Details

Time bar (total: 5.4s)

sample81.0ms

Algorithm
intervals
Results
18.0ms188×body80valid
15.0ms32×body2560valid
14.0ms25×body1280valid
9.0ms91×body80nan
5.0ms17×body640valid
3.0ms6×body5120valid
2.0ms7×body320valid
1.0ms3×body160valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1649
21149
31359
41449
51489
61489

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b
(- (* b b) (* 4.0 (* a c)))
0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 77
Calls
4 calls:
36.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series287.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
47.0ms
(- (* b b) (* 4.0 (* a c)))
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
67.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0404890
11481801
25001796

prune237.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.4b
(- (* b b) (* 4.0 (* a c)))
0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/r*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/r/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
22.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series362.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
43.0ms
(- (* b b) (* 4.0 (* a c)))
75.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0361863
11479768
25002759

prune224.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.4b
(- (* b b) (* 4.0 (* a c)))
0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
19×add-sqr-sqrt
16×*-un-lft-identity
13×add-cbrt-cube
10×prod-exp add-log-exp
8×add-cube-cbrt
7×pow1 associate-*r* associate-*l*
5×flip3-- sqrt-prod flip--
4×div-exp cbrt-unprod distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times sub-neg rec-exp distribute-rgt-neg-in sqrt-div 1-exp associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 85
Calls
4 calls:
57.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
3.0ms
(- (* b b) (* 4.0 (* a c)))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series280.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
46.0ms
(- (* b b) (* 4.0 (* a c)))
72.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify56.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0469991
12048866
25002857

prune220.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.0b

localize17.0ms

Local error

Found 4 expressions with local error:

1.4b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.7b
(* (/ 1 (* 2.0 a)) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))))
16.1b
(- (pow b 2) (pow b 2))
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
24×*-un-lft-identity
23×add-exp-log
22×unpow-prod-down
16×add-cube-cbrt difference-of-squares
13×add-cbrt-cube
12×unpow2 sqr-pow
10×distribute-rgt-out-- prod-exp add-log-exp
8×distribute-lft-out--
7×pow1 associate-*l*
4×div-exp cbrt-unprod
3×flip3-+ times-frac associate-*r* sqrt-prod flip-+
2×cbrt-undiv frac-times rec-exp flip3-- sqrt-div 1-exp associate-*r/ sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 distribute-rgt-in associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in distribute-lft-in sqrt-pow1 pow1/2 +-inverses diff-log pow-prod-down neg-log associate-*l/ *-commutative div-inv unswap-sqr
Counts
4 → 114
Calls
4 calls:
12.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
187.0ms
(* (/ 1 (* 2.0 a)) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))))
11.0ms
(- (pow b 2) (pow b 2))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series161.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms
(* (/ 1 (* 2.0 a)) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))))
1.0ms
(- (pow b 2) (pow b 2))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify32.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
0663841
15001626

prune292.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.0b

regimes170.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 29.1b

bsearch219.0ms

Steps
ItersRangePoint
8
5.408584085660923e+89
1.6744273082514658e+93
9.707084530269415e+92
9
8.576105435740817e-275
2.0823221738669132e-266
1.391640372823256e-271
7
-1.2511146020293208e+129
-2.5570389401985865e+127
-3.270912095499513e+127

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04425
14425

end0.0ms

sample2.3s

Algorithm
intervals
Results
577.0ms5792×body80valid
499.0ms1041×body2560valid
362.0ms916×body1280valid
261.0ms2838×body80nan
152.0ms481×body640valid
61.0ms250×body320valid
60.0ms107×body5120valid
18.0ms107×body160valid