Details

Time bar (total: 4.6s)

sample48.0ms

Algorithm
intervals
Results
10.0ms191×body80valid
8.0ms35×body2560valid
6.0ms35×body1280valid
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

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

rewrite103.0ms

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:
60.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
11.0ms
(- (* b b) (* 4.0 (* a c)))
22.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series249.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
40.0ms
(- (* b b) (* 4.0 (* a c)))
66.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
59.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0404890
11481801
25001796

prune235.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize12.0ms

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))))

rewrite85.0ms

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:
42.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
8.0ms
(- (* b b) (* 4.0 (* a c)))
24.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series322.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
41.0ms
(- (* b b) (* 4.0 (* a c)))
66.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
59.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0361864
11479768
25002759

prune215.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.7b

localize16.0ms

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))))

rewrite50.0ms

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:
24.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
8.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
8.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series249.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
61.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
62.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
59.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify98.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (91.0ms)

IterNodesCost
0207609
1768588
23109577
35001573

prune259.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.7b

localize18.0ms

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))))

rewrite165.0ms

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:
20.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
111.0ms
(/ a (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) 2.0))
21.0ms
(- (pow b 2) (pow b 2))
8.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series147.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(+ (- 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))
64.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify158.0ms

Algorithm
egg-herbie
Counts
159 → 159
Iterations

Useful iterations: 2 (142.0ms)

IterNodesCost
06911543
137991324
250011298

prune466.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.7b

regimes163.0ms

Accuracy

94.6% (1.3b remaining)

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

bsearch179.0ms

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

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04626
14626

end0.0ms

sample1.2s

Algorithm
intervals
Results
239.0ms1061×body2560valid
237.0ms5906×body80valid
169.0ms913×body1280valid
107.0ms2949×body80nan
66.0ms465×body640valid
28.0ms97×body5120valid
21.0ms196×body320valid
9.0ms119×body160valid