Details

Time bar (total: 5.2s)

sample51.0ms

Algorithm
intervals
Results
10.0ms163×body160valid
10.0ms553×pre80true
9.0ms297×body80nan
4.0ms39×body320valid
2.0ms54×body80valid

simplify47.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01217
12217
24216
38216
410016
510816
done10816

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 3.0 a) c))
0.3b
(* (* 3.0 a) c)
0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
41.3b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
14×add-exp-log add-cbrt-cube
10×add-sqr-sqrt add-cube-cbrt fma-def add-log-exp
9×pow1
6×distribute-rgt-neg-in distribute-lft-out
5×times-frac associate-/l*
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u
3×distribute-lft-neg-in associate-*r* pow-prod-down
2×cbrt-undiv neg-sub0 associate-+l- flip3-+ div-exp sum-log flip-+ associate-/l/
1×+-commutative neg-mul-1 sub-neg flip3-- frac-2neg fma-neg diff-log div-sub associate-*l* prod-diff neg-log clear-num associate-/r* *-commutative flip-- div-inv
Counts
4 → 93
Calls
4 calls:
3.0ms
(- (* b b) (* (* 3.0 a) c))
7.0ms
(* (* 3.0 a) c)
36.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series245.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* b b) (* (* 3.0 a) c))
20.0ms
(* (* 3.0 a) c)
101.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify669.0ms

Counts
105 → 105
Iterations

Useful iterations: done (666.0ms)

IterNodesCost
01671559
14451478
217721247
done50011246

prune258.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.9b

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

prune33.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.9b

localize7.0ms

Local error

Found 3 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))

rewrite23.0ms

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)
9.0ms
(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))
8.0ms
(* -1.5 (/ (* a c) b))

series67.0ms

Counts
3 → 9
Calls
3 calls:
18.0ms
(/ (* a c) b)
22.0ms
(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))
27.0ms
(* -1.5 (/ (* a c) b))

simplify787.0ms

Counts
93 → 93
Iterations

Useful iterations: 2 (163.0ms)

IterNodesCost
01291138
13831097
22010813
done5000813

prune189.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 4.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* a c) b)
0.3b
(/ (* -1.5 (expm1 (log1p (/ (* a c) b)))) (* 3.0 a))
0.3b
(* -1.5 (expm1 (log1p (/ (* a c) b))))
0.3b
(expm1 (log1p (/ (* a c) b)))

rewrite13.0ms

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)
5.0ms
(/ (* -1.5 (expm1 (log1p (/ (* a c) b)))) (* 3.0 a))
3.0ms
(* -1.5 (expm1 (log1p (/ (* a c) b))))
0.0ms
(expm1 (log1p (/ (* a c) b)))

series289.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(/ (* a c) b)
85.0ms
(/ (* -1.5 (expm1 (log1p (/ (* a c) b)))) (* 3.0 a))
97.0ms
(* -1.5 (expm1 (log1p (/ (* a c) b))))
89.0ms
(expm1 (log1p (/ (* a c) b)))

simplify528.0ms

Counts
89 → 89
Iterations

Useful iterations: done (526.0ms)

IterNodesCost
01541143
1379967
21727783
done5001780

prune162.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 4.9b

regimes354.0ms

Accuracy

13.7% (6.0b remaining)

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

bsearch43.0ms

Steps
ItersRangePoint
6
0.00017659738910379716
0.0013183985859660308
0.00017936624356974993

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02340
12940
23740
done3740

end0.0ms

sample1.4s

Algorithm
intervals
Results
307.0ms4846×body160valid
290.0ms16153×pre80true
251.0ms8153×body80nan
129.0ms1342×body320valid
60.0ms1812×body80valid