Details

Time bar (total: 9.2s)

sample37.0ms

Algorithm
intervals
Results
8.0ms39×body2560valid
6.0ms36×body1280valid
6.0ms165×body80valid
3.0ms86×body80nan
2.0ms13×body640valid
1.0ms8×body320valid
1.0ms2×body5120valid
0.0ms4×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: 33.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
1.0b
(- (* b b) (* (* 3.0 a) c))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.6b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
10×pow1 add-sqr-sqrt fma-def add-log-exp
9×add-exp-log add-cube-cbrt add-cbrt-cube
4×expm1-log1p-u distribute-rgt-neg-in log1p-expm1-u
3×distribute-lft-neg-in associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×flip3-- sqrt-div sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log associate-*l* prod-diff neg-log *-commutative flip-+
Counts
4 → 80
Calls
4 calls:
6.0ms
(* (* 3.0 a) c)
3.0ms
(- (* b b) (* (* 3.0 a) c))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series207.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (* 3.0 a) c)
42.0ms
(- (* b b) (* (* 3.0 a) c))
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
69.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.3s

Counts
92 → 92
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01351109
13341006
21204900
done5000890

prune239.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
1.0b
(- (* b b) (* (* 3.0 a) c))
1.4b
(- b (sqrt (- (* b b) (* (* 3.0 a) c))))
22.6b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
21×*-un-lft-identity
19×add-cube-cbrt prod-diff
13×sqrt-prod
10×pow1
9×add-exp-log add-cbrt-cube
8×add-log-exp
4×expm1-log1p-u fma-neg 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 → 91
Calls
4 calls:
6.0ms
(* (* 3.0 a) c)
3.0ms
(- (* b b) (* (* 3.0 a) c))
9.0ms
(- b (sqrt (- (* b b) (* (* 3.0 a) c))))
5.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series210.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (* 3.0 a) c)
43.0ms
(- (* b b) (* (* 3.0 a) c))
76.0ms
(- b (sqrt (- (* b b) (* (* 3.0 a) c))))
70.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.3s

Counts
103 → 103
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01642550
13681887
212461557
done50001549

prune252.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.3b

localize14.0ms

Local error

Found 4 expressions with local error:

15.3b
(cbrt (* (* 3.0 a) c))
15.3b
(cbrt (* (* 3.0 a) c))
15.3b
(cbrt (* (* 3.0 a) c))
22.6b
(sqrt (- (* b b) (* (* (cbrt (* (* 3.0 a) c)) (cbrt (* (* 3.0 a) c))) (cbrt (* (* 3.0 a) c)))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-prod pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
Counts
4 → 50
Calls
4 calls:
5.0ms
(cbrt (* (* 3.0 a) c))
5.0ms
(cbrt (* (* 3.0 a) c))
5.0ms
(cbrt (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* (cbrt (* (* 3.0 a) c)) (cbrt (* (* 3.0 a) c))) (cbrt (* (* 3.0 a) c)))))

series418.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(cbrt (* (* 3.0 a) c))
95.0ms
(cbrt (* (* 3.0 a) c))
97.0ms
(cbrt (* (* 3.0 a) c))
130.0ms
(sqrt (- (* b b) (* (* (cbrt (* (* 3.0 a) c)) (cbrt (* (* 3.0 a) c))) (cbrt (* (* 3.0 a) c)))))

simplify890.0ms

Counts
62 → 62
Iterations

Useful iterations: done (888.0ms)

IterNodesCost
0921075
1217987
2556590
31888575
done5001574

prune247.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 14.3b

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
1.4b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
22.6b
(sqrt (- (* b b) (* (* 3.0 a) c)))
22.6b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
36×prod-diff
34×add-cube-cbrt
32×sqrt-prod
12×fma-neg
8×add-log-exp
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u difference-of-squares
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 116
Calls
4 calls:
23.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
25.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
5.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
5.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series299.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
79.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
68.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
71.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.7s

Counts
128 → 128
Iterations

Useful iterations: 3 (636.0ms)

IterNodesCost
01132856
12622310
27561948
328771774
done50011774

prune332.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 14.3b

regimes282.0ms

Accuracy

96.1% (0.8b remaining)

Error of 13.0b against oracle of 12.2b and baseline of 33.7b

bsearch179.0ms

Steps
ItersRangePoint
7
2.703506994090381e+152
2.308573696785045e+154
2.482156797684751e+153
9
2.365685850767504e-168
1.2053288471691685e-161
5.896946928525934e-166
10
-2.699314103090194e+180
-2.227381996671495e+165
-2.272454186637281e+165

simplify11.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03885
14780
25980
36180
46780
done6780

end0.0ms

sample1.1s

Algorithm
intervals
Results
219.0ms1025×body2560valid
214.0ms5915×body80valid
155.0ms893×body1280valid
101.0ms2995×body80nan
62.0ms447×body640valid
28.0ms107×body5120valid
23.0ms210×body320valid
7.0ms103×body160valid