Details

Time bar (total: 7.0s)

sample43.0ms

Algorithm
intervals
Results
8.0ms34×body2560valid
7.0ms172×body80valid
6.0ms32×body1280valid
3.0ms79×body80nan
3.0ms9×body5120valid
2.0ms16×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

prune3.0ms

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)))

rewrite130.0ms

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:
39.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
24.0ms
(- (* 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)))

series298.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
48.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify74.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
06282253
125172157
250012140

prune423.0ms

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

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
177×add-sqr-sqrt
156×*-un-lft-identity
117×frac-times
95×associate-/l*
72×associate-/r*
69×add-cube-cbrt
42×unswap-sqr
31×times-frac associate-*l*
30×distribute-lft-out difference-of-squares
26×add-exp-log
25×clear-num
24×frac-2neg sqrt-prod
20×associate-/l/
19×associate-*r*
16×add-cbrt-cube
15×distribute-rgt-neg-in
13×associate-*r/
12×distribute-lft-out--
11×flip3-+ flip-+
10×add-log-exp
9×associate-*l/
8×div-exp prod-exp
7×pow1 *-commutative
6×swap-sqr
4×cbrt-undiv un-div-inv cbrt-unprod
2×rec-exp flip3-- sqrt-div 1-exp sum-log flip-- div-inv
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log pow-prod-down neg-log
Counts
4 → 286
Calls
4 calls:
52.0ms
(* (/ 1 a) (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 2.0))
21.0ms
(- (* b b) (* (* 4.0 a) c))
36.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series338.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(* (/ 1 a) (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 2.0))
44.0ms
(- (* b b) (* (* 4.0 a) c))
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify60.0ms

Algorithm
egg-herbie
Counts
298 → 298
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012393598
150013362

prune547.0ms

Filtered
298 candidates to 149 candidates (50.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2944298
Fresh448
Picked011
Done000
Total2989307

Merged error: 6.0b

Counts
307 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
98×add-sqr-sqrt
48×sqrt-prod
38×*-un-lft-identity
36×unswap-sqr
30×difference-of-squares
18×associate-*l*
12×distribute-lft-out-- add-log-exp
6×pow1 add-cube-cbrt swap-sqr *-commutative
4×add-exp-log sqrt-div sum-log add-cbrt-cube distribute-lft-out
2×+-commutative neg-sub0 associate-+l- rem-sqrt-square flip3-- distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 neg-log flip-- flip-+
Counts
4 → 102
Calls
4 calls:
35.0ms
(+ (- b) (sqrt (- (* 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)))
21.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series297.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
65.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify143.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 3 (132.0ms)

IterNodesCost
02911054
110121012
24226996
35001980

prune364.0ms

Filtered
114 candidates to 72 candidates (63.2%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1140114
Fresh077
Picked011
Done011
Total1149123

Merged error: 6.0b

Counts
123 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

3.6b
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
8.8b
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
18.3b
(- (pow b 2) (pow b 2))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite309.0ms

Algorithm
rewrite-expression-head
Rules
1810×*-un-lft-identity
1346×times-frac
968×add-sqr-sqrt
414×distribute-lft-out--
400×distribute-lft-out
394×add-cube-cbrt
377×associate-*l*
231×difference-of-squares
168×associate-*r*
124×sqrt-prod
100×distribute-rgt-neg-in
74×unswap-sqr
69×associate-/l*
59×*-commutative
28×associate-/r/
26×associate-/r*
23×associate-/l/
22×unpow-prod-down
18×add-exp-log add-cbrt-cube
16×flip3-- flip--
15×div-inv
12×unpow2 sqr-pow
10×distribute-rgt-out--
7×cbrt-undiv div-exp
6×add-log-exp
5×pow1
3×frac-2neg div-sub swap-sqr clear-num
2×associate-+l- flip3-+ sqrt-div prod-exp cbrt-unprod flip-+
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 +-inverses diff-log
Counts
4 → 928
Calls
4 calls:
105.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
81.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms
(- (pow b 2) (pow b 2))
26.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series362.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
164.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
1.0ms
(- (pow b 2) (pow b 2))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify236.0ms

Algorithm
egg-herbie
Counts
940 → 940
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0187524016
1500123140

prune1.6s

Filtered
940 candidates to 301 candidates (32.0%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New9382940
Fresh246
Picked011
Done022
Total9409949

Merged error: 6.0b

Counts
949 → 9

regimes230.0ms

Accuracy

84.9% (4.4b remaining)

Error of 9.8b against oracle of 5.4b and baseline of 34.7b

bsearch84.0ms

Steps
ItersRangePoint
4
2.7062129888597453e-95
4.861630376334293e-95
3.8681552371770574e-95
9
-1.8864815038392082e+94
-1.5243980513895428e+89
-6.875360452843506e+92

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03716
13716

end0.0ms

sample1.2s

Algorithm
intervals
Results
259.0ms1052×body2560valid
235.0ms5820×body80valid
187.0ms891×body1280valid
113.0ms2865×body80nan
72.0ms469×body640valid
33.0ms111×body5120valid
27.0ms235×body320valid
12.0ms122×body160valid