Details

Time bar (total: 4.8s)

sample47.0ms

Algorithm
intervals
Results
8.0ms35×body1280valid
7.0ms35×body2560valid
7.0ms191×body80valid
4.0ms115×body80nan
2.0ms11×body640valid
1.0ms4×body5120valid
1.0ms5×body160valid
0.0ms3×body320valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1649
21149
31359
41449
51489
61489

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize12.0ms

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)))
1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite113.0ms

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:
67.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
11.0ms
(- (* b b) (* 4.0 (* a c)))
23.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series267.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
44.0ms
(- (* b b) (* 4.0 (* a c)))
71.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
64.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0404890
11481801
25001796

prune252.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize14.0ms

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)))
1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite93.0ms

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:
46.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
9.0ms
(- (* b b) (* 4.0 (* a c)))
23.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series344.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
68.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
65.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0361863
11479768
25002759

prune236.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.7b

localize18.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.8b
(sqrt (- (* b b) (* 4.0 (* a c))))
23.8b
(sqrt (- (* b b) (* 4.0 (* a c))))
23.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×*-un-lft-identity
10×sqrt-prod
8×add-log-exp
7×pow1 add-cube-cbrt
6×sqrt-div
4×add-exp-log flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg distribute-rgt-neg-in neg-log
Counts
4 → 63
Calls
4 calls:
26.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series271.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
67.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
67.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
63.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify106.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (98.0ms)

IterNodesCost
0207609
1768588
23109577
35001573

prune282.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.7b

localize19.0ms

Local error

Found 4 expressions with local error:

1.7b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.5b
(/ a (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) 2.0))
19.0b
(- (pow b 2) (pow b 2))
23.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
72×add-sqr-sqrt
63×*-un-lft-identity
55×add-cube-cbrt
22×unpow-prod-down
16×difference-of-squares
13×associate-/r*
12×unpow2 sqr-pow
10×distribute-rgt-out-- add-log-exp
9×add-exp-log add-cbrt-cube
8×distribute-lft-out--
5×pow1 div-inv
3×cbrt-undiv div-exp sqrt-prod associate-/l*
2×flip3-- sqrt-div sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 flip3-+ pow1/2 +-inverses diff-log neg-log clear-num associate-/r/ flip-+
Counts
4 → 147
Calls
4 calls:
22.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
123.0ms
(/ a (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) 2.0))
22.0ms
(- (pow b 2) (pow b 2))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series157.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms
(/ a (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) 2.0))
1.0ms
(- (pow b 2) (pow b 2))
68.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify163.0ms

Algorithm
egg-herbie
Counts
159 → 159
Iterations

Useful iterations: 2 (147.0ms)

IterNodesCost
06911543
137991324
250011298

prune485.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.7b

regimes170.0ms

Accuracy

94.6% (1.3b remaining)

Error of 6.8b against oracle of 5.4b and baseline of 30.1b

bsearch190.0ms

Steps
ItersRangePoint
9
1.7695728335377845e+74
3.738006738925262e+80
2.1545230570852197e+80
10
-7.974158366206419e-290
-1.2877603006343203e-300
-1.3008221290903186e-300
8
-1.0016636615098116e+114
-3.260864156300871e+111
-8.723712166727036e+113

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04626
14626

end0.0ms

sample1.2s

Algorithm
intervals
Results
236.0ms1061×body2560valid
222.0ms5906×body80valid
165.0ms913×body1280valid
101.0ms2949×body80nan
64.0ms465×body640valid
25.0ms97×body5120valid
20.0ms196×body320valid
8.0ms119×body160valid