Details

Time bar (total: 7.4s)

sample281.0ms

Algorithm
intervals
Results
8.0ms189×body80valid
5.0ms28×body2560valid
5.0ms34×body1280valid
3.0ms92×body80nan
2.0ms16×body640valid
2.0ms7×body5120valid
0.0ms4×body160valid
0.0ms2×body320valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0157
1237
2307
3327
4347
5347

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.1b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b
(- (* b_2 b_2) (* a c))
25.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
19×add-sqr-sqrt
18×add-cube-cbrt
15×times-frac
10×fma-def distribute-lft-out add-log-exp
8×distribute-rgt-neg-in
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in associate-/r* sqrt-prod
2×neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div sum-log flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub div-exp prod-diff neg-log clear-num div-inv
Counts
4 → 100
Calls
4 calls:
46.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms
(- (* b_2 b_2) (* a c))
7.0ms
(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))
74.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0389850
11366779
25001753

prune315.0ms

Filtered
112 candidates to 88 candidates (78.6%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b_2 b_2) (* a c))
2.3b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.9b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
25.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite88.0ms

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 expm1-log1p-u div-exp log1p-expm1-u
3×associate-/l/
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff flip-+
Counts
4 → 210
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
44.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
26.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series411.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* b_2 b_2) (* a c))
153.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
167.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
58.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify121.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
07613434
134903258
250023250

prune543.0ms

Filtered
222 candidates to 152 candidates (68.5%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.8b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b
(- (* b_2 b_2) (* a c))
16.5b
(/ a (* a c))
25.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
53×add-sqr-sqrt
52×*-un-lft-identity
48×add-cube-cbrt
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1
5×pow1
4×expm1-log1p-u log1p-expm1-u
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 frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 146
Calls
4 calls:
16.0ms
(- (- 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)))

series173.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
32.0ms
(- (* b_2 b_2) (* a c))
6.0ms
(/ a (* a c))
63.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify63.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
04732541
116081646
250011557

prune291.0ms

Filtered
158 candidates to 80 candidates (50.6%)
Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.8b

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b_2 b_2) (* a c))
1.8b
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
2.3b
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
25.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite297.0ms

Algorithm
rewrite-expression-head
Rules
3489×times-frac
1827×add-sqr-sqrt
1826×*-un-lft-identity
1346×add-cube-cbrt
267×associate-/l*
240×distribute-lft-out-- difference-of-squares
123×sqrt-prod
120×distribute-rgt-neg-in
58×div-inv
41×add-exp-log
28×div-exp
23×add-cbrt-cube
13×cbrt-undiv
6×associate-/r* add-log-exp
5×pow1
4×expm1-log1p-u associate-/r/ log1p-expm1-u
3×rec-exp 1-exp
2×flip3-- frac-2neg sqrt-div div-sub clear-num flip-- associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 1152
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
38.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
106.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series298.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* b_2 b_2) (* a c))
92.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
115.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
59.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify272.0ms

Algorithm
egg-herbie
Counts
1164 → 1164
Iterations

Useful iterations: 1 (69.0ms)

IterNodesCost
0427024794
1500124128

prune2.4s

Filtered
1164 candidates to 582 candidates (50.0%)
Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.8b

regimes203.0ms

Accuracy

91.5% (2.1b remaining)

Error of 7.9b against oracle of 5.7b and baseline of 30.5b

bsearch152.0ms

Steps
ItersRangePoint
10
3.333152020693271e-42
2.392002655991594e-31
2.357286367173993e-31
6
8.954106309325026e-259
7.042142210042974e-258
9.074871364580517e-259
8
-3.734333779790662e+128
-2.2987999557012895e+125
-4.0600238625570494e+127

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05140
15140

end0.0ms

sample978.0ms

Algorithm
intervals
Results
194.0ms1048×body2560valid
192.0ms5872×body80valid
149.0ms910×body1280valid
84.0ms2861×body80nan
53.0ms454×body640valid
23.0ms100×body5120valid
19.0ms219×body320valid
7.0ms123×body160valid