Details

Time bar (total: 4.4s)

sample38.0ms

Algorithm
intervals
Results
8.0ms37×body2560valid
7.0ms197×body80valid
4.0ms24×body1280valid
3.0ms77×body80nan
2.0ms16×body640valid
0.0ms4×body160valid
0.0ms2×body320valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

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)))

rewrite29.0ms

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))
10.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series420.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
173.0ms
(- (* b b) (* (* 4.0 a) c))
73.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify43.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0405779
11563685
25001674

prune215.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.9b

localize16.0ms

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)))

rewrite31.0ms

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:
12.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
7.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series332.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ 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))))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify64.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05251588
125701375
250011308

prune246.0ms

Filtered
126 candidates to 72 candidates (57.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt 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
101×times-frac
75×*-un-lft-identity
44×add-sqr-sqrt
43×add-cube-cbrt
39×sqrt-prod
16×distribute-lft-out
15×associate-/r/
13×add-exp-log add-cbrt-cube
11×associate-/r*
10×add-log-exp
8×distribute-rgt-neg-in flip3-+ flip-+ div-inv
6×associate-/l*
5×pow1 cbrt-undiv div-exp
2×flip3-- sqrt-div sum-log flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log neg-log prod-exp clear-num cbrt-unprod
Counts
4 → 142
Calls
4 calls:
13.0ms
(/ (sqrt 1) (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
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)))

series331.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(/ (sqrt 1) (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
44.0ms
(- (* b b) (* (* 4.0 a) c))
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify74.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
05812422
127152170
250031885

prune259.0ms

Filtered
154 candidates to 72 candidates (46.8%)
Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.9b

localize18.0ms

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)))

rewrite43.0ms

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))))
19.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (* 2.0 a))
7.0ms
(- (pow b 2) (pow b 2))
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series154.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (* 2.0 a))
1.0ms
(- (pow b 2) (pow b 2))
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify158.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (145.0ms)

IterNodesCost
0516756
13101606
25001569

prune296.0ms

Filtered
116 candidates to 75 candidates (64.7%)
Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.9b

regimes221.0ms

Accuracy

95.9% (1.0b remaining)

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

bsearch181.0ms

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
258.0ms1045×body2560valid
246.0ms5938×body80valid
173.0ms852×body1280valid
113.0ms2870×body80nan
68.0ms442×body640valid
32.0ms112×body5120valid
32.0ms226×body320valid
9.0ms119×body160valid