Details

Time bar (total: 5.6s)

sample49.0ms

Algorithm
intervals
Results
11.0ms509×pre80true
9.0ms155×body160valid
7.0ms253×body80nan
4.0ms44×body320valid
2.0ms57×body80valid

simplify46.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01217
12217
24216
38316
410216
511016
done11016

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 3.0 a) c))
0.2b
(* (* 3.0 a) c)
0.3b
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
39.7b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

rewrite78.0ms

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:
3.0ms
(- (* b b) (* (* 3.0 a) c))
6.0ms
(* (* 3.0 a) c)
43.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
22.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

series251.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b b) (* (* 3.0 a) c))
19.0ms
(* (* 3.0 a) c)
106.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
78.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

simplify754.0ms

Counts
121 → 121
Iterations

Useful iterations: done (751.0ms)

IterNodesCost
02012338
15172065
222201729
done50001728

prune263.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 4.5b

localize3.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune41.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 4.5b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite22.0ms

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:
3.0ms
(/ (* a c) b)
8.0ms
(* -1.5 (/ (* a c) b))
8.0ms
(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

series69.0ms

Counts
3 → 9
Calls
3 calls:
19.0ms
(/ (* a c) b)
27.0ms
(* -1.5 (/ (* a c) b))
24.0ms
(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

simplify743.0ms

Counts
93 → 93
Iterations

Useful iterations: 2 (136.0ms)

IterNodesCost
01291138
13941097
22297813
done5000813

prune374.0ms

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 4.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* a c) b)
0.3b
(* -1.5 (expm1 (log1p (/ (* a c) b))))
0.3b
(expm1 (log1p (/ (* a c) b)))
0.3b
(/ (* -1.5 (expm1 (log1p (/ (* a c) b)))) (* 3.0 a))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-undiv div-exp prod-exp cbrt-unprod
4×expm1-log1p-u times-frac associate-/r* log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
2×frac-2neg clear-num div-inv associate-/l*
1×expm1-log1p pow-prod-down *-commutative expm1-udef unswap-sqr
Counts
4 → 77
Calls
4 calls:
3.0ms
(/ (* a c) b)
3.0ms
(* -1.5 (expm1 (log1p (/ (* a c) b))))
0.0ms
(expm1 (log1p (/ (* a c) b)))
4.0ms
(/ (* -1.5 (expm1 (log1p (/ (* a c) b)))) (* 3.0 a))

series289.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(/ (* a c) b)
97.0ms
(* -1.5 (expm1 (log1p (/ (* a c) b))))
88.0ms
(expm1 (log1p (/ (* a c) b)))
85.0ms
(/ (* -1.5 (expm1 (log1p (/ (* a c) b)))) (* 3.0 a))

simplify568.0ms

Counts
89 → 89
Iterations

Useful iterations: done (566.0ms)

IterNodesCost
01541143
1390967
21936783
done5000780

prune167.0ms

Pruning

31 alts after pruning (30 fresh and 1 done)

Merged error: 4.5b

regimes415.0ms

Accuracy

10.6% (6.2b remaining)

Error of 11.2b against oracle of 4.9b and baseline of 11.9b

bsearch38.0ms

Steps
ItersRangePoint
6
1.379156024488757e-05
6.0655022642923514e-05
2.0899682798920903e-05

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02051
12551
done2551

end0.0ms

sample1.3s

Algorithm
intervals
Results
295.0ms4830×body160valid
294.0ms16360×pre80true
242.0ms8360×body80nan
128.0ms1361×body320valid
55.0ms1809×body80valid