Details

Time bar (total: 6.7s)

sample302.0ms

Algorithm
intervals
Results
11.0ms188×body80valid
10.0ms33×body2560valid
5.0ms97×body80nan
5.0ms26×body1280valid
3.0ms15×body640valid
2.0ms12×body320valid
0.0ms1×body5120valid
0.0ms3×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1337
2467
3497
4497

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.2b
(- (* b_2 b_2) (* a c))
1.4b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite92.0ms

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:
53.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms
(- (* b_2 b_2) (* a c))
18.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series262.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms
(- (* b_2 b_2) (* a c))
71.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
74.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify69.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05493055
118262150
250022063

prune356.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
1.2b
(- (* b_2 b_2) (* a c))
7.6b
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
23.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite192.0ms

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:
8.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
3.0ms
(- (* b_2 b_2) (* a c))
85.0ms
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
5.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series289.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
38.0ms
(- (* b_2 b_2) (* a c))
88.0ms
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
60.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify262.0ms

Algorithm
egg-herbie
Counts
901 → 901
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0195839816
1500125884

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
1.2b
(- (* b_2 b_2) (* a c))
1.4b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
181×prod-diff
146×add-sqr-sqrt
139×*-un-lft-identity
130×add-cube-cbrt
95×sqrt-prod
62×distribute-rgt-in distribute-lft-in
59×distribute-rgt-neg-in
57×distribute-lft-neg-in
19×neg-mul-1
13×add-exp-log associate-*l*
11×times-frac fma-neg
10×add-log-exp
9×add-cbrt-cube
7×pow1 associate-*r*
5×flip3-- flip--
4×expm1-log1p-u sub-neg prod-exp log1p-expm1-u distribute-lft-out-- difference-of-squares
3×diff-log unswap-sqr
2×frac-times sqrt-div associate-*r/ div-exp cbrt-unprod
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down neg-log associate-*l/ *-commutative div-inv
Counts
4 → 292
Calls
4 calls:
67.0ms
(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
3.0ms
(- (* b_2 b_2) (* a c))
21.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
39.0ms
(- (* b_2 b_2) (* a c))
68.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
64.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify108.0ms

Algorithm
egg-herbie
Counts
304 → 304
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
09067441
132954548
250014309

prune361.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.2b
(- (* b_2 b_2) (* a c))
1.4b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite79.0ms

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:
46.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms
(- (* b_2 b_2) (* a c))
18.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series252.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms
(- (* b_2 b_2) (* a c))
72.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
60.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify71.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05493056
118142150
250012063

prune281.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.5b

regimes245.0ms

Accuracy

84.5% (4.5b remaining)

Error of 10.3b against oracle of 5.8b and baseline of 34.8b

bsearch123.0ms

Steps
ItersRangePoint
11
3.0336165705843857e+124
3.3022304128508224e+146
1.2699491303403745e+143
10
-2.4076762225838956e-89
-7.528955394503449e-103
-2.37327700068816e-89

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02511
12511

end0.0ms

sample1.4s

Algorithm
intervals
Results
340.0ms5757×body80valid
251.0ms1061×body2560valid
195.0ms968×body1280valid
163.0ms2883×body80nan
73.0ms459×body640valid
29.0ms103×body5120valid
28.0ms220×body320valid
14.0ms118×body160valid