Details

Time bar (total: 4.4s)

sample278.0ms

Algorithm
intervals
Results
7.0ms35×body2560valid
6.0ms197×body80valid
4.0ms28×body1280valid
4.0ms90×body80nan
2.0ms13×body640valid
1.0ms11×body320valid
0.0ms2×body5120valid
0.0ms2×body160valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0147
1227
2257
3277
4297
5297

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
22.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
16×add-sqr-sqrt
15×add-cube-cbrt times-frac
10×distribute-lft-out add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in associate-/l*
3×associate-/r* sqrt-prod
2×neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div sum-log flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp neg-log clear-num div-inv
Counts
4 → 80
Calls
4 calls:
45.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
11.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms
(- (* b_2 b_2) (* a c))
6.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series269.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
72.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
33.0ms
(- (* b_2 b_2) (* a c))
75.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify40.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0358790
11261727
25001705

prune230.0ms

Filtered
92 candidates to 69 candidates (75.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.7b

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b_2 b_2) (* a c))
3.7b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.4b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
186×times-frac
154×add-sqr-sqrt
153×*-un-lft-identity
89×add-cube-cbrt
32×distribute-lft-out-- difference-of-squares
30×associate-/l*
19×sqrt-prod
16×distribute-rgt-neg-in
11×add-exp-log add-cbrt-cube
10×associate-/r* associate-/r/
7×flip3-- flip--
6×div-inv add-log-exp
5×pow1
4×cbrt-undiv div-exp
3×associate-/l/
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 200
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
41.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
28.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series398.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* b_2 b_2) (* a c))
137.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
166.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify108.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
07293368
133203193
250013167

prune473.0ms

Filtered
212 candidates to 142 candidates (67.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.6b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
12.1b
(/ a (* a c))
22.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
11×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt
5×pow1
4×sqrt-prod
3×flip3-- times-frac diff-log flip-- associate-/l*
2×cbrt-undiv sub-neg sqrt-div div-exp 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 prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 66
Calls
4 calls:
12.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms
(- (* b_2 b_2) (* a c))
3.0ms
(/ a (* a c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series166.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
32.0ms
(- (* b_2 b_2) (* a c))
6.0ms
(/ a (* a c))
60.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify143.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0294461
11076416
24954406
35001406

prune181.0ms

Filtered
78 candidates to 56 candidates (71.8%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (* (/ 1 c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
22.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
16×div-exp
13×add-cbrt-cube
12×add-sqr-sqrt prod-exp
11×*-un-lft-identity
10×add-log-exp
8×pow1 rec-exp 1-exp
7×add-cube-cbrt
5×flip3-- associate-/r/ flip--
4×cbrt-undiv sqrt-prod
3×times-frac diff-log associate-/l*
2×frac-times sub-neg pow-flip sqrt-div associate-*r/ cbrt-unprod distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 pow-prod-down neg-log associate-*l/ clear-num associate-/r* div-inv inv-pow
Counts
4 → 88
Calls
4 calls:
31.0ms
(/ 1 (* (/ 1 c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
12.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms
(- (* b_2 b_2) (* a c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series328.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(/ 1 (* (/ 1 c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
69.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
32.0ms
(- (* b_2 b_2) (* a c))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify52.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0444855
11958714
25001700

prune187.0ms

Filtered
100 candidates to 63 candidates (63.0%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.6b

regimes147.0ms

Accuracy

94.5% (1.3b remaining)

Error of 6.5b against oracle of 5.2b and baseline of 28.9b

bsearch143.0ms

Steps
ItersRangePoint
9
8.465625442272063e+58
8.825425083170634e+65
1.5590000675849395e+64
7
-6.207156945681686e-303
-1.2633929192945347e-304
-2.1189943210807787e-304
11
-1.7053146236540368e+120
-1.0719231849388273e+91
-3.5940112039867074e+100

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04022
14222
24222

end0.0ms

sample984.0ms

Algorithm
intervals
Results
208.0ms1083×body2560valid
190.0ms5784×body80valid
141.0ms926×body1280valid
91.0ms2977×body80nan
55.0ms453×body640valid
25.0ms106×body5120valid
23.0ms258×body320valid
7.0ms119×body160valid