Details

Time bar (total: 7.8s)

sample2.3s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 25.292969%

Guaranteed chance to sample good point: 75.886438%

Results
23.0ms256×body80valid
1.0ms13×body80invalid
1.0ms11×body80nan

simplify343.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03518
16618
211618
314418
415918
516118
616118

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 18.4b

Counts
2 → 1

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.7b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×add-sqr-sqrt add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log sqrt-div add-cbrt-cube
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 diff-log neg-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 63
Calls
4 calls:
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series72.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify118.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (109.0ms)

IterNodesCost
0248644
1898606
23865590
35001586

prune206.0ms

Filtered
60 candidates to 75 candidates (-25.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New66975
Fresh000
Picked101
Done000
Total67976

Merged error: 5.9b

Counts
76 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

8.1b
(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×add-log-exp
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-exp-log flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 60
Calls
4 calls:
4.0ms
(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series57.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify109.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (101.0ms)

IterNodesCost
0221722
1829631
23533612
35001592

prune215.0ms

Filtered
58 candidates to 72 candidates (-24.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New72072
Fresh088
Picked011
Done000
Total72981

Merged error: 5.9b

Counts
81 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.6b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
5.5b
(/ (* a c) b)
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
13×*-un-lft-identity
10×add-sqr-sqrt
9×add-cube-cbrt
8×add-log-exp
6×times-frac associate-/r*
5×pow1
4×cbrt-undiv div-exp
3×sqrt-prod
2×flip3-- frac-2neg sqrt-div prod-exp clear-num sum-log associate-/r/ flip-- cbrt-unprod div-inv distribute-lft-out associate-/l*
1×+-commutative neg-sub0 associate-+l- rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 74
Calls
4 calls:
7.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
4.0ms
(/ (* a c) b)
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series53.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
5.0ms
(/ (* a c) b)
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0455639
12202559
25001553

prune183.0ms

Filtered
65 candidates to 86 candidates (-32.3%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New81586
Fresh347
Picked101
Done011
Total851095

Merged error: 5.4b

Counts
95 → 10

localize31.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.6b
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
3.1b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
31×times-frac
30×add-exp-log
26×*-un-lft-identity
23×add-cbrt-cube
22×add-cube-cbrt associate-*r*
11×cbrt-prod
9×cbrt-undiv div-exp prod-exp cbrt-unprod
8×add-log-exp
7×pow1 associate-*l*
6×unswap-sqr
3×associate-/r* sqrt-prod div-inv
2×flip3-- sqrt-div sum-log associate-/r/ flip-- distribute-lft-out
1×+-commutative neg-sub0 frac-times associate-+l- rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 112
Calls
4 calls:
7.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
13.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series63.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
13.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify87.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
07501327
137841149
250011098

prune202.0ms

Filtered
91 candidates to 124 candidates (-36.3%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1213124
Fresh088
Picked101
Done011
Total12212134

Merged error: 5.4b

Counts
134 → 12

regimes404.0ms

Accuracy

93.9% (0.9b remaining)

Error of 7.6b against oracle of 6.7b and baseline of 20.8b

bsearch49.0ms

Steps
ItersRangePoint
5
8.909061361562253e+148
3.2637422250965086e+149
9.057180734231854e+148
6
-2.3967332165160093e+156
-1.9392961947131683e+155
-1.969367761925598e+155

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06080
16080

end0.0ms

sample3.1s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 25.292969%

Guaranteed chance to sample good point: 75.886438%

Results
701.0ms8000×body80valid
34.0ms379×body80nan
27.0ms328×body80invalid

Profiling

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