Details

Time bar (total: 6.3s)

sample45.0ms

Algorithm
intervals
Results
9.0ms37×body2560valid
7.0ms180×body80valid
7.0ms35×body1280valid
4.0ms110×body80nan
2.0ms14×body640valid
1.0ms4×body5120valid
0.0ms4×body320valid
0.0ms5×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.7b

Counts
2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b
(- (* b b) (* 4.0 (* a c)))
1.8b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
483×add-sqr-sqrt
330×prod-diff
312×associate-*r*
301×*-un-lft-identity
229×add-cube-cbrt
185×associate-*l*
125×unswap-sqr
75×swap-sqr
65×*-commutative
60×times-frac
30×difference-of-squares
28×distribute-lft-out
22×sqrt-prod
17×distribute-rgt-neg-in
15×fma-neg
12×associate-/r*
10×fma-def add-log-exp
9×add-exp-log add-cbrt-cube
8×distribute-lft-out--
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 → 537
Calls
4 calls:
42.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
32.0ms
(- (* b b) (* 4.0 (* a c)))
33.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
46.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series476.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
50.0ms
(- (* b b) (* 4.0 (* a c)))
235.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
82.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify111.0ms

Algorithm
egg-herbie
Counts
549 → 549
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
014339161
150016646

prune520.0ms

Filtered
549 candidates to 170 candidates (69.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New53910549
Fresh000
Picked101
Done000
Total54010550

Merged error: 5.1b

Counts
550 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b
(- (* b b) (* 4.0 (* a c)))
1.8b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
483×add-sqr-sqrt
330×prod-diff
312×associate-*r*
301×*-un-lft-identity
229×add-cube-cbrt
185×associate-*l*
125×unswap-sqr
75×swap-sqr
65×*-commutative
60×times-frac
30×difference-of-squares
28×distribute-lft-out
22×sqrt-prod
17×distribute-rgt-neg-in
15×fma-neg
12×associate-/r*
10×fma-def add-log-exp
9×add-exp-log add-cbrt-cube
8×distribute-lft-out--
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 → 537
Calls
4 calls:
42.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
29.0ms
(- (* b b) (* 4.0 (* a c)))
35.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series318.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
49.0ms
(- (* b b) (* 4.0 (* a c)))
82.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
78.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify111.0ms

Algorithm
egg-herbie
Counts
549 → 549
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
014339161
150016646

prune519.0ms

Filtered
549 candidates to 170 candidates (69.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New5454549
Fresh549
Picked011
Done000
Total5509559

Merged error: 5.1b

Counts
559 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b b) (* 4.0 (* a c)))
0.4b
(* (sqrt 2.0) a)
1.8b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
447×add-sqr-sqrt
330×prod-diff
297×associate-*r*
221×*-un-lft-identity
201×add-cube-cbrt
173×associate-*l*
121×unswap-sqr
75×swap-sqr
60×*-commutative
30×difference-of-squares
26×sqrt-prod
15×fma-neg
10×fma-def add-log-exp
8×distribute-lft-out--
7×pow1
6×add-exp-log add-cbrt-cube
4×expm1-log1p-u distribute-rgt-neg-in log1p-expm1-u
3×distribute-lft-neg-in
2×flip3-- sqrt-div sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log pow-prod-down neg-log prod-exp cbrt-unprod flip-+
Counts
4 → 465
Calls
4 calls:
34.0ms
(- (* b b) (* 4.0 (* a c)))
5.0ms
(* (sqrt 2.0) a)
32.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series263.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b b) (* 4.0 (* a c)))
47.0ms
(* (sqrt 2.0) a)
87.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
82.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify172.0ms

Algorithm
egg-herbie
Counts
477 → 477
Iterations

Useful iterations: 2 (102.0ms)

IterNodesCost
011707791
137385336
250015330

prune467.0ms

Filtered
477 candidates to 128 candidates (73.2%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New4770477
Fresh077
Picked011
Done011
Total4779486

Merged error: 5.1b

Counts
486 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

1.8b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.8b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.4b
(sqrt (- (* b b) (* 4.0 (* a c))))
22.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
104×add-sqr-sqrt
44×sqrt-prod
36×*-un-lft-identity unswap-sqr
30×difference-of-squares
20×fma-def
12×add-cube-cbrt add-log-exp
8×distribute-rgt-neg-in associate-*l* distribute-lft-out--
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 → 126
Calls
4 calls:
35.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
33.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
46.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
45.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series324.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
85.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
78.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify141.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 3 (128.0ms)

IterNodesCost
03061100
110481042
242261026
350011022

prune411.0ms

Filtered
138 candidates to 100 candidates (27.5%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1362138
Fresh066
Picked101
Done022
Total13710147

Merged error: 5.1b

Counts
147 → 10

regimes326.0ms

Accuracy

85.7% (4.1b remaining)

Error of 9.7b against oracle of 5.6b and baseline of 34.4b

bsearch124.0ms

Steps
ItersRangePoint
9
2.9593950748212843e-63
2.4702945119117623e-58
1.301803315389237e-62
8
-8.122802074996069e+81
-2.6359676868927157e+78
-8.403193116555128e+80

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04017
14417
24417

end0.0ms

sample1.2s

Algorithm
intervals
Results
264.0ms1098×body2560valid
250.0ms5797×body80valid
178.0ms885×body1280valid
108.0ms2780×body80nan
72.0ms464×body640valid
43.0ms116×body5120valid
28.0ms249×body320valid
9.0ms117×body160valid