Details

Time bar (total: 5.8s)

sample53.0ms

Algorithm
intervals
Results
31.0ms279×body80valid
6.0ms65×body80nan

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03918
18018
214318
317718
418918
519318
619318

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.5b

localize118.0ms

Local error

Found 4 expressions with local error:

0.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
58×*-un-lft-identity
56×add-sqr-sqrt
50×add-cube-cbrt
37×sqrt-prod
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
12×add-log-exp
10×fma-def fma-neg
8×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square 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 → 151
Calls
4 calls:
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(- (- b) (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)))

series290.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify61.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04183058
114712008
250011917

prune439.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.9b

localize114.0ms

Local error

Found 4 expressions with local error:

11.3b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
10×add-cube-cbrt fma-def *-un-lft-identity
9×sqrt-prod
8×add-log-exp
7×pow1
6×sqrt-div
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×distribute-lft-neg-in rem-sqrt-square flip3-- distribute-rgt-neg-in sqrt-pow1 pow1/2 flip--
2×sum-log
1×+-commutative neg-sub0 associate-+l- neg-mul-1 flip3-+ neg-log flip-+
Counts
4 → 76
Calls
4 calls:
7.0ms
(+ (- 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)))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series281.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify114.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 3 (107.0ms)

IterNodesCost
0249756
1969641
24038626
35001624

prune394.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.9b

localize114.0ms

Local error

Found 4 expressions with local error:

10.1b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
10×fma-neg prod-diff
9×sqrt-prod
8×add-log-exp
7×pow1
6×distribute-lft-neg-in distribute-rgt-neg-in sqrt-div
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×neg-mul-1 diff-log
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 88
Calls
4 calls:
8.0ms
(- (- 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)))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series283.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify176.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
02831391
19981121
247231013
350011013

prune435.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.9b

localize118.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.7b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
4.9b
(/ (* a c) b)
23.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
55×add-sqr-sqrt
54×*-un-lft-identity
50×add-cube-cbrt
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
14×add-exp-log add-cbrt-cube
10×fma-neg
8×add-log-exp
7×neg-mul-1
6×times-frac associate-/r*
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×flip3-- flip--
2×frac-2neg sqrt-div diff-log prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l* distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 155
Calls
4 calls:
20.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
3.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series231.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
64.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
23.0ms
(/ (* a c) b)
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify86.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06203085
126922005
250021927

prune433.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.4b

regimes200.0ms

Accuracy

94.5% (0.7b remaining)

Error of 7.9b against oracle of 7.1b and baseline of 20.3b

bsearch190.0ms

Steps
ItersRangePoint
10
9.168682727753708e+124
1.4581761209996442e+140
8.191367562681431e+126
6
-4.297055379359757e+148
-3.3081908876611885e+147
-4.309632596365889e+147

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05863
15863

end0.0ms

sample1.5s

Algorithm
intervals
Results
965.0ms8686×body80valid
269.0ms2712×body80nan