Details

Time bar (total: 14.3s)

sample141.0ms

Algorithm
intervals
Results
47.0ms33×body2560valid
25.0ms185×body80valid
23.0ms32×body1280valid
12.0ms97×body80nan
6.0ms12×body640valid
4.0ms5×body5120valid
3.0ms7×body320valid
1.0ms4×body160valid

simplify85.0ms

Counts
1 → 1
Iterations
IterNodes
done93
793
692
590
482
366
240
121
012

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* 3 a) c)
0.6b
(- (* b b) (* (* 3 a) c))
1.1b
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
22.2b
(sqrt (- (* b b) (* (* 3 a) c)))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-cbrt-cube add-exp-log
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod insert-posit16
3×flip3-- associate-*r* pow-prod-down prod-exp cbrt-unprod flip--
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 → 64
Calls
4 calls:
18.0ms
(* (* 3 a) c)
16.0ms
(- (* b b) (* (* 3 a) c))
58.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
8.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

series270.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (* 3 a) c)
48.0ms
(- (* b b) (* (* 3 a) c))
111.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
87.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.1s

Counts
76 → 76
Iterations
IterNodes
done2002
32002
2910
1297
0123

prune502.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 11.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 3 a) c))
13.3b
(- (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))) b)
22.2b
(sqrt (- (* b b) (* (* 3 a) c)))
22.2b
(sqrt (- (* b b) (* (* 3 a) c)))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×add-log-exp
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 flip--
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log
1×difference-of-squares
Counts
4 → 59
Calls
4 calls:
7.0ms
(- (* b b) (* (* 3 a) c))
65.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))) b)
12.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
7.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

series397.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (* b b) (* (* 3 a) c))
115.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))) b)
99.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
104.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.1s

Counts
71 → 71
Iterations
IterNodes
done2009
32009
2723
1232
096

prune505.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 11.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 3 a) c))
13.3b
(+ (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))) (- b))
22.2b
(sqrt (- (* b b) (* (* 3 a) c)))
22.2b
(sqrt (- (* b b) (* (* 3 a) c)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×add-cbrt-cube sqrt-div add-exp-log insert-posit16
3×flip3-- flip--
2×rem-sqrt-square sum-log sqrt-pow1 pow1/2
1×neg-sub0 +-commutative associate-+r- sub-neg flip3-+ diff-log unsub-neg neg-log flip-+
Counts
4 → 61
Calls
4 calls:
8.0ms
(- (* b b) (* (* 3 a) c))
39.0ms
(+ (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))) (- b))
10.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
17.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

series411.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (* b b) (* (* 3 a) c))
108.0ms
(+ (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))) (- b))
126.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
95.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

simplify931.0ms

Counts
73 → 73
Iterations
IterNodes
done2001
32001
2871
1258
099

prune493.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 11.3b

localize95.0ms

Local error

Found 4 expressions with local error:

22.2b
(sqrt (* (* (cbrt (- (* b b) (* (* 3 a) c))) (cbrt (- (* b b) (* (* 3 a) c)))) (cbrt (- (* b b) (* (* 3 a) c)))))
22.9b
(cbrt (- (* b b) (* (* 3 a) c)))
22.9b
(cbrt (- (* b b) (* (* 3 a) c)))
22.9b
(cbrt (- (* b b) (* (* 3 a) c)))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
60×cbrt-div
30×flip3-- flip--
28×frac-times
26×sqrt-div
24×pow1
15×sqrt-pow1
14×associate-*l/
12×pow1/3
9×cbrt-prod pow-prod-up
8×associate-*r/
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow-plus
5×pow-prod-down
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 93
Calls
4 calls:
90.0ms
(sqrt (* (* (cbrt (- (* b b) (* (* 3 a) c))) (cbrt (- (* b b) (* (* 3 a) c)))) (cbrt (- (* b b) (* (* 3 a) c)))))
6.0ms
(cbrt (- (* b b) (* (* 3 a) c)))
18.0ms
(cbrt (- (* b b) (* (* 3 a) c)))
10.0ms
(cbrt (- (* b b) (* (* 3 a) c)))

series497.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(sqrt (* (* (cbrt (- (* b b) (* (* 3 a) c))) (cbrt (- (* b b) (* (* 3 a) c)))) (cbrt (- (* b b) (* (* 3 a) c)))))
115.0ms
(cbrt (- (* b b) (* (* 3 a) c)))
113.0ms
(cbrt (- (* b b) (* (* 3 a) c)))
166.0ms
(cbrt (- (* b b) (* (* 3 a) c)))

simplify1.2s

Counts
105 → 105
Iterations
IterNodes
done2002
32002
2730
1350
0188

prune649.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 11.3b

regimes620.0ms

Accuracy

85.5% (3.0b remaining)

Error of 15.2b against oracle of 12.2b and baseline of 33.0b

bsearch240.0ms

Steps
ItersRangePoint
10
1.6102415927742825e-37
1.759369773493009e-27
2.044680244795305e-37
9
-2.1334120614975372e+160
-5.220116064693227e+150
-1.3229656994274289e+154

simplify5.0ms

Iterations
IterNodes
done32
132
027

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.4s1105×body2560valid
1.0s843×body1280valid
830.0ms5935×body80valid
514.0ms2940×body80nan
272.0ms437×body640valid
102.0ms120×body5120valid
80.0ms210×body320valid
26.0ms111×body160valid