Details

Time bar (total: 4.6s)

sample42.0ms

Algorithm
intervals
Results
9.0ms187×body80valid
8.0ms40×body2560valid
4.0ms21×body1280valid
3.0ms86×body80nan
2.0ms12×body640valid
1.0ms10×body320valid
1.0ms3×body5120valid
0.0ms4×body160valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1649
21149
31359
41449
51489
61489

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b
(- (* b b) (* 4.0 (* a c)))
1.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 77
Calls
4 calls:
62.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms
(- (* b b) (* 4.0 (* a c)))
24.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series263.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
44.0ms
(- (* b b) (* 4.0 (* a c)))
67.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
65.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify49.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0404890
11481801
25001796

prune262.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b
(- (* b b) (* 4.0 (* a c)))
1.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
67×times-frac
48×add-sqr-sqrt
47×*-un-lft-identity
27×add-cube-cbrt
25×add-exp-log
13×associate-/r* add-cbrt-cube
12×div-exp
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
8×sqrt-prod
7×flip3-- flip--
6×pow1
5×cbrt-undiv distribute-rgt-neg-in div-inv
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 125
Calls
4 calls:
48.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
9.0ms
(- (* b b) (* 4.0 (* a c)))
22.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series276.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
43.0ms
(- (* b b) (* 4.0 (* a c)))
66.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
66.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify72.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
05331805
125441605
250021531

prune263.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.1b

localize18.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×*-un-lft-identity
10×sqrt-prod
8×add-log-exp
7×pow1 add-cube-cbrt
6×sqrt-div
4×add-exp-log flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg distribute-rgt-neg-in neg-log
Counts
4 → 63
Calls
4 calls:
24.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series252.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
62.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
62.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
60.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify99.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (92.0ms)

IterNodesCost
0207609
1768588
23109577
35001573

prune291.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.1b

localize18.0ms

Local error

Found 4 expressions with local error:

1.8b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.8b
(- (pow b 2) (pow b 2))
15.9b
(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
23×*-un-lft-identity
22×unpow-prod-down
19×add-exp-log
16×difference-of-squares
15×add-cube-cbrt
13×add-cbrt-cube
12×unpow2 sqr-pow
10×distribute-rgt-out-- add-log-exp
8×distribute-lft-out--
7×div-exp
5×pow1 associate-/l/
4×cbrt-undiv prod-exp
3×flip3-+ times-frac associate-/r* sqrt-prod flip-+
2×frac-times flip3-- sqrt-div associate-*r/ sum-log flip-- cbrt-unprod distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square rec-exp distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 +-inverses diff-log 1-exp neg-log associate-*l/ clear-num div-inv associate-/l*
Counts
4 → 107
Calls
4 calls:
20.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.0ms
(- (pow b 2) (pow b 2))
124.0ms
(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
11.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series141.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0ms
(- (pow b 2) (pow b 2))
11.0ms
(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
59.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify195.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (186.0ms)

IterNodesCost
0595778
13991571
25002555

prune302.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.1b

regimes281.0ms

Accuracy

95% (1.2b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 29.5b

bsearch152.0ms

Steps
ItersRangePoint
7
7.363656180201337e+60
1.0503009045500217e+63
1.0273828621120979e+63
8
2.5487727292066854e-249
1.8198961796190227e-246
1.0545287641463871e-247
8
-5.3591540899030606e+132
-7.727081080122102e+128
-5.005006561769842e+132

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04425
14425

end0.0ms

sample1.1s

Algorithm
intervals
Results
228.0ms1089×body2560valid
217.0ms5871×body80valid
145.0ms857×body1280valid
94.0ms2807×body80nan
63.0ms459×body640valid
32.0ms119×body5120valid
23.0ms231×body320valid
7.0ms110×body160valid