Details

Time bar (total: 18.9s)

sample67.0ms

Algorithm
intervals
Results
15.0ms44×body2560valid
10.0ms167×body80valid
9.0ms32×body1280valid
5.0ms100×body80nan
3.0ms14×body640valid
1.0ms3×body5120valid
1.0ms7×body320valid
0.0ms3×body160valid

simplify134.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
01417
12517
24616
38716
412016
512916
done12916

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 4.0 a) c)
0.8b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.0b
(- (* b b) (* (* 4.0 a) c))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
19×prod-diff
16×sqrt-prod
10×pow1
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
4×expm1-log1p-u log1p-expm1-u
3×flip3-- associate-*r* pow-prod-down prod-exp flip-- cbrt-unprod
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 94
Calls
4 calls:
25.0ms
(* (* 4.0 a) c)
73.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series308.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (* 4.0 a) c)
118.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
67.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts
106 → 106
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01611863
14131576
220891334
done50021267

prune467.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.9b

localize34.0ms

Local error

Found 4 expressions with local error:

24.7b
(fma (sqrt (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c))))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))) (- b))
26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))
26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))
26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-div
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-- pow1/3 flip--
1×fma-udef
Counts
4 → 55
Calls
4 calls:
0.0ms
(fma (sqrt (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c))))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))) (- b))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series576.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(fma (sqrt (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c))))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))) (- b))
153.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
127.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
129.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.8s

Counts
67 → 67
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
0881442
12051264
27021121
337421103
done50001103

prune521.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.1b

localize38.0ms

Local error

Found 4 expressions with local error:

26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))
26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))
26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))
26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt cbrt-div *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u flip3-- pow1/3 add-cbrt-cube flip-- log1p-expm1-u add-log-exp
Counts
4 → 60
Calls
4 calls:
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series600.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
155.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
144.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
141.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.1s

Counts
72 → 72
Iterations

Useful iterations: 3 (954.0ms)

IterNodesCost
0671268
11691224
26101100
333741076
done50001076

prune520.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.1b

localize53.0ms

Local error

Found 4 expressions with local error:

26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))
26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))
26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))
26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt cbrt-div *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u flip3-- pow1/3 add-cbrt-cube flip-- log1p-expm1-u add-log-exp
Counts
4 → 60
Calls
4 calls:
11.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series576.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
135.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
127.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
180.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts
72 → 72
Iterations

Useful iterations: 3 (923.0ms)

IterNodesCost
0671268
11691224
26101100
333741076
done50001076

prune576.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 12.1b

regimes407.0ms

Accuracy

86.8% (3.2b remaining)

Error of 14.1b against oracle of 11.0b and baseline of 34.9b

bsearch187.0ms

Steps
ItersRangePoint
8
2.5460852775314814e-33
4.614087934274923e-30
5.1985673003108055e-33
10
-8.097032161796104e+150
-8.691973301260876e+137
-2.486593375467686e+143

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02742
13342
done3342

end0.0ms

sample2.9s

Algorithm
intervals
Results
904.0ms5717×body80valid
691.0ms1127×body2560valid
368.0ms936×body1280valid
243.0ms2905×body80nan
104.0ms448×body640valid
52.0ms111×body5120valid
40.0ms223×body320valid
13.0ms112×body160valid