Details

Time bar (total: 4.1s)

sample48.0ms

Algorithm
intervals
Results
9.0ms40×body2560valid
8.0ms31×body1280valid
7.0ms186×body80valid
3.0ms96×body80nan
2.0ms8×body5120valid
1.0ms9×body640valid
1.0ms6×body320valid
0.0ms3×body160valid

simplify17.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0299
1659
21219
31519
41609
51649
61649

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b
(- (* b b) (* 4.0 (* a c)))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
28.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 157
Calls
4 calls:
75.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms
(- (* b b) (* 4.0 (* a c)))
30.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series256.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
39.0ms
(- (* b b) (* 4.0 (* a c)))
68.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
64.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify77.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05903305
121012212
250022128

prune338.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.5b

localize4.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune18.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- b))
0.8b
(- (* b b) (* 4.0 (* a c)))
23.1b
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (sqrt (- (* b b) (* 4.0 (* a c))))))
28.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
10×cbrt-prod
9×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×add-log-exp
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod
2×flip3-- sqrt-div flip--
1×neg-mul-1 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg pow1/3 diff-log prod-diff fma-udef
Counts
4 → 63
Calls
4 calls:
4.0ms
(cbrt (- b))
9.0ms
(- (* b b) (* 4.0 (* a c)))
0.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (sqrt (- (* b b) (* 4.0 (* a c))))))
11.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series423.0ms

Counts
4 → 12
Calls
4 calls:
185.0ms
(cbrt (- b))
39.0ms
(- (* b b) (* 4.0 (* a c)))
139.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (sqrt (- (* b b) (* 4.0 (* a c))))))
60.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify98.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (92.0ms)

IterNodesCost
0249569
1776512
23355496
35001491

prune262.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 8.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* 4.0 (* a c)))
5.6b
(exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))
22.9b
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))))
28.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
7×pow1
6×log-prod exp-prod exp-sum sqrt-prod add-log-exp
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
3×flip3-- log-pow flip--
2×log-div sqrt-pow1 pow1/2 exp-diff
1×sub-neg rem-sqrt-square fma-neg diff-log prod-diff fma-udef rem-exp-log
Counts
4 → 67
Calls
4 calls:
9.0ms
(- (* b b) (* 4.0 (* a c)))
12.0ms
(exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))
0.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series308.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(- (* b b) (* 4.0 (* a c)))
66.0ms
(exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))
137.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))))
65.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify97.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 3 (89.0ms)

IterNodesCost
0256707
1771647
23295616
35003604

prune275.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 8.5b

regimes330.0ms

Accuracy

87.1% (4.4b remaining)

Error of 10.2b against oracle of 5.7b and baseline of 40.0b

bsearch100.0ms

Steps
ItersRangePoint
6
4.231934083523606e+52
2.717919616353272e+53
2.678238127073729e+53
9
-1.1345718484749e-82
-1.1127264026331332e-88
-1.3696943711263392e-83

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03522
13522

end0.0ms

sample1.2s

Algorithm
intervals
Results
234.0ms5880×body80valid
230.0ms1050×body2560valid
170.0ms921×body1280valid
108.0ms2795×body80nan
60.0ms426×body640valid
30.0ms111×body5120valid
25.0ms231×body320valid
7.0ms103×body160valid