Details

Time bar (total: 4.6s)

sample44.0ms

Algorithm
intervals
Results
10.0ms186×body80valid
8.0ms34×body2560valid
5.0ms25×body1280valid
3.0ms88×body80nan
2.0ms14×body640valid
1.0ms13×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1649
21149
31359
41449
51489
61489

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b
(- (* b b) (* 4.0 (* a c)))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite56.0ms

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:
35.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
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))))

series278.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
73.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
46.0ms
(- (* b b) (* 4.0 (* a c)))
67.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0404890
11481801
25001796

prune256.0ms

Filtered
89 candidates to 65 candidates (73.0%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b
(- (* b b) (* 4.0 (* a c)))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite77.0ms

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:
56.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
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))))

series281.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
75.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms
(- (* b b) (* 4.0 (* a c)))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify57.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0469992
12048866
25002857

prune237.0ms

Filtered
97 candidates to 64 candidates (66.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.8b

localize16.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* 4.0 (* a c)))
4.4b
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
11.0b
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt
61×*-un-lft-identity
52×times-frac
51×add-exp-log
30×add-cube-cbrt associate-*l*
27×add-cbrt-cube
20×prod-exp
18×difference-of-squares
16×div-exp
13×distribute-lft-out
12×sqrt-prod
9×distribute-lft-out--
8×cbrt-undiv cbrt-unprod
7×pow1 associate-*r*
6×associate-/r* add-log-exp
4×rec-exp flip3-- 1-exp associate-/r/ flip-- associate-/l*
3×div-inv
2×sqrt-div associate-/l/ unswap-sqr
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 149
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
65.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
28.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series466.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* 4.0 (* a c)))
159.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
194.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify118.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 2 (94.0ms)

IterNodesCost
07602359
137422008
250011985

prune389.0ms

Filtered
161 candidates to 102 candidates (63.4%)
Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.7b

localize14.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.4b
(- (* b b) (* 4.0 (* a c)))
14.5b
(/ (* 4.0 (* a c)) (* 2.0 a))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×prod-exp cbrt-unprod
8×add-log-exp
7×*-un-lft-identity
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square frac-2neg sqrt-pow1 times-frac pow1/2 clear-num associate-/r* div-inv associate-/l* distribute-lft-out--
Counts
4 → 67
Calls
4 calls:
20.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(/ (* 4.0 (* a c)) (* 2.0 a))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series200.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
43.0ms
(- (* b b) (* 4.0 (* a c)))
13.0ms
(/ (* 4.0 (* a c)) (* 2.0 a))
68.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify56.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0403576
12221498
25001498

prune196.0ms

Filtered
79 candidates to 54 candidates (68.4%)
Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.7b

regimes293.0ms

Accuracy

95.6% (1.1b remaining)

Error of 6.8b against oracle of 5.7b and baseline of 29.6b

bsearch141.0ms

Steps
ItersRangePoint
5
1.1874868645648804e+84
3.824179182553312e+84
1.5849721394456554e+84
7
5.816336440788529e-167
1.4589371595794865e-165
5.877669040907696e-167
8
-3.734333779790662e+128
-2.2987999557012895e+125
-2.4028493234920365e+128

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04324
14324

end0.0ms

sample1.1s

Algorithm
intervals
Results
251.0ms1089×body2560valid
228.0ms5868×body80valid
168.0ms894×body1280valid
104.0ms2862×body80nan
68.0ms441×body640valid
34.0ms105×body5120valid
23.0ms212×body320valid
8.0ms116×body160valid