c) a) (pow b 2)) 3))
228.0ms
(pow (fma 4.0 (* (- c) a) (pow b 2)) 3)

simplify2.2s

Counts
187 → 187
Iterations
IterNodes
done5000
23888
1736
0287

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize71.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sqrt (fma (- 4.0) (* a c) (pow b 2))) 3)
0.4b
(pow (sqrt (fma (- 4.0) (* a c) (pow b 2))) 3)
0.5b
(cbrt (* (pow (sqrt (fma (- 4.0) (* a c) (pow b 2))) 3) (pow (sqrt (fma (- 4.0) (* a c) (pow b 2))) 3)))
0.5b
(* (pow (sqrt (fma (- 4.0) (* a c) (pow b 2))) 3) (pow (sqrt (fma (- 4.0) (* a c) (pow b 2))) 3))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
118×add-sqr-sqrt
80×unpow-prod-down cube-prod sqrt-prod
42×*-un-lft-identity add-cube-cbrt
38×swap-sqr
36×unswap-sqr
18×associate-*r* associate-*l* add-exp-log sqr-pow
9×prod-exp
8×pow-to-exp pow1 add-cbrt-cube pow-exp
6×cube-mult pow-unpow pow-pow unpow3
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×sqrt-pow1 pow1/2 pow-prod-down sqrt-pow2 rem-cube-cbrt
1×cbrt-prod pow2 pow1/3 pow-sqr *-commutative pow-prod-up rem-cbrt-cube cbrt-unprod
Counts
4 → 214
Calls
4 calls:
8.0ms
(pow (sqrt (fma (- 4.0) (* a c) (pow b 2))) 3)
3.0ms
(pow (sqrt (fma (- 4.0) (* a c) (pow b 2))) 3)
9.0ms
(cbrt (* (pow (sqrt (fma (- 4.0) (* a c) (pow b 2))) 3) (pow (sqrt (fma (- 4.0) (* a c) (pow b 2))) 3)))
26.0ms
(* (pow (sqrt (fma (- 4.0) (* a c) (pow b 2))) 3) (pow (sqrt (fma (- 4.0) (* a c) (pow b 2))) 3))

series2.3s

Counts
4 → 12
Calls
4 calls:
1.2s
(pow (sqrt (fma (- 4.0) (* a c) (pow b 2))) 3)
779.0ms
(pow (sqrt (fma (- 4.0) (* a c) (pow b 2))) 3)
94.0ms
(cbrt (* (pow (sqrt (fma (- 4.0) (* a c) (pow b 2))) 3) (pow (sqrt (fma (- 4.0) (* a c) (pow b 2))) 3)))
221.0ms
(* (pow (sqrt (fma (- 4.0) (* a c) (pow b 2))) 3) (pow (sqrt (fma (- 4.0) (* a c) (pow b 2))) 3))

simplify2.9s

Counts
226 → 226
Iterations
IterNodes
done5000
22824
1378
0133

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes351.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done37
337
236
131
022

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.1s16215×pre80true
865.0ms4804×body160valid
757.0ms8215×body80nan
380.0ms1294×body320valid
181.0ms1902×body80valid