Details

Time bar (total: 9.5s)

sample41.0ms

Algorithm
intervals
Results
8.0ms37×body2560valid
6.0ms177×body80valid
5.0ms92×body80nan
5.0ms31×body1280valid
2.0ms16×body640valid
1.0ms5×body5120valid
1.0ms6×body320valid
0.0ms3×body160valid

simplify54.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01217
12217
24216
38216
410016
510816
done10816

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
0.4b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
0.8b
(- (* b b) (* (* 3.0 a) c))
27.3b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite77.0ms

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:
44.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
22.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
3.0ms
(- (* b b) (* (* 3.0 a) c))
5.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series288.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
76.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
42.0ms
(- (* b b) (* (* 3.0 a) c))
68.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify743.0ms

Counts
118 → 118
Iterations

Useful iterations: done (740.0ms)

IterNodesCost
01952476
14792171
214931863
done50001839

prune281.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.4b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
0.8b
(- (* b b) (* (* 3.0 a) c))
27.3b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
19×prod-diff
16×sqrt-prod
10×pow1
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
4×expm1-log1p-u log1p-expm1-u
3×flip3-- associate-*r* pow-prod-down prod-exp flip-- cbrt-unprod
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 94
Calls
4 calls:
6.0ms
(* (* 3.0 a) c)
22.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
3.0ms
(- (* b b) (* (* 3.0 a) c))
5.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series206.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (* 3.0 a) c)
75.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
44.0ms
(- (* b b) (* (* 3.0 a) c))
67.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.3s

Counts
106 → 106
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01611863
13691562
212041333
done50001246

prune231.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (* 3.0 a))
0.4b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
0.8b
(- (* b b) (* (* 3.0 a) c))
27.3b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
23×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
16×sqrt-prod
15×add-exp-log
9×add-cbrt-cube
8×pow1 add-log-exp
7×fma-neg
4×expm1-log1p-u div-exp log1p-expm1-u
3×flip3-- times-frac prod-exp flip-- associate-/l*
2×cbrt-undiv sub-neg rec-exp pow-flip sqrt-div diff-log 1-exp difference-of-squares
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down clear-num associate-/r* cbrt-unprod div-inv distribute-lft-out-- inv-pow
Counts
4 → 104
Calls
4 calls:
4.0ms
(/ 1 (* 3.0 a))
22.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
3.0ms
(- (* b b) (* (* 3.0 a) c))
5.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series207.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(/ 1 (* 3.0 a))
72.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
46.0ms
(- (* b b) (* (* 3.0 a) c))
69.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.2s

Counts
116 → 116
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
01781913
13971595
211531358
348491271
done50001271

prune255.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ 1 3.0) a)
0.4b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
0.8b
(- (* b b) (* (* 3.0 a) c))
27.3b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
66×add-sqr-sqrt
63×*-un-lft-identity
61×add-cube-cbrt
19×prod-diff
16×sqrt-prod
13×add-exp-log associate-/l*
9×add-cbrt-cube
8×add-log-exp
7×fma-neg
6×div-exp
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv flip3-- associate-/r* flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square rec-exp frac-2neg sqrt-pow1 pow1/2 1-exp clear-num associate-/l/ distribute-lft-out--
Counts
4 → 148
Calls
4 calls:
6.0ms
(/ (/ 1 3.0) a)
22.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
3.0ms
(- (* b b) (* (* 3.0 a) c))
5.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series212.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(/ (/ 1 3.0) a)
78.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
42.0ms
(- (* b b) (* (* 3.0 a) c))
71.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.3s

Counts
160 → 160
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02732575
16052183
215871901
done50001814

prune308.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 4.0b

regimes504.0ms

Accuracy

85% (4.3b remaining)

Error of 9.9b against oracle of 5.7b and baseline of 33.9b

bsearch120.0ms

Steps
ItersRangePoint
11
4.489865195692553e-133
5.932607888300091e-106
1.961082134151116e-106
8
-6.10058349091927e+155
-9.408528429616011e+151
-7.93152454634662e+153

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02942
13742
done3742

end0.0ms

sample1.1s

Algorithm
intervals
Results
225.0ms5917×body80valid
224.0ms1046×body2560valid
150.0ms862×body1280valid
100.0ms2864×body80nan
60.0ms451×body640valid
32.0ms113×body5120valid
23.0ms230×body320valid
7.0ms101×body160valid