Details

Time bar (total: 4.3s)

sample41.0ms

Algorithm
intervals
Results
8.0ms206×body80valid
8.0ms32×body2560valid
4.0ms23×body1280valid
4.0ms103×body80nan
3.0ms19×body640valid
0.0ms3×body320valid
0.0ms2×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: 33.7b

Counts
2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b
(- (* b b) (* (* 4.0 a) c))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
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 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
11.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series285.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
75.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms
(- (* b b) (* (* 4.0 a) c))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0438854
11702750
25001735

prune266.0ms

Filtered
102 candidates to 82 candidates (80.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New939102
Fresh000
Picked101
Done000
Total949103

Merged error: 6.1b

Counts
103 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b
(- (* b b) (* (* 4.0 a) c))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
19×*-un-lft-identity
14×add-sqr-sqrt
13×add-cbrt-cube
11×add-cube-cbrt
10×fma-def prod-exp add-log-exp
7×pow1 associate-*r*
5×distribute-rgt-neg-in associate-*l*
4×expm1-log1p-u div-exp cbrt-unprod log1p-expm1-u distribute-lft-out
3×distribute-lft-neg-in flip3-+ times-frac sqrt-prod flip-+
2×cbrt-undiv frac-times rec-exp flip3-- sqrt-div 1-exp associate-*l/ sum-log flip--
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log associate-*r/ prod-diff pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 100
Calls
4 calls:
18.0ms
(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series289.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms
(- (* b b) (* (* 4.0 a) c))
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify65.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05141011
12322856
25001843

prune274.0ms

Filtered
112 candidates to 85 candidates (75.9%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1093112
Fresh358
Picked101
Done000
Total1138121

Merged error: 6.1b

Counts
121 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.8b
(- (* b b) (* (* 4.0 a) c))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
18×sqrt-prod
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
6×times-frac associate-/l* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 106
Calls
4 calls:
12.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
8.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series289.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
75.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
43.0ms
(- (* b b) (* (* 4.0 a) c))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify69.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
04851246
119211004
25002972

prune233.0ms

Filtered
118 candidates to 78 candidates (66.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1171118
Fresh167
Picked011
Done000
Total1188126

Merged error: 6.1b

Counts
126 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.8b
(- (* b b) (* (* 4.0 a) c))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
60×times-frac
50×*-un-lft-identity
40×add-cube-cbrt
25×add-exp-log
20×sqrt-prod
19×prod-diff
13×add-cbrt-cube
12×div-exp associate-/r*
10×difference-of-squares
9×associate-/r/
8×add-log-exp
7×flip3-- fma-neg flip--
6×pow1
5×cbrt-undiv div-inv distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u
3×rec-exp 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num cbrt-unprod inv-pow
Counts
4 → 152
Calls
4 calls:
13.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
8.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series319.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
76.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
46.0ms
(- (* b b) (* (* 4.0 a) c))
65.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify86.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
06062062
128751719
250011630

prune256.0ms

Filtered
164 candidates to 90 candidates (54.9%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1631164
Fresh066
Picked011
Done011
Total1639172

Merged error: 6.0b

Counts
172 → 9

regimes226.0ms

Accuracy

83.2% (4.8b remaining)

Error of 10.2b against oracle of 5.4b and baseline of 33.8b

bsearch124.0ms

Steps
ItersRangePoint
10
2.319058093766752e-122
4.8666627780759835e-109
2.953170968414131e-109
8
-7.85932808106197e+156
-9.798525195327539e+152
-3.0445487110986845e+153

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03114
13114

end0.0ms

sample1.2s

Algorithm
intervals
Results
259.0ms1055×body2560valid
240.0ms5771×body80valid
190.0ms952×body1280valid
112.0ms2946×body80nan
76.0ms483×body640valid
33.0ms115×body5120valid
26.0ms228×body320valid
8.0ms110×body160valid