Details

Time bar (total: 4.9s)

sample42.0ms

Algorithm
intervals
Results
8.0ms37×body2560valid
8.0ms197×body80valid
5.0ms24×body1280valid
3.0ms77×body80nan
2.0ms2×body320valid
2.0ms16×body640valid
0.0ms4×body160valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b
(- (* b b) (* 4.0 (* a c)))
0.8b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

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:
11.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series299.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
46.0ms
(- (* b b) (* 4.0 (* a c)))
78.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0403779
11514685
25002674

prune222.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b
(- (* b b) (* 4.0 (* a c)))
0.8b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

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:
13.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series380.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
46.0ms
(- (* b b) (* 4.0 (* a c)))
119.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
80.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify65.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05211588
125221375
250021308

prune237.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 2.0) (/ a (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b
(- (* b b) (* 4.0 (* a c)))
0.8b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
681×times-frac
457×*-un-lft-identity
286×add-sqr-sqrt
285×add-cube-cbrt
86×distribute-lft-out
43×distribute-rgt-neg-in
37×div-inv
29×associate-/r/
26×add-exp-log
21×associate-/r*
16×div-exp add-cbrt-cube
15×flip3-+ flip-+
13×associate-/l*
10×add-log-exp
8×cbrt-undiv
5×pow1
3×sqrt-prod
2×rec-exp flip3-- sqrt-div 1-exp sum-log flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log neg-log clear-num associate-/l/
Counts
4 → 373
Calls
4 calls:
37.0ms
(/ (/ 1 2.0) (/ a (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series331.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(/ (/ 1 2.0) (/ a (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
43.0ms
(- (* b b) (* 4.0 (* a c)))
78.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify92.0ms

Algorithm
egg-herbie
Counts
385 → 385
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
015587436
150016965

prune740.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.9b

localize17.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.5b
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (* 2.0 a))
16.8b
(- (pow b 2) (pow b 2))
24.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite45.0ms

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:
11.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (* 2.0 a))
8.0ms
(- (pow b 2) (pow b 2))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series160.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (* 2.0 a))
1.0ms
(- (pow b 2) (pow b 2))
68.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify154.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (140.0ms)

IterNodesCost
0505756
12990603
25001569

prune279.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.9b

regimes197.0ms

Accuracy

95.9% (1.0b remaining)

Error of 6.7b against oracle of 5.7b and baseline of 30.2b

bsearch185.0ms

Steps
ItersRangePoint
6
1.7071993853452014e+98
1.0593861995340862e+99
4.183383812955318e+98
10
-1.5874629985996245e-243
-1.1285126360225932e-253
-3.9510377053298673e-253
10
-4.4721271386820616e+151
-9.712280864301115e+136
-7.700313305414632e+138

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04024
14024

end0.0ms

sample1.2s

Algorithm
intervals
Results
256.0ms1045×body2560valid
237.0ms5938×body80valid
171.0ms852×body1280valid
110.0ms2870×body80nan
66.0ms442×body640valid
33.0ms112×body5120valid
25.0ms226×body320valid
9.0ms119×body160valid