Details

Time bar (total: 18.8s)

sample113.0ms

Algorithm
intervals
Results
25.0ms44×body2560valid
16.0ms167×body80valid
15.0ms100×body80nan
15.0ms32×body1280valid
5.0ms14×body640valid
2.0ms7×body320valid
2.0ms3×body5120valid
1.0ms3×body160valid

simplify121.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01417
12517
24616
38716
412016
512916
done12916

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize14.0ms

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)))

rewrite139.0ms

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:
26.0ms
(* (* 4.0 a) c)
71.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
16.0ms
(- (* b b) (* (* 4.0 a) c))
25.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series271.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (* 4.0 a) c)
103.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
64.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts
106 → 106
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01611863
14131576
220891334
done50021267

prune476.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.9b

localize46.0ms

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)))

rewrite57.0ms

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:
1.0ms
(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))
13.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
28.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series624.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(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))
149.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
140.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
180.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts
67 → 67
Iterations

Useful iterations: 3 (1.0s)

IterNodesCost
0881442
12051264
27021121
337421103
done50001103

prune710.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.1b

localize62.0ms

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)))

rewrite37.0ms

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)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
16.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series539.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
149.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
142.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
128.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts
72 → 72
Iterations

Useful iterations: 3 (869.0ms)

IterNodesCost
0671268
11691224
26101100
333741076
done50001076

prune660.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.1b

localize67.0ms

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)))

rewrite33.0ms

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:
12.0ms
(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)))
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series581.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
134.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
143.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
154.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.8s

Counts
72 → 72
Iterations

Useful iterations: 3 (1.0s)

IterNodesCost
0671268
11691224
26101100
333741076
done50001076

prune666.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.1b

regimes365.0ms

Accuracy

86.8% (3.2b remaining)

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

bsearch208.0ms

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

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02742
13342
done3342

end0.0ms

sample3.1s

Algorithm
intervals
Results
635.0ms5717×body80valid
556.0ms1127×body2560valid
480.0ms223×body320valid
376.0ms2905×body80nan
339.0ms936×body1280valid
119.0ms448×body640valid
98.0ms111×body5120valid
15.0ms112×body160valid