Details

Time bar (total: 20.4s)

sample298.0ms

Algorithm
intervals
Results
8.0ms40×body2560valid
6.0ms181×body80valid
6.0ms36×body1280valid
4.0ms21×body640valid
3.0ms100×body80nan
0.0ms5×body320valid
0.0ms1×body5120valid
0.0ms2×body160valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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: 34.8b

localize11.0ms

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))))
0.6b
(- (* b_2 b_2) (* a c))
23.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite45.0ms

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:
22.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms
(- (* b_2 b_2) (* a c))
6.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series271.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
70.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
40.0ms
(- (* b_2 b_2) (* a c))
68.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify49.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0389850
11366779
25001753

prune298.0ms

Filtered
112 candidates to 88 candidates (78.6%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.4b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.5b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
199×add-sqr-sqrt
198×*-un-lft-identity
186×times-frac
130×add-cube-cbrt
60×prod-diff
50×sqrt-prod
38×distribute-rgt-neg-in
34×distribute-lft-out-- difference-of-squares
30×associate-/l*
21×distribute-lft-neg-in
11×add-exp-log add-cbrt-cube
10×fma-neg associate-/r* associate-/r/
8×add-log-exp
7×neg-mul-1 flip3-- flip--
6×div-inv
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×associate-/l/
2×frac-2neg sqrt-div diff-log clear-num
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 284
Calls
4 calls:
11.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series442.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
139.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
170.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify143.0ms

Algorithm
egg-herbie
Counts
296 → 296
Iterations

Useful iterations: 2 (100.0ms)

IterNodesCost
09195579
139184508
250014505

prune589.0ms

Filtered
296 candidates to 172 candidates (58.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.7b
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
4.4b
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
23.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
3489×times-frac
1872×add-sqr-sqrt
1871×*-un-lft-identity
1387×add-cube-cbrt
267×associate-/l*
242×distribute-lft-out-- difference-of-squares
154×sqrt-prod
142×distribute-rgt-neg-in
60×prod-diff
58×div-inv
41×add-exp-log
28×div-exp
23×add-cbrt-cube
21×distribute-lft-neg-in
13×cbrt-undiv
10×fma-neg
8×add-log-exp
7×neg-mul-1
6×associate-/r*
5×pow1
4×expm1-log1p-u associate-/r/ log1p-expm1-u
3×rec-exp 1-exp
2×flip3-- frac-2neg sqrt-div diff-log div-sub clear-num flip-- associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 1226
Calls
4 calls:
11.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
65.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
93.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
110.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
68.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify281.0ms

Algorithm
egg-herbie
Counts
1238 → 1238
Iterations

Useful iterations: 1 (68.0ms)

IterNodesCost
0446326936
1500225697

prune2.5s

Filtered
1238 candidates to 612 candidates (49.4%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)
1.5b
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
23.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite665.0ms

Algorithm
rewrite-expression-head
Rules
11418×times-frac
5965×add-sqr-sqrt
5964×*-un-lft-identity
4352×add-cube-cbrt
2703×cbrt-prod
806×distribute-lft-out-- difference-of-squares
477×associate-/l*
436×sqrt-prod
424×distribute-rgt-neg-in
97×div-inv
60×prod-diff
41×add-exp-log
28×div-exp
21×distribute-lft-neg-in
17×add-cbrt-cube
13×cbrt-undiv
10×fma-neg
9×associate-/r*
8×add-log-exp
7×neg-mul-1 associate-/r/
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×rec-exp 1-exp
2×flip3-- frac-2neg sqrt-div diff-log div-sub clear-num flip-- associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 3362
Calls
4 calls:
10.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)
135.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series459.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
219.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)
106.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify741.0ms

Algorithm
egg-herbie
Counts
3374 → 3374
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
0500194251

prune11.5s

Filtered
3374 candidates to 2023 candidates (60.0%)
Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.0b

regimes226.0ms

Accuracy

88.8% (2.8b remaining)

Error of 8.5b against oracle of 5.7b and baseline of 30.4b

bsearch165.0ms

Steps
ItersRangePoint
7
4.0940537712502537e+21
1.2145431101494081e+23
9.700127799776669e+22
10
-1.5615949759157218e-303
2.965657841234824e-295
2.5644244811738995e-299
10
-2693.2368339428763
-1.4570494276460042e-08
-2655.8773955326765

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05440
15440

end0.0ms

sample1.0s

Algorithm
intervals
Results
220.0ms1142×body2560valid
197.0ms5759×body80valid
149.0ms938×body1280valid
92.0ms2985×body80nan
58.0ms468×body640valid
23.0ms90×body5120valid
21.0ms230×body320valid
7.0ms113×body160valid