Details

Time bar (total: 6.8s)

sample54.0ms

Algorithm
intervals
Results
9.0ms153×body160valid
9.0ms543×pre80true
8.0ms287×body80nan
4.0ms41×body320valid
2.0ms62×body80valid

simplify69.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01217
12217
24216
38216
410416
511216
done11216

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.9b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 3.0 a) c))
0.3b
(* (* 3.0 a) c)
0.3b
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
39.0b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

rewrite165.0ms

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:
8.0ms
(- (* b b) (* (* 3.0 a) c))
16.0ms
(* (* 3.0 a) c)
87.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
50.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

series268.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(- (* b b) (* (* 3.0 a) c))
20.0ms
(* (* 3.0 a) c)
112.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
84.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

simplify1.2s

Counts
121 → 121
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02012338
14952065
216681747
done50001676

prune290.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 5.3b

localize4.0ms

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

prune47.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 5.3b

localize8.0ms

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))

rewrite54.0ms

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:
9.0ms
(/ (* a c) b)
17.0ms
(* -1.5 (/ (* a c) b))
24.0ms
(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

series75.0ms

Counts
3 → 9
Calls
3 calls:
20.0ms
(/ (* a c) b)
33.0ms
(* -1.5 (/ (* a c) b))
22.0ms
(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

simplify653.0ms

Counts
93 → 93
Iterations

Useful iterations: 2 (219.0ms)

IterNodesCost
01291138
13531097
21740813
done5000813

prune199.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 5.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* a c) b)
0.3b
(* -1.5 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))))
0.4b
(/ (* -1.5 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) (* 3.0 a))
0.5b
(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

rewrite211.0ms

Algorithm
rewrite-expression-head
Rules
37×add-exp-log add-cbrt-cube
34×sqrt-prod
32×add-sqr-sqrt
24×pow1
19×add-cube-cbrt *-un-lft-identity
16×times-frac
14×prod-exp cbrt-unprod
13×associate-*l*
12×sqrt-div swap-sqr
11×associate-*r*
9×associate-*r/
8×cbrt-undiv sqrt-pow1 pow1/2 div-exp
6×pow-prod-down div-inv
5×pow-prod-up unswap-sqr
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
3×frac-times associate-*l/ pow-sqr associate-/l/
2×frac-2neg clear-num *-commutative associate-/l*
1×pow2 pow-plus sqrt-unprod rem-square-sqrt
Counts
4 → 143
Calls
4 calls:
9.0ms
(/ (* a c) b)
77.0ms
(* -1.5 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))))
83.0ms
(/ (* -1.5 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) (* 3.0 a))
37.0ms
(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

series195.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(/ (* a c) b)
66.0ms
(* -1.5 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))))
48.0ms
(/ (* -1.5 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) (* 3.0 a))
60.0ms
(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

simplify1.1s

Counts
155 → 155
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01942600
14241584
220991304
done50011289

prune254.0ms

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 5.3b

regimes433.0ms

Accuracy

13.9% (6.0b remaining)

Error of 11.1b against oracle of 5.1b and baseline of 12.1b

bsearch42.0ms

Steps
ItersRangePoint
6
0.004134462677295373
0.021871828225844332
0.004205915758382604

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02038
12438
done2438

end0.0ms

sample1.5s

Algorithm
intervals
Results
295.0ms4753×body160valid
274.0ms16322×pre80true
257.0ms8322×body80nan
134.0ms1439×body320valid
57.0ms1808×body80valid