Details

Time bar (total: 11.5s)

sample97.0ms

Algorithm
intervals
Results
20.0ms144×body160valid
18.0ms255×body80nan
17.0ms511×pre80true
8.0ms112×body80valid

simplify127.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
01217
12217
24216
38216
410416
511216
done11216

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.3b
(- (* b b) (* (* 3.0 a) c))
0.3b
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
28.4b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

rewrite285.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
15×sqrt-prod
14×add-exp-log add-cbrt-cube
9×pow1
8×add-log-exp
7×fma-neg
6×times-frac associate-/l* difference-of-squares
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u
3×flip3-- associate-*r* pow-prod-down flip-- distribute-lft-out--
2×cbrt-undiv sub-neg diff-log div-exp associate-/l/
1×frac-2neg div-sub associate-*l* clear-num associate-/r* *-commutative div-inv
Counts
4 → 109
Calls
4 calls:
20.0ms
(* (* 3.0 a) c)
10.0ms
(- (* b b) (* (* 3.0 a) c))
152.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
99.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

series439.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (* 3.0 a) c)
86.0ms
(- (* b b) (* (* 3.0 a) c))
186.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
123.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

simplify1.7s

Counts
121 → 121
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02012338
14952065
216741747
done50001676

prune385.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.8b

localize8.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune93.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 9.8b

localize27.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (* a c) b)
0.3b
(* -1.5 (/ (* a c) b))
0.4b
(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log add-cbrt-cube
17×prod-exp cbrt-unprod
16×cbrt-undiv div-exp
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
7×times-frac associate-*r*
5×pow1
4×associate-/r*
3×expm1-log1p-u associate-*l* log1p-expm1-u div-inv add-log-exp
2×frac-2neg associate-*r/ clear-num associate-/l*
1×pow-prod-down *-commutative associate-/l/ unswap-sqr
Counts
3 → 84
Calls
3 calls:
11.0ms
(/ (* a c) b)
23.0ms
(* -1.5 (/ (* a c) b))
45.0ms
(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

series85.0ms

Counts
3 → 9
Calls
3 calls:
23.0ms
(/ (* a c) b)
32.0ms
(* -1.5 (/ (* a c) b))
29.0ms
(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

simplify1.0s

Counts
93 → 93
Iterations

Useful iterations: 2 (297.0ms)

IterNodesCost
01291138
13531097
21740813
done5000813

prune371.0ms

Pruning

31 alts after pruning (30 fresh and 1 done)

Merged error: 9.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* a c) b)
0.3b
(/ (/ (* -1.5 (/ (* a c) b)) 3.0) a)
0.3b
(/ (* -1.5 (/ (* a c) b)) 3.0)
0.3b
(* -1.5 (/ (* a c) b))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
52×add-exp-log add-cbrt-cube
42×times-frac
29×add-sqr-sqrt
27×add-cube-cbrt *-un-lft-identity
21×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
9×associate-/r* associate-/l*
8×div-inv
7×associate-*r*
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg associate-*l* clear-num
2×associate-*r/ associate-/l/
1×pow-prod-down *-commutative unswap-sqr
Counts
4 → 134
Calls
4 calls:
22.0ms
(/ (* a c) b)
49.0ms
(/ (/ (* -1.5 (/ (* a c) b)) 3.0) a)
40.0ms
(/ (* -1.5 (/ (* a c) b)) 3.0)
24.0ms
(* -1.5 (/ (* a c) b))

series169.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ (* a c) b)
44.0ms
(/ (/ (* -1.5 (/ (* a c) b)) 3.0) a)
36.0ms
(/ (* -1.5 (/ (* a c) b)) 3.0)
53.0ms
(* -1.5 (/ (* a c) b))

simplify1.2s

Counts
146 → 146
Iterations

Useful iterations: 2 (403.0ms)

IterNodesCost
02001928
14901858
218471550
done50001550

prune376.0ms

Pruning

35 alts after pruning (35 fresh and 0 done)

Merged error: 9.6b

regimes988.0ms

Accuracy

44.1% (7.7b remaining)

Error of 16.6b against oracle of 8.9b and baseline of 22.7b

bsearch11.0ms

Steps
ItersRangePoint
1
172.19531990517868
188.1359396834071
176.18047484973576

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02544
13244
done3244

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.1s4451×body160valid
869.0ms16506×pre80true
690.0ms8506×body80nan
300.0ms3549×body80valid