Details

Time bar (total: 9.6s)

sample40.0ms

Algorithm
intervals
Results
7.0ms206×body80valid
6.0ms28×body2560valid
5.0ms28×body1280valid
4.0ms107×body80nan
2.0ms13×body640valid
0.0ms2×body5120valid
0.0ms6×body160valid
0.0ms4×body320valid

simplify72.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b
(- (* b b) (* (* 4.0 a) c))
1.2b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
67.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(- (* b b) (* (* 4.0 a) c))
21.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series319.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
50.0ms
(- (* b b) (* (* 4.0 a) c))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify877.0ms

Counts
102 → 102
Iterations

Useful iterations: done (875.0ms)

IterNodesCost
01671697
14331584
214881361
done50001347

prune300.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b
(- (* b b) (* (* 4.0 a) c))
1.2b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
65.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(- (* b b) (* (* 4.0 a) c))
25.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series320.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
51.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
102 → 102
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01671697
14331584
214881361
done50001347

prune292.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
1.0b
(- (* b b) (* (* 4.0 a) c))
1.2b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
60×times-frac
50×*-un-lft-identity
40×add-cube-cbrt
25×add-exp-log
20×sqrt-prod
19×prod-diff
13×add-cbrt-cube
12×div-exp associate-/r*
10×difference-of-squares
9×associate-/r/
8×add-log-exp
7×flip3-- fma-neg flip--
6×pow1
5×cbrt-undiv div-inv distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u
3×rec-exp 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num cbrt-unprod inv-pow
Counts
4 → 152
Calls
4 calls:
56.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
8.0ms
(- (* b b) (* (* 4.0 a) c))
49.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series347.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
46.0ms
(- (* b b) (* (* 4.0 a) c))
82.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify884.0ms

Counts
164 → 164
Iterations

Useful iterations: done (879.0ms)

IterNodesCost
02614025
15873484
216563082
done50012938

prune312.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 2.0) (/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
1.0b
(- (* b b) (* (* 4.0 a) c))
1.2b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
789×times-frac
507×add-sqr-sqrt
420×*-un-lft-identity
334×add-cube-cbrt
86×difference-of-squares
58×sqrt-prod
43×distribute-lft-out--
40×div-inv
29×associate-/r/
26×add-exp-log
24×associate-/r*
19×prod-diff
17×flip3-- flip--
16×div-exp add-cbrt-cube
13×associate-/l*
8×cbrt-undiv add-log-exp
7×fma-neg
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×sub-neg rec-exp sqrt-div diff-log 1-exp
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 449
Calls
4 calls:
62.0ms
(/ (/ 1 2.0) (/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
8.0ms
(- (* b b) (* (* 4.0 a) c))
48.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series342.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ (/ 1 2.0) (/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
48.0ms
(- (* b b) (* (* 4.0 a) c))
82.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
461 → 461
Iterations

Useful iterations: 2 (862.0ms)

IterNodesCost
066216613
1178114874
2447214121
done500014121

prune648.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.4b

regimes289.0ms

Accuracy

83.5% (4.6b remaining)

Error of 10.0b against oracle of 5.4b and baseline of 33.5b

bsearch201.0ms

Steps
ItersRangePoint
6
2.0335150395734557e+19
1.0746392320557105e+20
2.9494967590524297e+19
6
3.6410892437809104e-110
3.0960233903298005e-109
3.7052502960789305e-110
8
1.0691773024250323e-170
5.5548132533506025e-168
2.175674080408203e-169
9
-1.4924982923623064e+60
-5.817343306680769e+54
-1.4784065354805617e+60

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
04483
16071
done6071

end0.0ms

sample1.1s

Algorithm
intervals
Results
226.0ms1042×body2560valid
215.0ms5926×body80valid
154.0ms905×body1280valid
99.0ms2856×body80nan
61.0ms463×body640valid
26.0ms102×body5120valid
22.0ms225×body320valid
6.0ms95×body160valid