Details

Time bar (total: 21.2s)

sample121.0ms

Algorithm
intervals
Results
25.0ms43×body2560valid
18.0ms106×body80nan
17.0ms176×body80valid
14.0ms31×body1280valid
7.0ms18×body640valid
3.0ms4×body5120valid
2.0ms7×body320valid
1.0ms4×body160valid

simplify140.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
01417
12817
27016
312716
414016
done14016

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.8b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite244.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
18×sqrt-prod
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
6×times-frac associate-/l* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 106
Calls
4 calls:
131.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
12.0ms
(- (* b b) (* (* 4.0 a) c))
67.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
31.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series465.0ms

Counts
4 → 12
Calls
4 calls:
169.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
70.0ms
(- (* b b) (* (* 4.0 a) c))
117.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.3s

Counts
118 → 118
Iterations

Useful iterations: done (4.3s)

IterNodesCost
01952476
121712096
done50011877

prune439.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize6.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune17.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 (* 2.0 a)))
0.8b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite358.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
26×*-un-lft-identity
23×add-exp-log
22×add-cube-cbrt
19×prod-diff
17×sqrt-prod
13×add-cbrt-cube
10×prod-exp
8×add-log-exp
7×pow1 fma-neg associate-*r*
6×associate-*l*
5×flip3-- flip--
4×expm1-log1p-u div-exp cbrt-unprod log1p-expm1-u difference-of-squares
3×times-frac
2×cbrt-undiv frac-times sub-neg rec-exp sqrt-div diff-log 1-exp associate-*l/ distribute-lft-out--
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 115
Calls
4 calls:
236.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 (* 2.0 a)))
9.0ms
(- (* b b) (* (* 4.0 a) c))
95.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series451.0ms

Counts
4 → 12
Calls
4 calls:
169.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 (* 2.0 a)))
59.0ms
(- (* b b) (* (* 4.0 a) c))
119.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
104.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.7s

Counts
127 → 127
Iterations

Useful iterations: done (4.7s)

IterNodesCost
02212739
122472239
done50011980

prune473.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 5.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.8b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite259.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
18×sqrt-prod
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
6×times-frac associate-/l* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 106
Calls
4 calls:
133.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
10.0ms
(- (* b b) (* (* 4.0 a) c))
92.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series434.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
54.0ms
(- (* b b) (* (* 4.0 a) c))
129.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
95.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.4s

Counts
118 → 118
Iterations

Useful iterations: done (4.4s)

IterNodesCost
01952476
121712096
done50011877

prune526.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 5.3b

regimes216.0ms

Accuracy

83.4% (5.6b remaining)

Error of 11.6b against oracle of 6.0b and baseline of 39.8b

bsearch141.0ms

Steps
ItersRangePoint
6
1.6855676195581707e-170
7.565529323099765e-170
7.455592343308264e-170
6
-2.3823986784004295e+101
-2.936095699822542e+100
-1.555632367828989e+101

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02840
13638
done3638

end0.0ms

sample3.4s

Algorithm
intervals
Results
985.0ms1074×body2560valid
597.0ms3010×body80nan
583.0ms5876×body80valid
470.0ms885×body1280valid
141.0ms492×body640valid
59.0ms107×body5120valid
45.0ms218×body320valid
12.0ms92×body160valid