Details

Time bar (total: 6.7s)

sample44.0ms

Algorithm
intervals
Results
8.0ms32×body1280valid
8.0ms34×body2560valid
7.0ms172×body80valid
3.0ms79×body80nan
2.0ms9×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
0259
1469
2869
31139
41219
51219

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)))

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
483×add-sqr-sqrt
330×associate-*l* prod-diff
309×*-un-lft-identity
229×add-cube-cbrt
177×associate-*r*
125×unswap-sqr
75×swap-sqr
65×*-commutative
60×times-frac
30×difference-of-squares
28×distribute-lft-out
24×sqrt-prod
17×distribute-rgt-neg-in
15×fma-neg
12×associate-/r* distribute-lft-out--
10×fma-def add-log-exp
9×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative neg-mul-1 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 → 541
Calls
4 calls:
40.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
33.0ms
(- (* b b) (* (* 4.0 a) c))
34.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series292.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
43.0ms
(- (* b b) (* (* 4.0 a) c))
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify185.0ms

Algorithm
egg-herbie
Counts
553 → 553
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
014499181
149916678
250016678

prune645.0ms

Filtered
553 candidates to 170 candidates (30.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New5449553
Fresh000
Picked101
Done000
Total5459554

Merged error: 6.1b

Counts
554 → 9

localize13.0ms

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)))

rewrite213.0ms

Algorithm
rewrite-expression-head
Rules
521×add-sqr-sqrt
349×*-un-lft-identity
330×prod-diff
325×associate-*l*
262×add-cube-cbrt
178×associate-*r*
125×unswap-sqr
117×frac-times
95×associate-/l*
75×swap-sqr
72×associate-/r*
60×*-commutative
31×times-frac
30×distribute-lft-out difference-of-squares
26×add-exp-log
25×clear-num
24×frac-2neg sqrt-prod
20×associate-/l/
18×distribute-rgt-neg-in
16×add-cbrt-cube
15×fma-neg
13×associate-*r/
12×distribute-lft-out--
11×flip3-+ flip-+
10×fma-def add-log-exp
9×associate-*l/
8×div-exp prod-exp
7×pow1
4×cbrt-undiv expm1-log1p-u un-div-inv cbrt-unprod log1p-expm1-u
3×distribute-lft-neg-in
2×rec-exp flip3-- sqrt-div 1-exp sum-log flip-- div-inv
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log pow-prod-down neg-log
Counts
4 → 649
Calls
4 calls:
55.0ms
(* (/ 1 a) (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 2.0))
30.0ms
(- (* b b) (* (* 4.0 a) c))
38.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series383.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(* (/ 1 a) (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 2.0))
49.0ms
(- (* b b) (* (* 4.0 a) c))
111.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify124.0ms

Algorithm
egg-herbie
Counts
661 → 661
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0205010597
150028682

prune963.0ms

Filtered
661 candidates to 255 candidates (38.6%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New6565661
Fresh538
Picked011
Done000
Total6619670

Merged error: 6.0b

Counts
670 → 9

localize16.0ms

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)))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
104×add-sqr-sqrt
48×sqrt-prod
44×*-un-lft-identity
36×unswap-sqr
30×difference-of-squares
20×fma-def
18×associate-*l*
12×add-cube-cbrt distribute-lft-out-- add-log-exp
8×distribute-rgt-neg-in
6×pow1 distribute-lft-neg-in swap-sqr *-commutative
4×add-exp-log expm1-log1p-u sqrt-div sum-log add-cbrt-cube log1p-expm1-u distribute-lft-out
2×+-commutative neg-sub0 associate-+l- neg-mul-1 rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 neg-log flip-- flip-+
Counts
4 → 130
Calls
4 calls:
35.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
37.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
46.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series301.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify147.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
03141124
111171066
247741050
350011050

prune476.0ms

Filtered
142 candidates to 100 candidates (70.4%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1420142
Fresh077
Picked011
Done011
Total1429151

Merged error: 6.0b

Counts
151 → 9

localize14.0ms

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)))

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
104×add-sqr-sqrt
48×sqrt-prod
44×*-un-lft-identity
36×unswap-sqr
30×difference-of-squares
20×fma-def
18×associate-*l*
12×add-cube-cbrt distribute-lft-out-- add-log-exp
8×distribute-rgt-neg-in
6×pow1 distribute-lft-neg-in swap-sqr *-commutative
4×add-exp-log expm1-log1p-u sqrt-div sum-log add-cbrt-cube log1p-expm1-u distribute-lft-out
2×+-commutative neg-sub0 associate-+l- neg-mul-1 rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 neg-log flip-- flip-+
Counts
4 → 130
Calls
4 calls:
36.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
34.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
46.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series295.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify147.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
03141124
111171066
247741050
350011050

prune414.0ms

Filtered
142 candidates to 100 candidates (70.4%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1420142
Fresh066
Picked011
Done022
Total1429151

Merged error: 6.0b

Counts
151 → 9

regimes246.0ms

Accuracy

84.8% (4.3b remaining)

Error of 9.8b against oracle of 5.5b and baseline of 33.9b

bsearch88.0ms

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

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03716
13716

end0.0ms

sample1.2s

Algorithm
intervals
Results
245.0ms1052×body2560valid
237.0ms5820×body80valid
173.0ms891×body1280valid
107.0ms2865×body80nan
69.0ms469×body640valid
39.0ms111×body5120valid
26.0ms235×body320valid
9.0ms122×body160valid