Details

Time bar (total: 34.8s)

sample341.0ms

Algorithm
intervals
Results
7.0ms42×body2560valid
6.0ms193×body80valid
4.0ms99×body80nan
2.0ms16×body1280valid
2.0ms17×body640valid
1.0ms3×body5120valid
1.0ms7×body320valid
0.0ms5×body160valid

simplify33.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
0147
1227
2257
3277
4297
5297

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

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))
1.3b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
16×add-sqr-sqrt
15×add-cube-cbrt times-frac
10×distribute-lft-out add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in associate-/l*
3×associate-/r* sqrt-prod
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 → 80
Calls
4 calls:
65.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms
(- (* b_2 b_2) (* a c))
20.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series282.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms
(- (* b_2 b_2) (* a c))
76.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
76.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify41.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0358790
11261727
25001705

prune227.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b_2 b_2) (* a c))
4.4b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
9.4b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
20.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite157.0ms

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 div-exp
3×associate-/l/
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 200
Calls
4 calls:
8.0ms
(- (* b_2 b_2) (* a c))
77.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
53.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series420.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* b_2 b_2) (* a c))
143.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
176.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
66.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify114.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
07293368
133203193
250013167

prune476.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b_2 b_2) (* a c))
2.3b
(/ (/ (- (- 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)
20.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite346.0ms

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×associate-/r/
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 diff-log
Counts
4 → 1142
Calls
4 calls:
8.0ms
(- (* b_2 b_2) (* a c))
65.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
131.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series313.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* b_2 b_2) (* a c))
96.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
119.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify246.0ms

Algorithm
egg-herbie
Counts
1154 → 1154
Iterations

Useful iterations: 1 (66.0ms)

IterNodesCost
0424224730
1500124067

prune2.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b_2 b_2) (* a c))
1.1b
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)
1.6b
(/ (/ (cbrt 1) (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
20.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
22500×times-frac
11588×add-sqr-sqrt
11587×*-un-lft-identity
8467×add-cube-cbrt
8286×cbrt-prod
1560×distribute-lft-out-- difference-of-squares
903×associate-/l*
783×sqrt-prod
780×distribute-rgt-neg-in
181×div-inv
23×add-exp-log
14×add-cbrt-cube
13×cbrt-undiv div-exp
9×associate-/r*
7×associate-/r/
6×add-log-exp
5×pow1
2×flip3-- frac-2neg sqrt-div div-sub clear-num flip-- associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 6254
Calls
4 calls:
8.0ms
(- (* b_2 b_2) (* a c))
69.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)
332.0ms
(/ (/ (cbrt 1) (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(- (* b_2 b_2) (* a c))
234.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)
113.0ms
(/ (/ (cbrt 1) (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
69.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Algorithm
egg-herbie
Counts
6266 → 6266
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
05530191847

prune24.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.0b

regimes196.0ms

Accuracy

94.1% (1.4b remaining)

Error of 6.8b against oracle of 5.3b and baseline of 30.0b

bsearch182.0ms

Steps
ItersRangePoint
8
1.3935572344016303e+91
7.757676313950008e+95
7.593488147818344e+95
11
-1.026203141381591e-268
-2.600157470066103e-290
-1.3076396850415123e-287
7
-3.11898899158337e+65
-2.3526715177838076e+63
-3.0609761389176743e+65

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06158
16158

end0.0ms

sample1.0s

Algorithm
intervals
Results
187.0ms5906×body80valid
175.0ms1024×body2560valid
117.0ms846×body1280valid
90.0ms2940×body80nan
57.0ms456×body640valid
26.0ms120×body5120valid
19.0ms230×body320valid
6.0ms100×body160valid