Details

Time bar (total: 4.9s)

sample40.0ms

Algorithm
intervals
Results
7.0ms183×body80valid
6.0ms28×body2560valid
5.0ms29×body1280valid
3.0ms89×body80nan
3.0ms22×body640valid
1.0ms5×body5120valid
0.0ms7×body160valid
0.0ms1×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: 36.0b

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 b) (* 4.0 (* a c)))
1.8b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite105.0ms

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:
64.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms
(- (* b b) (* 4.0 (* a c)))
23.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series313.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
46.0ms
(- (* b b) (* 4.0 (* a c)))
84.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0403779
11514685
25002674

prune228.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.5b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
10.9b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
25.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 154
Calls
4 calls:
21.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
80.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
55.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
11.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series488.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
152.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
184.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify99.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
06402692
129442439
250012426

prune401.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.5b

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* 4.0 (* a c)))
1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.5b
(/ (* 2.0 a) (* 4.0 (* a c)))
25.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt add-log-exp
9×*-un-lft-identity prod-exp cbrt-unprod
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- diff-log flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 70
Calls
4 calls:
8.0ms
(- (* b b) (* 4.0 (* a c)))
24.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
8.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series222.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* 4.0 (* a c)))
85.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
76.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify57.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0413627
12231543
25001535

prune204.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
1.0b
(- (* b b) (* 4.0 (* a c)))
1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
295×add-exp-log
166×div-exp
119×prod-exp
64×1-exp
60×add-cbrt-cube
34×rec-exp
31×times-frac
26×cbrt-undiv
24×add-sqr-sqrt
23×*-un-lft-identity
19×add-cube-cbrt
18×cbrt-unprod
14×associate-/r/
13×associate-/l*
11×frac-times
10×add-log-exp
8×flip3-- flip--
7×associate-*l/
5×pow1 associate-*r/
4×sqrt-prod
3×diff-log un-div-inv div-inv
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/r* associate-/l/
Counts
4 → 179
Calls
4 calls:
65.0ms
(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
10.0ms
(- (* b b) (* 4.0 (* a c)))
21.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series385.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
49.0ms
(- (* b b) (* 4.0 (* a c)))
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
76.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify41.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
011682503
150012016

prune288.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.5b

regimes171.0ms

Accuracy

94.9% (1.2b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 30.1b

bsearch210.0ms

Steps
ItersRangePoint
8
3.1248942757642245e+89
1.1714167766929137e+92
6.09240124692818e+90
12
-2.833440705943036e-251
-4.668939852252329e-295
-2.1023086245622604e-293
10
-7.651517840437919e+135
-3.890563902308465e+123
-4.739386840053889e+131

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05028
15028

end0.0ms

sample1.1s

Algorithm
intervals
Results
223.0ms1058×body2560valid
211.0ms5792×body80valid
159.0ms935×body1280valid
99.0ms2915×body80nan
61.0ms453×body640valid
27.0ms101×body5120valid
22.0ms225×body320valid
8.0ms113×body160valid