Details

Time bar (total: 4.5s)

sample40.0ms

Algorithm
intervals
Results
8.0ms201×body80valid
6.0ms31×body1280valid
5.0ms21×body2560valid
4.0ms103×body80nan
2.0ms13×body640valid
1.0ms3×body5120valid
1.0ms7×body320valid
0.0ms5×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: 29.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite59.0ms

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))
14.0ms
(+ (- 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)))

series295.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(- (* b b) (* (* 4.0 a) c))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify50.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0405779
11563685
25001674

prune228.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite52.0ms

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:
27.0ms
(/ 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)))

series331.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms
(- (* b b) (* (* 4.0 a) c))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify71.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05251588
125701375
250011308

prune254.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.4b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
3.4b
(exp (log (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
10×add-log-exp
8×add-sqr-sqrt
7×add-cube-cbrt
6×pow1
5×log-prod exp-sum
4×add-exp-log exp-prod add-cbrt-cube distribute-lft-out
3×sqrt-prod
2×log-div flip3-- distribute-rgt-neg-in flip3-+ exp-diff sqrt-div sum-log flip-- flip-+
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log neg-log log-pow rem-exp-log
Counts
4 → 61
Calls
4 calls:
14.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(exp (log (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series273.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms
(- (* b b) (* (* 4.0 a) c))
79.0ms
(exp (log (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify121.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 3 (113.0ms)

IterNodesCost
0273626
1990574
24222541
35002528

prune227.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.4b

localize19.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0b
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (* 2.0 a))
14.8b
(- (pow b 2) (pow b 2))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite196.0ms

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))))
161.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (* 2.0 a))
12.0ms
(- (pow b 2) (pow b 2))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series161.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- 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))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify166.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (155.0ms)

IterNodesCost
0516756
13101606
25001569

prune303.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.4b

regimes206.0ms

Accuracy

96.4% (1.0b remaining)

Error of 6.5b against oracle of 5.5b and baseline of 34.1b

bsearch198.0ms

Steps
ItersRangePoint
8
4.989131466200188e+139
3.737025446948691e+142
3.256101961139753e+141
9
3.1425740402568386e-306
5.4379290726615864e-300
3.2001964328628576e-306
10
-1.5405955983178716e+163
-1.402598515452623e+153
-2.3044033969831823e+153

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04024
14024

end0.0ms

sample1.2s

Algorithm
intervals
Results
267.0ms1101×body2560valid
239.0ms5850×body80valid
184.0ms921×body1280valid
110.0ms2888×body80nan
70.0ms450×body640valid
31.0ms228×body320valid
30.0ms103×body5120valid
9.0ms121×body160valid