Details

Time bar (total: 4.4s)

sample39.0ms

Algorithm
intervals
Results
9.0ms40×body2560valid
7.0ms194×body80valid
5.0ms28×body1280valid
3.0ms76×body80nan
1.0ms10×body640valid
1.0ms2×body5120valid
0.0ms3×body320valid
0.0ms1×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.4b
(- (* b b) (* 4.0 (* a c)))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
36.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
12.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series311.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
81.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
50.0ms
(- (* b b) (* 4.0 (* a c)))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0403779
11514685
25002674

prune228.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.2b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.4b
(- (* b b) (* 4.0 (* a c)))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
53×times-frac
45×*-un-lft-identity
26×add-sqr-sqrt
25×add-exp-log add-cube-cbrt
13×add-cbrt-cube
12×div-exp
11×associate-/r*
10×distribute-lft-out add-log-exp
9×associate-/r/
6×pow1
5×cbrt-undiv distribute-rgt-neg-in flip3-+ flip-+ div-inv
3×rec-exp 1-exp prod-exp sqrt-prod associate-/l*
2×flip3-- sqrt-div sum-log flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 diff-log neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 114
Calls
4 calls:
30.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
12.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series339.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
80.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify64.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05211588
125221375
250021308

prune250.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b b) (* 4.0 (* a c)))
0.4b
(- (* b b) (* 4.0 (* a c)))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 54
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
3.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series239.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* 4.0 (* a c)))
51.0ms
(- (* b b) (* 4.0 (* a c)))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify78.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
0145476
1528446
22232444
35002440

prune231.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.7b

localize17.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.2b
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (* 2.0 a))
19.5b
(- (pow b 2) (pow b 2))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
23×*-un-lft-identity
22×unpow-prod-down
18×difference-of-squares
15×add-cube-cbrt
12×unpow2 sqr-pow
10×distribute-rgt-out-- distribute-lft-out-- add-log-exp
9×add-exp-log add-cbrt-cube
5×pow1
4×sqrt-prod
3×flip3-- times-frac diff-log flip-- associate-/l*
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 associate-+l- rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 flip3-+ pow1/2 +-inverses div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod flip-+ div-inv
Counts
4 → 104
Calls
4 calls:
13.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
162.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (* 2.0 a))
11.0ms
(- (pow b 2) (pow b 2))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series163.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (* 2.0 a))
1.0ms
(- (pow b 2) (pow b 2))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify150.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (141.0ms)

IterNodesCost
0505756
12990603
25001569

prune282.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 5.7b

regimes190.0ms

Accuracy

95.2% (1.1b remaining)

Error of 6.9b against oracle of 5.8b and baseline of 29.5b

bsearch207.0ms

Steps
ItersRangePoint
8
1.5276508475467709e+44
4.1560730947117816e+46
4.1199128263687574e+46
10
9.410701402418836e-271
4.7345175229648096e-260
9.52089004516142e-271
11
-1.829086240692416e+154
-2.187052964502477e+134
-8.555281377770497e+140

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04024
14024

end0.0ms

sample1.1s

Algorithm
intervals
Results
265.0ms1104×body2560valid
228.0ms5868×body80valid
169.0ms910×body1280valid
105.0ms2861×body80nan
64.0ms422×body640valid
27.0ms96×body5120valid
23.0ms212×body320valid
9.0ms120×body160valid