Details

Time bar (total: 16.9s)

sample448.0ms

Algorithm
intervals
Results
64.0ms115×body320valid
51.0ms515×pre80true
50.0ms101×body160valid
21.0ms259×body80nan
3.0ms10×body640valid
2.0ms30×body80valid

simplify315.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
014365
125365
246325
386325
4119325
5128325
done128325

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
0.1b
(- (* b b) (* (* 4.0 a) c))
27.5b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
19×prod-diff
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×fma-neg
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv associate-/r* flip3-- div-exp flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 183
Calls
4 calls:
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
67.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
23.0ms
(- (* b b) (* (* 4.0 a) c))
85.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series550.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
188.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
87.0ms
(- (* b b) (* (* 4.0 a) c))
166.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify2.7s

Counts
195 → 195
Iterations

Useful iterations: done (2.7s)

IterNodesCost
0321102660
181896062
2388991817
done500091727

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.7b

localize10.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune111.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 2.7b

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
0.3b
(/ (* a c) b)

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
27×add-cbrt-cube add-exp-log
20×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
13×cbrt-undiv div-exp
8×associate-/l*
6×associate-/r* div-inv
5×prod-exp cbrt-unprod
2×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
1×associate-/l/
Counts
2 → 77
Calls
2 calls:
24.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
20.0ms
(/ (* a c) b)

series67.0ms

Counts
2 → 6
Calls
2 calls:
39.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
28.0ms
(/ (* a c) b)

simplify2.1s

Counts
83 → 83
Iterations

Useful iterations: done (2.1s)

IterNodesCost
017124170
146822409
2299521888
done500121648

prune543.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 2.6b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(log1p (/ (* a c) b))
0.2b
(/ (/ (* -2.0 (expm1 (log1p (/ (* a c) b)))) 2.0) a)
0.3b
(expm1 (log1p (/ (* a c) b)))
0.3b
(/ (* a c) b)

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
22×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×add-cbrt-cube add-exp-log
8×associate-/l*
7×cbrt-undiv div-exp
6×associate-/r* div-inv
5×expm1-log1p-u
4×pow1 log1p-expm1-u add-log-exp
2×clear-num frac-2neg prod-exp cbrt-unprod
1×log1p-udef expm1-log1p log1p-expm1 expm1-udef associate-/l/
Counts
4 → 95
Calls
4 calls:
1.0ms
(log1p (/ (* a c) b))
20.0ms
(/ (/ (* -2.0 (expm1 (log1p (/ (* a c) b)))) 2.0) a)
0.0ms
(expm1 (log1p (/ (* a c) b)))
15.0ms
(/ (* a c) b)

series370.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(log1p (/ (* a c) b))
128.0ms
(/ (/ (* -2.0 (expm1 (log1p (/ (* a c) b)))) 2.0) a)
132.0ms
(expm1 (log1p (/ (* a c) b)))
30.0ms
(/ (* a c) b)

simplify2.3s

Counts
107 → 107
Iterations

Useful iterations: done (2.3s)

IterNodesCost
020638972
150227607
2262326778
done500125628

prune717.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 2.6b

regimes826.0ms

Accuracy

0% (3.5b remaining)

Error of 6.2b against oracle of 2.7b and baseline of 6.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0583
1683
done683

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.3s16315×pre80true
887.0ms3639×body320valid
799.0ms8315×body80nan
464.0ms2975×body160valid
137.0ms493×body640valid
91.0ms893×body80valid