Details

Time bar (total: 11.2s)

sample122.0ms

Algorithm
intervals
Results
38.0ms298×body80nan
22.0ms151×body160valid
20.0ms554×pre80true
8.0ms105×body80valid

simplify131.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01217
12217
24216
38216
410416
511216
done11216

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 3.0 a) c))
0.3b
(* (* 3.0 a) c)
0.4b
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
30.4b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

rewrite279.0ms

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:
19.0ms
(- (* b b) (* (* 3.0 a) c))
23.0ms
(* (* 3.0 a) c)
145.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
85.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

series422.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (* b b) (* (* 3.0 a) c))
25.0ms
(* (* 3.0 a) c)
176.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
138.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

simplify1.8s

Counts
121 → 121
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02012338
14952065
216681747
done50001676

prune458.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.1b

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

prune55.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 9.1b

localize9.0ms

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))

rewrite63.0ms

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)
19.0ms
(* -1.5 (/ (* a c) b))
30.0ms
(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

series97.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(/ (* a c) b)
36.0ms
(* -1.5 (/ (* a c) b))
25.0ms
(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

simplify996.0ms

Counts
93 → 93
Iterations

Useful iterations: 2 (311.0ms)

IterNodesCost
01291138
13531097
21740813
done5000813

prune386.0ms

Pruning

34 alts after pruning (33 fresh and 1 done)

Merged error: 9.0b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log add-cbrt-cube
21×prod-exp cbrt-unprod
17×add-sqr-sqrt
14×associate-*r*
12×cbrt-undiv add-cube-cbrt *-un-lft-identity div-exp
11×times-frac
10×pow1
6×associate-*l*
5×associate-*r/
4×pow-prod-down
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×*-commutative div-inv unswap-sqr
1×frac-2neg clear-num associate-/r* associate-/l/ associate-/l*
Counts
3 → 89
Calls
3 calls:
25.0ms
(* -1.5 (* a (/ c b)))
23.0ms
(* a (/ c b))
43.0ms
(/ (* -1.5 (* a (/ c b))) (* 3.0 a))

series110.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(* -1.5 (* a (/ c b)))
44.0ms
(* a (/ c b))
27.0ms
(/ (* -1.5 (* a (/ c b))) (* 3.0 a))

simplify1.5s

Counts
98 → 98
Iterations

Useful iterations: 2 (374.0ms)

IterNodesCost
01451170
13931123
21928839
done5001839

prune212.0ms

Pruning

35 alts after pruning (34 fresh and 1 done)

Merged error: 9.0b

regimes855.0ms

Accuracy

45.4% (7.6b remaining)

Error of 16.6b against oracle of 9.0b and baseline of 22.9b

bsearch2.0ms

Steps
ItersRangePoint
0
396.1014485756044
405.97882290570107
401.0401357406527

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02038
12438
done2438

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.0s16466×pre80true
850.0ms4467×body160valid
670.0ms8466×body80nan
234.0ms3533×body80valid