Details

Time bar (total: 6.3s)

sample35.0ms

Algorithm
intervals
Results
7.0ms39×body2560valid
6.0ms171×body80valid
4.0ms26×body1280valid
2.0ms74×body80nan
2.0ms9×body5120valid
2.0ms13×body640valid
1.0ms13×body320valid
0.0ms2×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1337
2467
3497
4497

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b
(- (* b_2 b_2) (* a c))
25.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
78×*-un-lft-identity
61×prod-diff
58×add-cube-cbrt
38×sqrt-prod
26×distribute-rgt-neg-in
21×distribute-lft-neg-in times-frac
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
7×neg-mul-1 associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 171
Calls
4 calls:
39.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
19.0ms
(- (- 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)))

series417.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
69.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
32.0ms
(- (* b_2 b_2) (* a c))
236.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify68.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05493055
118262150
250012063

prune343.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
1.0b
(- (* b_2 b_2) (* a c))
8.2b
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
25.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
1339×times-frac
946×add-sqr-sqrt
940×*-un-lft-identity
926×add-cube-cbrt
749×prod-diff
323×sqrt-prod
210×distribute-rgt-neg-in
207×distribute-lft-neg-in
69×neg-mul-1
60×div-inv
35×fma-neg
8×add-log-exp
7×distribute-lft-out--
6×add-exp-log add-cbrt-cube associate-/l* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- sqrt-div flip-- log1p-expm1-u
3×associate-/r*
2×sub-neg diff-log associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square distribute-rgt-out-- frac-2neg sqrt-pow1 pow1/2 div-sub div-exp clear-num frac-sub sub-div
Counts
4 → 889
Calls
4 calls:
9.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
3.0ms
(- (* b_2 b_2) (* a c))
74.0ms
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series278.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
33.0ms
(- (* b_2 b_2) (* a c))
86.0ms
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify263.0ms

Algorithm
egg-herbie
Counts
901 → 901
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
0195839816
1500125884

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.4b

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b_2 b_2) (* a c))
15.7b
(- (/ (- b_2) a) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) a)))
25.6b
(sqrt (- (* b_2 b_2) (* a c)))
25.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
48×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
35×fma-neg prod-diff
18×distribute-lft-neg-in distribute-rgt-neg-in
12×sqrt-div
8×add-log-exp
6×pow1 neg-mul-1 flip3-- sqrt-prod flip--
5×frac-sub
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
2×frac-times sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-*r/ associate-*l/ div-inv
1×associate--l- neg-sub0 div-sub sub-div
Counts
4 → 139
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
33.0ms
(- (/ (- b_2) a) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) a)))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series239.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(- (* b_2 b_2) (* a c))
87.0ms
(- (/ (- b_2) a) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) a)))
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))
60.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify62.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
05752867
118511830
250021766

prune456.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.4b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b_2 b_2) (* a c))
15.8b
(- (/ (- b_2) a) (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (cbrt (- (* b_2 b_2) (* a c)))) a)))
26.4b
(cbrt (- (* b_2 b_2) (* a c)))
26.4b
(cbrt (- (* b_2 b_2) (* a c)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
46×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
35×fma-neg prod-diff
18×distribute-lft-neg-in distribute-rgt-neg-in
8×add-log-exp
6×cbrt-prod neg-mul-1
4×pow1 add-exp-log expm1-log1p-u cbrt-div flip3-- add-cbrt-cube flip-- log1p-expm1-u
2×sub-neg pow1/3 diff-log associate-*r/ div-inv
1×associate--l- neg-sub0 div-sub frac-sub sub-div
Counts
4 → 131
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
32.0ms
(- (/ (- b_2) a) (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (cbrt (- (* b_2 b_2) (* a c)))) a)))
2.0ms
(cbrt (- (* b_2 b_2) (* a c)))
2.0ms
(cbrt (- (* b_2 b_2) (* a c)))

series316.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* b_2 b_2) (* a c))
113.0ms
(- (/ (- b_2) a) (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (cbrt (- (* b_2 b_2) (* a c)))) a)))
85.0ms
(cbrt (- (* b_2 b_2) (* a c)))
86.0ms
(cbrt (- (* b_2 b_2) (* a c)))

simplify76.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05812809
121262500
250022458

prune511.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.4b

regimes243.0ms

Accuracy

84.6% (4.4b remaining)

Error of 9.9b against oracle of 5.5b and baseline of 34.3b

bsearch96.0ms

Steps
ItersRangePoint
8
1.9559514031553493e+101
2.0413668072230428e+104
1.6764314440115407e+104
11
-1.4160683835321931e-14
-4.058620405728376e-48
-8.260729798395838e-43

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02917
12917

end0.0ms

sample1.0s

Algorithm
intervals
Results
214.0ms1069×body2560valid
191.0ms5806×body80valid
139.0ms855×body1280valid
92.0ms2840×body80nan
63.0ms469×body640valid
26.0ms110×body5120valid
23.0ms244×body320valid
9.0ms144×body160valid