Details

Time bar (total: 4.1s)

sample41.0ms

Algorithm
intervals
Results
11.0ms37×body2560valid
8.0ms197×body80valid
5.0ms24×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

prune3.0ms

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)))

rewrite26.0ms

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))
7.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series289.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
42.0ms
(- (* b b) (* (* 4.0 a) c))
75.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify44.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0405779
11563685
25001674

prune215.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.9b

localize12.0ms

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)))

rewrite30.0ms

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))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series324.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
46.0ms
(- (* b b) (* (* 4.0 a) c))
76.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms
(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

prune242.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* (cbrt 1) (cbrt 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
25×add-exp-log
21×*-un-lft-identity times-frac
19×add-cbrt-cube
11×associate-/r*
10×cbrt-undiv add-sqr-sqrt div-exp add-log-exp
9×add-cube-cbrt
6×distribute-lft-out
5×pow1 prod-exp associate-/r/ cbrt-unprod
3×distribute-rgt-neg-in flip3-+ sqrt-prod flip-+ div-inv
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 clear-num associate-/l*
Counts
4 → 88
Calls
4 calls:
14.0ms
(/ (* (cbrt 1) (cbrt 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)))

series330.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
46.0ms
(- (* 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)))

simplify63.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05191272
126311040
25001949

prune255.0ms

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:
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.0ms
(/ (+ (- (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)))

series156.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (* 2.0 a))
1.0ms
(- (pow b 2) (pow b 2))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify156.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (147.0ms)

IterNodesCost
0516756
13101606
25001569

prune291.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.9b

regimes189.0ms

Accuracy

95.9% (1.0b remaining)

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

bsearch163.0ms

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

sample1.1s

Algorithm
intervals
Results
248.0ms1045×body2560valid
237.0ms5938×body80valid
157.0ms852×body1280valid
102.0ms2870×body80nan
64.0ms442×body640valid
31.0ms112×body5120valid
25.0ms226×body320valid
9.0ms119×body160valid