Details

Time bar (total: 16.5s)

sample99.0ms

Algorithm
intervals
Results
31.0ms25×body2560valid
17.0ms45×body1280valid
16.0ms184×body80valid
5.0ms69×body80nan
5.0ms17×body640valid
2.0ms8×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

simplify119.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.2b
(- (* b b) (* (* 4.0 a) c))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite323.0ms

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:
188.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
88.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
19.0ms
(- (* b b) (* (* 4.0 a) c))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series484.0ms

Counts
4 → 12
Calls
4 calls:
168.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
126.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
76.0ms
(- (* b b) (* (* 4.0 a) c))
113.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts
118 → 118
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01952476
14802169
214411861
done50001789

prune552.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 (* 2.0 a)))
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.2b
(- (* b b) (* (* 4.0 a) c))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite404.0ms

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:
240.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 (* 2.0 a)))
109.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
18.0ms
(- (* b b) (* (* 4.0 a) c))
26.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series478.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 (* 2.0 a)))
132.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
61.0ms
(- (* b b) (* (* 4.0 a) c))
110.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
127 → 127
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02212739
15362324
216871964
done50001892

prune511.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.2b
(- (* b b) (* (* 4.0 a) c))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite261.0ms

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:
149.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
83.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series493.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
125.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
73.0ms
(- (* b b) (* (* 4.0 a) c))
123.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts
118 → 118
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01952476
14802169
214411861
done50001789

prune492.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.2b
(- (* b b) (* (* 4.0 a) c))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
60×times-frac
50×*-un-lft-identity
40×add-cube-cbrt
25×add-exp-log
20×sqrt-prod
19×prod-diff
13×add-cbrt-cube
12×div-exp associate-/r*
10×difference-of-squares
9×associate-/r/
8×add-log-exp
7×flip3-- fma-neg flip--
6×pow1
5×cbrt-undiv div-inv distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u
3×rec-exp 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num cbrt-unprod inv-pow
Counts
4 → 152
Calls
4 calls:
89.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
65.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(- (* b b) (* (* 4.0 a) c))
26.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series522.0ms

Counts
4 → 12
Calls
4 calls:
233.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
113.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
86.0ms
(- (* b b) (* (* 4.0 a) c))
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
164 → 164
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02614025
15873484
216523082
done50012938

prune480.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.3b

regimes304.0ms

Accuracy

84.3% (4.5b remaining)

Error of 10.0b against oracle of 5.5b and baseline of 34.1b

bsearch222.0ms

Steps
ItersRangePoint
7
1.5383510854529177e-107
7.914847206339754e-106
4.718890261991469e-106
10
-2.386196042261592e+160
-1.0923850232644114e+143
-1.119811545308531e+143

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
02840
13538
done3538

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.3s1056×body2560valid
1.2s5848×body80valid
442.0ms922×body1280valid
222.0ms2941×body80nan
190.0ms479×body640valid
166.0ms113×body5120valid
50.0ms208×body320valid
16.0ms109×body160valid