Details

Time bar (total: 5.8s)

sample45.0ms

Algorithm
intervals
Results
8.0ms32×body1280valid
8.0ms34×body2560valid
7.0ms172×body80valid
3.0ms79×body80nan
3.0ms9×body5120valid
3.0ms16×body640valid
1.0ms9×body320valid
0.0ms3×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 35.6b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b
(- (* b b) (* (* 4.0 a) c))
1.2b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
139×add-sqr-sqrt
116×*-un-lft-identity
60×times-frac
42×unswap-sqr
36×add-cube-cbrt associate-*l*
30×difference-of-squares
28×distribute-lft-out
24×sqrt-prod
18×associate-*r*
14×distribute-rgt-neg-in
12×associate-/r* *-commutative distribute-lft-out--
10×add-log-exp
9×add-exp-log add-cbrt-cube
6×swap-sqr
5×pow1 associate-/l*
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num cbrt-unprod div-inv
Counts
4 → 178
Calls
4 calls:
41.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
21.0ms
(- (* b b) (* (* 4.0 a) c))
34.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series296.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
43.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify76.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
06282253
125172157
250012140

prune399.0ms

Filtered
190 candidates to 109 candidates (57.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1819190
Fresh000
Picked101
Done000
Total1829191

Merged error: 6.1b

Counts
191 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
0.8b
(- (* b b) (* (* 4.0 a) c))
1.2b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
157×add-sqr-sqrt
75×*-un-lft-identity
58×associate-*r*
49×unswap-sqr
41×associate-*l*
40×add-cube-cbrt times-frac
36×frac-times associate-/r*
30×difference-of-squares
24×sqrt-prod
23×add-exp-log
20×flip3-+ flip-+
18×associate-*r/
13×*-commutative add-cbrt-cube
12×distribute-lft-out--
10×prod-exp associate-/l* add-log-exp
7×pow1
6×swap-sqr
4×div-exp clear-num cbrt-unprod distribute-lft-out
3×frac-2neg un-div-inv
2×cbrt-undiv rec-exp flip3-- distribute-rgt-neg-in sqrt-div 1-exp associate-*l/ sum-log flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log pow-prod-down neg-log div-inv
Counts
4 → 212
Calls
4 calls:
53.0ms
(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
23.0ms
(- (* b b) (* (* 4.0 a) c))
32.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series291.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
46.0ms
(- (* b b) (* (* 4.0 a) c))
73.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify53.0ms

Algorithm
egg-herbie
Counts
224 → 224
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09392773
150012578

prune496.0ms

Filtered
224 candidates to 138 candidates (61.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2204224
Fresh538
Picked011
Done000
Total2258233

Merged error: 6.1b

Counts
233 → 8

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a)
0.8b
(- (* b b) (* (* 4.0 a) c))
1.2b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
106×add-sqr-sqrt
59×*-un-lft-identity
36×unswap-sqr
30×difference-of-squares
24×sqrt-prod
18×associate-*l*
15×add-cube-cbrt times-frac
12×distribute-lft-out--
10×distribute-lft-out add-log-exp
6×add-exp-log swap-sqr *-commutative add-cbrt-cube
5×pow1 distribute-rgt-neg-in associate-/l*
3×associate-/r*
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 → 122
Calls
4 calls:
37.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a)
21.0ms
(- (* b b) (* (* 4.0 a) c))
35.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
36.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series308.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a)
68.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04421315
116041244
250011225

prune319.0ms

Filtered
134 candidates to 81 candidates (60.4%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1313134
Fresh336
Picked011
Done011
Total1348142

Merged error: 6.1b

Counts
142 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
8.8b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
387×*-un-lft-identity
298×times-frac
273×add-sqr-sqrt
115×add-cube-cbrt
74×distribute-lft-out
71×difference-of-squares
62×distribute-lft-out--
52×sqrt-prod
51×associate-/l*
46×associate-*l*
28×distribute-rgt-neg-in
21×associate-/l/
18×unswap-sqr
17×associate-/r*
11×add-exp-log add-cbrt-cube
10×associate-/r/
8×add-log-exp
7×flip3-- flip--
6×div-inv
5×pow1
4×cbrt-undiv div-exp
3×frac-2neg swap-sqr clear-num *-commutative
2×flip3-+ sqrt-div diff-log flip-+
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 315
Calls
4 calls:
33.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
56.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
49.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
138.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
174.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify157.0ms

Algorithm
egg-herbie
Counts
327 → 327
Iterations

Useful iterations: 2 (106.0ms)

IterNodesCost
08535795
140685505
250025476

prune697.0ms

Filtered
327 candidates to 162 candidates (49.5%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New3252327
Fresh145
Picked011
Done022
Total3269335

Merged error: 6.0b

Counts
335 → 9

regimes219.0ms

Accuracy

83.7% (4.4b remaining)

Error of 9.7b against oracle of 5.4b and baseline of 32.1b

bsearch95.0ms

Steps
ItersRangePoint
4
2.7062129888597453e-95
4.861630376334293e-95
3.8681552371770574e-95
9
-1.8864815038392082e+94
-1.5243980513895428e+89
-9.911609721462535e+93

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04424
14424

end0.0ms

sample1.2s

Algorithm
intervals
Results
252.0ms1052×body2560valid
246.0ms5820×body80valid
184.0ms891×body1280valid
113.0ms2865×body80nan
73.0ms469×body640valid
38.0ms111×body5120valid
28.0ms235×body320valid
10.0ms122×body160valid