Details

Time bar (total: 16.1s)

sample94.0ms

Algorithm
intervals
Results
19.0ms206×body80valid
16.0ms29×body2560valid
13.0ms28×body1280valid
8.0ms96×body80nan
4.0ms12×body640valid
1.0ms4×body320valid
1.0ms1×body5120valid
1.0ms3×body160valid

simplify157.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12817
26417
311417
413017
513717
614117
done14117

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
24.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 77
Calls
4 calls:
102.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
51.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.0ms
(- (* b b) (* 4.0 (* a c)))
18.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series399.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
92.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
59.0ms
(- (* b b) (* 4.0 (* a c)))
128.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.5s

Counts
89 → 89
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
01571750
14021650
213221474
349551459
done50001459

prune422.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
24.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
67×times-frac
48×add-sqr-sqrt
47×*-un-lft-identity
27×add-cube-cbrt
25×add-exp-log
13×associate-/r* add-cbrt-cube
12×div-exp
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
8×sqrt-prod
7×flip3-- flip--
6×pow1
5×cbrt-undiv distribute-rgt-neg-in div-inv
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 125
Calls
4 calls:
68.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
35.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms
(- (* b b) (* 4.0 (* a c)))
20.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series449.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
107.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
52.0ms
(- (* b b) (* 4.0 (* a c)))
110.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts
137 → 137
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02263421
15183066
215412794
done50012684

prune417.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.6b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
1.2b
(- (* b b) (* 4.0 (* a c)))
5.1b
(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
24.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
12×add-sqr-sqrt
10×times-frac
9×add-exp-log add-cube-cbrt sqrt-prod add-cbrt-cube
8×add-log-exp
6×associate-/l*
5×pow1
4×flip3-- sqrt-div flip--
3×div-inv distribute-lft-out--
2×cbrt-undiv sub-neg diff-log div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-out-- distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* frac-sub cbrt-unprod sub-div difference-of-squares
Counts
4 → 76
Calls
4 calls:
40.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
18.0ms
(- (* b b) (* 4.0 (* a c)))
83.0ms
(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
18.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series526.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
78.0ms
(- (* b b) (* 4.0 (* a c)))
170.0ms
(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
106.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts
88 → 88
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01651798
14171643
213021511
done50001506

prune414.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.6b

localize47.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 4.0 (* a c)))
2.0b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.1b
(/ (+ 0 (* (* 4.0 a) c)) (* 2.0 a))
24.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
5×pow1
3×times-frac sqrt-prod associate-/l*
2×cbrt-undiv flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/ distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 diff-log neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 65
Calls
4 calls:
17.0ms
(- (* b b) (* 4.0 (* a c)))
54.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
56.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* 2.0 a))
19.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series332.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (* b b) (* 4.0 (* a c)))
142.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* 2.0 a))
98.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.0s

Counts
77 → 77
Iterations

Useful iterations: 2 (316.0ms)

IterNodesCost
01471241
13751068
21670950
done5001950

prune355.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.6b

regimes371.0ms

Accuracy

94.7% (1.3b remaining)

Error of 6.8b against oracle of 5.5b and baseline of 29.4b

bsearch736.0ms

Steps
ItersRangePoint
9
1.2073698495971617e+61
8.75865749938149e+67
5.099089738165329e+67
10
1.610059141238142e-239
1.618698210595833e-224
2.094358742794728e-239
10
-3.742210988141449e+103
-1.0235731023437291e+92
-3.359953003549157e+103

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03464
14364
done4364

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.2s5837×body80valid
657.0ms1047×body2560valid
437.0ms897×body1280valid
284.0ms2844×body80nan
140.0ms466×body640valid
63.0ms112×body5120valid
52.0ms241×body320valid
16.0ms106×body160valid