Details

Time bar (total: 22.5s)

sample77.0ms

Algorithm
intervals
Results
15.0ms8×body5120valid
15.0ms43×body2560valid
10.0ms164×body80valid
8.0ms32×body1280valid
6.0ms80×body80nan
3.0ms16×body640valid
1.0ms7×body320valid
1.0ms6×body160valid

simplify86.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
014365
125365
246325
386325
4119325
5128325
done128325

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize32.0ms

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)))

rewrite167.0ms

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:
91.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)
14.0ms
(* (* 4.0 a) c)
47.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series335.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)
30.0ms
(* (* 4.0 a) c)
115.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
78.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.3s

Counts
134 → 134
Iterations

Useful iterations: done (3.3s)

IterNodesCost
021050462
153846226
2243442317
done500242267

prune859.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 10.3b

localize85.0ms

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))))

rewrite105.0ms

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:
2.0ms
(cbrt c)
1.0ms
(cbrt c)
80.0ms
(- (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))))

series840.0ms

Counts
4 → 12
Calls
4 calls:
315.0ms
(cbrt c)
290.0ms
(cbrt c)
120.0ms
(- (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
115.0ms
(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

simplify1.7s

Counts
96 → 96
Iterations

Useful iterations: done (1.7s)

IterNodesCost
013840060
134236062
2144723290
done500023250

prune672.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 10.3b

localize63.0ms

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)))

rewrite290.0ms

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:
88.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (sqrt 2.0)) (sqrt 2.0))
83.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (sqrt 2.0))
56.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series778.0ms

Counts
4 → 12
Calls
4 calls:
316.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (sqrt 2.0)) (sqrt 2.0))
248.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (sqrt 2.0))
97.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
116.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts
439 → 439
Iterations

Useful iterations: done (1.5s)

IterNodesCost
0441316100
11132293955
done5000286015

prune1.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 9.9b

localize47.0ms

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)))

rewrite239.0ms

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:
120.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (sqrt (sqrt 2.0)))
13.0ms
(/ 1 (sqrt (sqrt 2.0)))
81.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series612.0ms

Counts
4 → 10
Calls
4 calls:
427.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (sqrt (sqrt 2.0)))
0.0ms
(/ 1 (sqrt (sqrt 2.0)))
102.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
82.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.2s

Counts
215 → 215
Iterations

Useful iterations: 2 (947.0ms)

IterNodesCost
0281101807
165591252
2279287612
done500187612

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 9.9b

regimes595.0ms

Accuracy

86.7% (3.2b remaining)

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

bsearch120.0ms

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

simplify9.0ms

Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
0341070
1421070
done421070

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.1s5792×body80valid
814.0ms887×body1280valid
537.0ms1094×body2560valid
352.0ms2874×body80nan
181.0ms467×body640valid
92.0ms243×body320valid
60.0ms108×body5120valid
17.0ms117×body160valid