Details

Time bar (total: 18.0s)

sample104.0ms

Algorithm
intervals
Results
35.0ms135×body160valid
15.0ms256×body80nan
12.0ms512×pre80true
8.0ms48×body320valid
4.0ms73×body80valid

simplify77.0ms

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

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.3b

localize35.0ms

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)

rewrite69.0ms

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))
42.0ms
(/ (- (sqrt (fma (- a) (* 4.0 c) (* b b))) b) a)
18.0ms
(- (sqrt (fma (- a) (* 4.0 c) (* b b))) b)

series549.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(sqrt (fma (- a) (* 4.0 c) (* b b)))
103.0ms
(fma (- a) (* 4.0 c) (* b b))
178.0ms
(/ (- (sqrt (fma (- a) (* 4.0 c) (* b b))) b) a)
142.0ms
(- (sqrt (fma (- a) (* 4.0 c) (* b b))) b)

simplify795.0ms

Counts
122 → 122
Iterations
IterNodes
done5001
21064
1336
0152

prune573.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize45.0ms

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)))))

rewrite86.0ms

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:
21.0ms
(+ b (sqrt (fma 4.0 (* c (- a)) (* b b))))
1.0ms
(fma 4.0 (* c (- a)) (* b b))
41.0ms
(/ (/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma 4.0 (* c (- a)) (* b b))))) a)
11.0ms
(/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma 4.0 (* c (- a)) (* b b)))))

series890.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(+ b (sqrt (fma 4.0 (* c (- a)) (* b b))))
87.0ms
(fma 4.0 (* c (- a)) (* b b))
336.0ms
(/ (/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma 4.0 (* c (- a)) (* b b))))) a)
353.0ms
(/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma 4.0 (* c (- a)) (* b b)))))

simplify1.3s

Counts
166 → 166
Iterations
IterNodes
done5000
22541
1605
0251

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-/l*
11×add-cbrt-cube add-exp-log
6×associate-/r* div-inv
4×expm1-log1p-u pow1 cbrt-undiv div-exp log1p-expm1-u add-log-exp
2×clear-num frac-2neg fma-udef
1×associate-/l/
Counts
4 → 121
Calls
4 calls:
0.0ms
(fma 4.0 (* c (- a)) (* b b))
0.0ms
(fma (sqrt b) (sqrt b) (sqrt (fma 4.0 (* c (- a)) (* b b))))
8.0ms
(/ (/ (fma (- (* a 4.0)) c 0) (fma (sqrt b) (sqrt b) (sqrt (fma 4.0 (* c (- a)) (* b b))))) a)
4.0ms
(/ (fma (- (* a 4.0)) c 0) (fma (sqrt b) (sqrt b) (sqrt (fma 4.0 (* c (- a)) (* b b)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
108.0ms
(fma 4.0 (* c (- a)) (* b b))
220.0ms
(fma (sqrt b) (sqrt b) (sqrt (fma 4.0 (* c (- a)) (* b b))))
414.0ms
(/ (/ (fma (- (* a 4.0)) c 0) (fma (sqrt b) (sqrt b) (sqrt (fma 4.0 (* c (- a)) (* b b))))) a)
354.0ms
(/ (fma (- (* a 4.0)) c 0) (fma (sqrt b) (sqrt b) (sqrt (fma 4.0 (* c (- a)) (* b b)))))

simplify1.3s

Counts
133 → 133
Iterations
IterNodes
done5000
22477
1560
0234

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
10×add-sqr-sqrt
9×add-cbrt-cube add-exp-log add-cube-cbrt
6×fma-def sqrt-prod add-log-exp
5×pow1
4×expm1-log1p-u associate-/r* times-frac log1p-expm1-u
3×distribute-lft-out
2×cbrt-undiv flip3-+ div-exp associate-/r/ flip-+
1×distribute-lft-neg-out +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 prod-exp distribute-frac-neg cbrt-unprod fma-udef div-inv associate-/l*
Counts
4 → 73
Calls
4 calls:
3.0ms
(sqrt (fma (- a) (* 4.0 c) (* b b)))
30.0ms
(/ (* (- 4.0) c) (+ (sqrt (fma (- a) (* 4.0 c) (* b b))) b))
7.0ms
(+ (sqrt (fma (- a) (* 4.0 c) (* b b))) b)
0.0ms
(fma (- a) (* 4.0 c) (* b b))

series663.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(sqrt (fma (- a) (* 4.0 c) (* b b)))
319.0ms
(/ (* (- 4.0) c) (+ (sqrt (fma (- a) (* 4.0 c) (* b b))) b))
140.0ms
(+ (sqrt (fma (- a) (* 4.0 c) (* b b))) b)
80.0ms
(fma (- a) (* 4.0 c) (* b b))

simplify865.0ms

Counts
85 → 85
Iterations
IterNodes
done5001
21554
1306
0120

prune450.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes269.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.8s

Iterations
IterNodes
done5000
133280
121728
11944
10544
9336
8224
7160
6120
587
452
337
233
127
020

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.3s4804×body160valid
1.3s8215×body80nan
561.0ms16215×pre80true
336.0ms1294×body320valid
177.0ms1902×body80valid