Details

Time bar (total: 22.5s)

sample83.0ms

Algorithm
intervals
Results
31.0ms32×body1280valid
14.0ms43×body2560valid
9.0ms164×body80valid
4.0ms80×body80nan
3.0ms8×body5120valid
3.0ms16×body640valid
1.0ms7×body320valid
1.0ms6×body160valid

simplify116.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
014365
125365
246325
386325
4119325
5128325
done128325

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)
0.2b
(* (* 4.0 a) c)
1.5b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite188.0ms

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt
41×*-un-lft-identity
31×add-cube-cbrt
20×sqrt-prod
18×times-frac prod-diff
11×add-cbrt-cube add-exp-log
10×pow1 difference-of-squares
6×fma-neg associate-/l* add-log-exp
5×distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u
3×associate-/r* flip3-- associate-*r* pow-prod-down prod-exp cbrt-unprod flip--
2×sqrt-div associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp associate-*l* *-commutative div-inv
Counts
4 → 122
Calls
4 calls:
107.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)
15.0ms
(* (* 4.0 a) c)
45.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series370.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)
31.0ms
(* (* 4.0 a) c)
115.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.2s

Counts
134 → 134
Iterations

Useful iterations: done (3.2s)

IterNodesCost
021050462
153846226
2243442317
done500242267

prune801.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 10.3b

localize75.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt c)
0.6b
(cbrt c)
1.5b
(- (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
21.2b
(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
23×*-un-lft-identity
21×add-cube-cbrt
18×prod-diff
16×sqrt-prod
6×cbrt-prod fma-neg add-log-exp
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u
2×flip3-- pow1/3 sqrt-div flip-- difference-of-squares
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 84
Calls
4 calls:
1.0ms
(cbrt c)
1.0ms
(cbrt c)
61.0ms
(- (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
17.0ms
(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

series835.0ms

Counts
4 → 12
Calls
4 calls:
279.0ms
(cbrt c)
290.0ms
(cbrt c)
145.0ms
(- (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
120.0ms
(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

simplify1.9s

Counts
96 → 96
Iterations

Useful iterations: done (1.9s)

IterNodesCost
013840060
134236062
2144723290
done500023250

prune663.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 10.3b

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (sqrt 2.0)) (sqrt 2.0))
0.4b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (sqrt 2.0))
1.5b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite289.0ms

Algorithm
rewrite-expression-head
Rules
528×times-frac
456×add-sqr-sqrt
355×*-un-lft-identity
335×sqrt-prod
255×add-cube-cbrt
100×difference-of-squares
50×distribute-lft-out--
46×associate-/l*
18×prod-diff
12×associate-/r*
11×add-cbrt-cube add-exp-log
9×div-inv
6×fma-neg add-log-exp
5×pow1
4×expm1-log1p-u cbrt-undiv div-exp log1p-expm1-u
3×flip3-- div-sub flip-- associate-/l/
2×clear-num frac-2neg sqrt-div
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log
Counts
4 → 427
Calls
4 calls:
96.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (sqrt 2.0)) (sqrt 2.0))
74.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (sqrt 2.0))
61.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series759.0ms

Counts
4 → 12
Calls
4 calls:
306.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (sqrt 2.0)) (sqrt 2.0))
223.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (sqrt 2.0))
108.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
122.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts
439 → 439
Iterations

Useful iterations: done (1.6s)

IterNodesCost
0441316100
11132293955
done5000286015

prune1.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 9.9b

localize53.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (sqrt (sqrt 2.0)))
1.0b
(/ 1 (sqrt (sqrt 2.0)))
1.5b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
125×sqrt-prod
117×add-sqr-sqrt
94×*-un-lft-identity
81×times-frac
72×add-cube-cbrt
22×difference-of-squares
18×associate-/r* prod-diff
11×distribute-lft-out--
10×add-exp-log
9×associate-/l*
8×pow1 add-cbrt-cube
6×fma-neg add-log-exp
5×sqrt-pow1 pow-flip
4×expm1-log1p-u log1p-expm1-u
3×flip3-- pow1/2 div-exp flip--
2×cbrt-undiv clear-num frac-2neg sqrt-div div-inv associate-/l/
1×rem-sqrt-square rec-exp sub-neg diff-log 1-exp div-sub inv-pow
Counts
4 → 205
Calls
4 calls:
97.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (sqrt (sqrt 2.0)))
14.0ms
(/ 1 (sqrt (sqrt 2.0)))
63.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series725.0ms

Counts
4 → 10
Calls
4 calls:
495.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (sqrt (sqrt 2.0)))
0.0ms
(/ 1 (sqrt (sqrt 2.0)))
111.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
118.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.2s

Counts
215 → 215
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
0281101807
165591252
2279287612
done500187612

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 9.9b

regimes539.0ms

Accuracy

86.7% (3.2b remaining)

Error of 13.8b against oracle of 10.7b and baseline of 34.4b

bsearch133.0ms

Steps
ItersRangePoint
4
1.2765290296533779e-46
2.1214586855945932e-46
1.627160326743934e-46
7
-5.856362438573669e+138
-1.280729871585891e+137
-3.7108875578650606e+138

simplify10.0ms

Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
0341070
1421070
done421070

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.0s1094×body2560valid
803.0ms887×body1280valid
635.0ms5792×body80valid
295.0ms2874×body80nan
230.0ms467×body640valid
60.0ms108×body5120valid
54.0ms243×body320valid
17.0ms117×body160valid