Details

Time bar (total: 16.8s)

sample146.0ms

Algorithm
intervals
Results
40.0ms39×body2560valid
30.0ms180×body80valid
24.0ms29×body1280valid
12.0ms21×body640valid
11.0ms70×body80nan
3.0ms7×body320valid
0.0ms1×body160valid

simplify132.0ms

Counts
1 → 1
Iterations
IterNodes
done105
7105
6104
5102
494
377
244
125
014

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* a -4) c)
1.0b
(- (sqrt (fma b b (* (* a -4) c))) b)
1.3b
(fma b b (* (* a -4) c))
19.1b
(sqrt (fma b b (* (* a -4) c)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
18×prod-diff
16×sqrt-prod
10×pow1
9×add-cbrt-cube add-exp-log
6×fma-neg add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×difference-of-squares
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log associate-*l* *-commutative fma-udef flip-- distribute-lft-out--
Counts
4 → 90
Calls
4 calls:
17.0ms
(* (* a -4) c)
9.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
0.0ms
(fma b b (* (* a -4) c))
2.0ms
(sqrt (fma b b (* (* a -4) c)))

series449.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (* a -4) c)
180.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
81.0ms
(fma b b (* (* a -4) c))
147.0ms
(sqrt (fma b b (* (* a -4) c)))

simplify2.5s

Counts
102 → 102
Iterations
IterNodes
done5002
33058
2887
1336
0146

prune553.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (fma b b (* -4 (* a c)))) b) a)
1.0b
(- (sqrt (fma b b (* -4 (* a c)))) b)
1.3b
(fma b b (* -4 (* a c)))
19.1b
(sqrt (fma b b (* -4 (* a c))))

rewrite39.0ms

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 insert-posit16 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 → 114
Calls
4 calls:
27.0ms
(/ (- (sqrt (fma b b (* -4 (* a c)))) b) a)
8.0ms
(- (sqrt (fma b b (* -4 (* a c)))) b)
0.0ms
(fma b b (* -4 (* a c)))
1.0ms
(sqrt (fma b b (* -4 (* a c))))

series563.0ms

Counts
4 → 12
Calls
4 calls:
207.0ms
(/ (- (sqrt (fma b b (* -4 (* a c)))) b) a)
141.0ms
(- (sqrt (fma b b (* -4 (* a c)))) b)
80.0ms
(fma b b (* -4 (* a c)))
136.0ms
(sqrt (fma b b (* -4 (* a c))))

simplify2.0s

Counts
126 → 126
Iterations
IterNodes
done5000
33513
21004
1422
0179

prune507.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (sqrt (fma b b (* -4 (* a c)))) b)))
1.0b
(- (sqrt (fma b b (* -4 (* a c)))) b)
1.3b
(fma b b (* -4 (* a c)))
19.1b
(sqrt (fma b b (* -4 (* a c))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
137×add-sqr-sqrt
110×*-un-lft-identity
84×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
24×associate-/r*
18×prod-diff
15×add-exp-log
13×distribute-lft-out--
9×add-cbrt-cube associate-/r/
7×div-exp
6×pow1 fma-neg add-log-exp
5×flip3-- div-inv flip--
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/l*
2×rec-exp 1-exp
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log fma-udef pow-flip inv-pow
Counts
4 → 192
Calls
4 calls:
19.0ms
(/ 1 (/ a (- (sqrt (fma b b (* -4 (* a c)))) b)))
8.0ms
(- (sqrt (fma b b (* -4 (* a c)))) b)
0.0ms
(fma b b (* -4 (* a c)))
1.0ms
(sqrt (fma b b (* -4 (* a c))))

series407.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(/ 1 (/ a (- (sqrt (fma b b (* -4 (* a c)))) b)))
101.0ms
(- (sqrt (fma b b (* -4 (* a c)))) b)
57.0ms
(fma b b (* -4 (* a c)))
92.0ms
(sqrt (fma b b (* -4 (* a c))))

simplify1.4s

Counts
204 → 204
Iterations
IterNodes
done5000
21768
1659
0283

prune709.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 a) (- (sqrt (fma b b (* -4 (* a c)))) b))
1.0b
(- (sqrt (fma b b (* -4 (* a c)))) b)
1.3b
(fma b b (* -4 (* a c)))
19.1b
(sqrt (fma b b (* -4 (* a c))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
67×add-sqr-sqrt
56×*-un-lft-identity
54×prod-diff
51×add-cube-cbrt
35×sqrt-prod
20×distribute-rgt-in distribute-lft-in
13×associate-*l* add-exp-log
11×times-frac
9×add-cbrt-cube
7×pow1
6×fma-neg associate-*r* add-log-exp
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u difference-of-squares
3×sub-neg flip3-- flip-- unswap-sqr
2×frac-times div-exp associate-*r/ cbrt-unprod distribute-lft-out--
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 diff-log 1-exp pow-prod-down associate-*l/ *-commutative fma-udef div-inv
Counts
4 → 154
Calls
4 calls:
33.0ms
(* (/ 1 a) (- (sqrt (fma b b (* -4 (* a c)))) b))
8.0ms
(- (sqrt (fma b b (* -4 (* a c)))) b)
0.0ms
(fma b b (* -4 (* a c)))
2.0ms
(sqrt (fma b b (* -4 (* a c))))

series723.0ms

Counts
4 → 12
Calls
4 calls:
470.0ms
(* (/ 1 a) (- (sqrt (fma b b (* -4 (* a c)))) b))
103.0ms
(- (sqrt (fma b b (* -4 (* a c)))) b)
62.0ms
(fma b b (* -4 (* a c)))
88.0ms
(sqrt (fma b b (* -4 (* a c))))

simplify2.0s

Counts
166 → 166
Iterations
IterNodes
done5000
34079
21354
1599
0223

prune484.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.2b

regimes300.0ms

Accuracy

84.5% (4.3b remaining)

Error of 10.0b against oracle of 5.7b and baseline of 33.3b

bsearch177.0ms

Steps
ItersRangePoint
9
1.542649851819534e-86
4.188981380654902e-77
1.2158870426682226e-82
6
-1.2115114540629089e+151
-9.504756559616229e+149
-7.397994825724217e+150

simplify7.0ms

Iterations
IterNodes
done34
134
028

end0.0ms

sample3.4s

Algorithm
intervals
Results
803.0ms895×body1280valid
786.0ms1057×body2560valid
778.0ms5900×body80valid
361.0ms2938×body80nan
192.0ms455×body640valid
151.0ms106×body5120valid
60.0ms211×body320valid
20.0ms97×body160valid