Details

Time bar (total: 19.4s)

sample163.0ms

Algorithm
intervals
Results
42.0ms39×body2560valid
39.0ms180×body80valid
27.0ms29×body1280valid
14.0ms21×body640valid
12.0ms70×body80nan
4.0ms7×body320valid
0.0ms1×body160valid

simplify147.0ms

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize38.0ms

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)))

rewrite43.0ms

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:
25.0ms
(* (* a -4) c)
14.0ms
(- (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)))

series312.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (* a -4) c)
128.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
66.0ms
(fma b b (* (* a -4) c))
95.0ms
(sqrt (fma b b (* (* a -4) c)))

simplify2.1s

Counts
102 → 102
Iterations
IterNodes
done5002
33058
2887
1336
0146

prune497.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.1b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

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:
26.0ms
(/ (- (sqrt (fma b b (* a (* -4 c)))) b) a)
15.0ms
(- (sqrt (fma b b (* a (* -4 c)))) b)
0.0ms
(fma b b (* a (* -4 c)))
3.0ms
(sqrt (fma b b (* a (* -4 c))))

series468.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(/ (- (sqrt (fma b b (* a (* -4 c)))) b) a)
149.0ms
(- (sqrt (fma b b (* a (* -4 c)))) b)
62.0ms
(fma b b (* a (* -4 c)))
122.0ms
(sqrt (fma b b (* a (* -4 c))))

simplify2.5s

Counts
126 → 126
Iterations
IterNodes
done5001
33501
21002
1424
0180

prune630.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.2b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

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 (* a (* -4 c)))) b)))
8.0ms
(- (sqrt (fma b b (* a (* -4 c)))) b)
0.0ms
(fma b b (* a (* -4 c)))
1.0ms
(sqrt (fma b b (* a (* -4 c))))

series501.0ms

Counts
4 → 12
Calls
4 calls:
215.0ms
(/ 1 (/ a (- (sqrt (fma b b (* a (* -4 c)))) b)))
114.0ms
(- (sqrt (fma b b (* a (* -4 c)))) b)
68.0ms
(fma b b (* a (* -4 c)))
105.0ms
(sqrt (fma b b (* a (* -4 c))))

simplify2.2s

Counts
204 → 204
Iterations
IterNodes
done5001
21831
1661
0284

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.2b

localize47.0ms

Local error

Found 4 expressions with local error:

1.3b
(fma b b (* a (* -4 c)))
19.1b
(sqrt (fma b b (* a (* -4 c))))
19.1b
(sqrt (fma b b (* a (* -4 c))))
23.4b
(fma (sqrt (sqrt (fma b b (* a (* -4 c))))) (sqrt (sqrt (fma b b (* a (* -4 c))))) (- b))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 54
Calls
4 calls:
0.0ms
(fma b b (* a (* -4 c)))
1.0ms
(sqrt (fma b b (* a (* -4 c))))
1.0ms
(sqrt (fma b b (* a (* -4 c))))
0.0ms
(fma (sqrt (sqrt (fma b b (* a (* -4 c))))) (sqrt (sqrt (fma b b (* a (* -4 c))))) (- b))

series423.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(fma b b (* a (* -4 c)))
96.0ms
(sqrt (fma b b (* a (* -4 c))))
122.0ms
(sqrt (fma b b (* a (* -4 c))))
141.0ms
(fma (sqrt (sqrt (fma b b (* a (* -4 c))))) (sqrt (sqrt (fma b b (* a (* -4 c))))) (- b))

simplify2.5s

Counts
66 → 66
Iterations
IterNodes
done5008
42208
3695
2264
1122
067

prune414.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.2b

regimes439.0ms

Accuracy

84.5% (4.3b remaining)

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

bsearch217.0ms

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

simplify13.0ms

Iterations
IterNodes
done34
134
028

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.0s1057×body2560valid
993.0ms5900×body80valid
751.0ms895×body1280valid
512.0ms2938×body80nan
447.0ms211×body320valid
275.0ms455×body640valid
104.0ms106×body5120valid
26.0ms97×body160valid