Details

Time bar (total: 6.4s)

sample38.0ms

Algorithm
intervals
Results
15.0ms288×body80valid
4.0ms96×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03618
16718
212318
316018
417518
517718
617718

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.5b

localize84.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
27.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
27.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
58×*-un-lft-identity
56×add-sqr-sqrt
50×add-cube-cbrt
37×sqrt-prod
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
12×add-log-exp
10×fma-def fma-neg
8×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 diff-log neg-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 151
Calls
4 calls:
29.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series266.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
61.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify70.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04183056
114712008
250011917

prune420.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.7b

localize87.0ms

Local error

Found 4 expressions with local error:

1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0b
(/ (* a c) b)
5.1b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
27.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-exp-log add-cbrt-cube
13×add-sqr-sqrt
12×add-cube-cbrt
10×fma-def
8×add-log-exp
6×times-frac associate-/r*
5×pow1
4×cbrt-undiv expm1-log1p-u distribute-rgt-neg-in div-exp log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×flip3-- frac-2neg sqrt-div prod-exp clear-num sum-log associate-/r/ flip-- cbrt-unprod div-inv distribute-lft-out associate-/l*
1×+-commutative neg-sub0 associate-+l- neg-mul-1 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 92
Calls
4 calls:
21.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(/ (* a c) b)
34.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series217.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(/ (* a c) b)
63.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
65.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify57.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0481697
12315607
25001601

prune402.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.5b

localize90.0ms

Local error

Found 4 expressions with local error:

1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.1b
(/ (* 2.0 c) (- (* 2.0 (/ a (/ b c))) (* 2 b)))
5.7b
(/ a (/ b c))
27.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
56×*-un-lft-identity
53×add-sqr-sqrt
52×add-cube-cbrt
16×associate-/r*
14×add-exp-log add-cbrt-cube
10×fma-def
8×add-log-exp
6×div-inv
5×pow1 cbrt-undiv div-exp
4×expm1-log1p-u distribute-rgt-neg-in log1p-expm1-u associate-/l*
3×distribute-lft-neg-in sqrt-prod associate-/r/
2×flip3-- frac-2neg sqrt-div clear-num sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log prod-exp cbrt-unprod flip-+
Counts
4 → 141
Calls
4 calls:
21.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
34.0ms
(/ (* 2.0 c) (- (* 2.0 (/ a (/ b c))) (* 2 b)))
8.0ms
(/ a (/ b c))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series223.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
65.0ms
(/ (* 2.0 c) (- (* 2.0 (/ a (/ b c))) (* 2 b)))
18.0ms
(/ a (/ b c))
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify78.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
07041064
13244968
25001963

prune642.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.5b

localize98.0ms

Local error

Found 4 expressions with local error:

1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.5b
(/ (cbrt a) (/ (sqrt b) c))
2.7b
(/ (* 2.0 c) (- (* 2.0 (* (/ (cbrt a) (/ (sqrt b) (cbrt a))) (/ (cbrt a) (/ (sqrt b) c)))) (* 2 b)))
27.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite299.0ms

Algorithm
rewrite-expression-head
Rules
261×times-frac
151×*-un-lft-identity
148×add-sqr-sqrt
147×add-cube-cbrt
69×cbrt-prod
66×sqrt-prod
25×associate-/r*
14×add-exp-log
12×add-cbrt-cube
10×fma-def
9×div-inv
8×add-log-exp
7×associate-/l*
5×pow1 cbrt-undiv div-exp
4×expm1-log1p-u distribute-rgt-neg-in log1p-expm1-u
3×distribute-lft-neg-in associate-/r/
2×flip3-- frac-2neg sqrt-div clear-num sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log prod-exp cbrt-unprod flip-+
Counts
4 → 246
Calls
4 calls:
21.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms
(/ (cbrt a) (/ (sqrt b) c))
234.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ (cbrt a) (/ (sqrt b) (cbrt a))) (/ (cbrt a) (/ (sqrt b) c)))) (* 2 b)))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series426.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
164.0ms
(/ (cbrt a) (/ (sqrt b) c))
126.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ (cbrt a) (/ (sqrt b) (cbrt a))) (/ (cbrt a) (/ (sqrt b) c)))) (* 2 b)))
61.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify57.0ms

Algorithm
egg-herbie
Counts
258 → 258
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011552891
150012696

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.5b

regimes227.0ms

Accuracy

87.2% (1.8b remaining)

Error of 8.5b against oracle of 6.7b and baseline of 20.9b

bsearch152.0ms

Steps
ItersRangePoint
6
4.231934083523606e+52
2.717919616353272e+53
1.3445730338690191e+53
9
-6.131233541432508e+155
-2.3408367770205974e+148
-1.3247403910271989e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06562
16562

end0.0ms

sample929.0ms

Algorithm
intervals
Results
436.0ms8769×body80valid
130.0ms2813×body80nan