Details

Time bar (total: 8.0s)

sample285.0ms

Algorithm
intervals
Results
7.0ms172×body80valid
7.0ms34×body2560valid
5.0ms32×body1280valid
2.0ms79×body80nan
2.0ms9×body5120valid
2.0ms16×body640valid
1.0ms9×body320valid
0.0ms3×body160valid

simplify21.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0147
1227
2257
3277
4297
5297

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 35.6b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b
(- (* b_2 b_2) (* a c))
1.2b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
51×*-un-lft-identity
20×difference-of-squares
17×sqrt-prod
15×add-cube-cbrt times-frac
14×unswap-sqr
10×distribute-lft-out add-log-exp
8×associate-*l* distribute-lft-out--
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in associate-/l*
4×swap-sqr *-commutative
3×associate-/r*
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 → 108
Calls
4 calls:
31.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
16.0ms
(- (* b_2 b_2) (* a c))
24.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
30.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series267.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms
(- (* b_2 b_2) (* a c))
73.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
70.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify48.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0404996
11431933
25001916

prune261.0ms

Filtered
120 candidates to 77 candidates (64.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New11010120
Fresh000
Picked101
Done000
Total11110121

Merged error: 6.1b

Counts
121 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.6b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.6b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
383×*-un-lft-identity
298×times-frac
253×add-sqr-sqrt
115×add-cube-cbrt
74×distribute-lft-out
66×difference-of-squares
60×distribute-lft-out--
51×associate-/l*
45×sqrt-prod
41×associate-*l*
28×distribute-rgt-neg-in
21×associate-/l/
17×associate-/r*
11×add-exp-log add-cbrt-cube
10×associate-/r/
8×add-log-exp
7×flip3-- flip-- unswap-sqr
6×div-inv
5×pow1
4×cbrt-undiv div-exp
3×frac-2neg clear-num
2×flip3-+ sqrt-div diff-log swap-sqr *-commutative flip-+
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 308
Calls
4 calls:
26.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
46.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
34.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
18.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series439.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
141.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
168.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
63.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify131.0ms

Algorithm
egg-herbie
Counts
320 → 320
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
08084888
136094626
250014600

prune535.0ms

Filtered
320 candidates to 160 candidates (50.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New3164320
Fresh369
Picked101
Done000
Total32010330

Merged error: 6.0b

Counts
330 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.1b
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.6b
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
1014×times-frac
682×add-sqr-sqrt
664×*-un-lft-identity
428×add-cube-cbrt
135×associate-/l*
124×difference-of-squares
118×distribute-lft-out--
75×associate-/r/
74×sqrt-prod
68×associate-/r*
57×distribute-rgt-neg-in
41×associate-/l/
23×div-inv
18×add-exp-log add-cbrt-cube
9×cbrt-undiv div-exp
8×frac-2neg clear-num add-log-exp
7×flip3-- flip-- unswap-sqr
5×pow1
4×associate-*l*
2×sqrt-div diff-log swap-sqr *-commutative
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 605
Calls
4 calls:
25.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
39.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
55.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
16.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series461.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
179.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
150.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
63.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify115.0ms

Algorithm
egg-herbie
Counts
617 → 617
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
0188410029
150019419

prune1.3s

Filtered
617 candidates to 371 candidates (60.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New6143617
Fresh459
Picked011
Done000
Total6189627

Merged error: 6.0b

Counts
627 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b_2 b_2) (* a c))
0.8b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0b
(/ (/ (cbrt a) (/ 1 c)) (cbrt a))
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
1479×times-frac
750×add-sqr-sqrt
715×*-un-lft-identity
695×add-cube-cbrt
552×cbrt-prod
118×associate-/l*
63×associate-/r/
51×div-inv
40×associate-/r*
27×add-cbrt-cube
22×cbrt-undiv associate-/l/ difference-of-squares
19×add-exp-log
18×sqrt-prod
14×unswap-sqr
11×div-exp
10×distribute-lft-out-- add-log-exp
9×frac-2neg clear-num
8×associate-*l*
5×pow1
4×swap-sqr *-commutative
3×flip3-- diff-log flip--
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square rec-exp distribute-rgt-neg-in sqrt-pow1 pow1/2 1-exp neg-log
Counts
4 → 763
Calls
4 calls:
15.0ms
(- (* b_2 b_2) (* a c))
29.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
34.0ms
(/ (/ (cbrt a) (/ 1 c)) (cbrt a))
15.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series174.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* b_2 b_2) (* a c))
70.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms
(/ (/ (cbrt a) (/ 1 c)) (cbrt a))
65.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify125.0ms

Algorithm
egg-herbie
Counts
775 → 775
Iterations

Useful iterations: 1 (44.0ms)

IterNodesCost
0253310064
150018493

prune2.0s

Filtered
775 candidates to 462 candidates (59.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New7732775
Fresh257
Picked101
Done011
Total7768784

Merged error: 6.0b

Counts
784 → 8

regimes160.0ms

Accuracy

81.8% (4.3b remaining)

Error of 9.7b against oracle of 5.4b and baseline of 29.1b

bsearch110.0ms

Steps
ItersRangePoint
9
4.546949039871578e+116
7.0067478635952275e+121
8.403598091093321e+118
10
-1.0320842654441656e-69
-6.354733239957269e-82
-2.7633434444009994e-73

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03717
13717

end0.0ms

sample980.0ms

Algorithm
intervals
Results
211.0ms1054×body2560valid
195.0ms5814×body80valid
142.0ms890×body1280valid
85.0ms2860×body80nan
60.0ms470×body640valid
26.0ms111×body5120valid
22.0ms235×body320valid
8.0ms126×body160valid