Details

Time bar (total: 4.1s)

sample36.0ms

Algorithm
intervals
Results
7.0ms35×body2560valid
7.0ms198×body80valid
4.0ms24×body1280valid
3.0ms92×body80nan
2.0ms15×body640valid
1.0ms5×body320valid
0.0ms2×body5120valid
0.0ms4×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0229
1439
2839
31109
41189
51189

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.9b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b
(- (* b b) (* (* 3.0 a) c))
23.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite57.0ms

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:
35.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series291.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
42.0ms
(- (* b b) (* (* 3.0 a) c))
69.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify47.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0433855
11670751
25001736

prune295.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.9b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b
(- (* b b) (* (* 3.0 a) c))
23.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
10×pow1 add-sqr-sqrt fma-def add-log-exp
9×add-exp-log add-cube-cbrt add-cbrt-cube
4×expm1-log1p-u distribute-rgt-neg-in log1p-expm1-u
3×distribute-lft-neg-in associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
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 fma-neg diff-log associate-*l* prod-diff neg-log *-commutative flip-+
Counts
4 → 80
Calls
4 calls:
6.0ms
(* (* 3.0 a) c)
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series215.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (* 3.0 a) c)
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
47.0ms
(- (* b b) (* (* 3.0 a) c))
71.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify44.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0337530
11440479
25002467

prune235.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (* 3.0 a))
0.9b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b
(- (* b b) (* (* 3.0 a) c))
23.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
15×add-exp-log
14×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-cbrt-cube
8×pow1
4×expm1-log1p-u distribute-rgt-neg-in div-exp log1p-expm1-u
3×distribute-lft-neg-in times-frac prod-exp sqrt-prod associate-/l*
2×cbrt-undiv rec-exp flip3-- pow-flip sqrt-div 1-exp sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff pow-prod-down neg-log clear-num associate-/r* cbrt-unprod flip-+ div-inv inv-pow
Counts
4 → 90
Calls
4 calls:
4.0ms
(/ 1 (* 3.0 a))
15.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series204.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(/ 1 (* 3.0 a))
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
43.0ms
(- (* b b) (* (* 3.0 a) c))
69.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify43.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0368554
11514497
25002477

prune248.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
0.9b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b
(- (* b b) (* (* 3.0 a) c))
23.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt *-un-lft-identity
31×times-frac
26×add-exp-log
24×add-cube-cbrt
19×associate-*r*
16×add-cbrt-cube
13×associate-*l*
10×fma-def add-log-exp
8×div-exp prod-exp distribute-lft-out
7×pow1 distribute-rgt-neg-in
6×unswap-sqr
4×cbrt-undiv expm1-log1p-u cbrt-unprod log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×rec-exp flip3-- sqrt-div 1-exp sum-log flip-- div-inv
1×+-commutative neg-sub0 frac-times associate-+l- neg-mul-1 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log associate-*r/ prod-diff pow-prod-down neg-log associate-*l/ *-commutative flip-+
Counts
4 → 124
Calls
4 calls:
55.0ms
(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series300.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
43.0ms
(- (* b b) (* (* 3.0 a) c))
70.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify77.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06451311
131291145
250011130

prune328.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.8b

regimes334.0ms

Accuracy

84.7% (4.5b remaining)

Error of 9.9b against oracle of 5.4b and baseline of 34.6b

bsearch110.0ms

Steps
ItersRangePoint
9
3.6106127752583374e-71
6.7695755698382385e-65
9.390367471089922e-69
9
-8.652530131639494e+154
-2.4576771469086066e+149
-3.0094639461563603e+149

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03416
13416

end0.0ms

sample1.1s

Algorithm
intervals
Results
229.0ms1113×body2560valid
205.0ms5729×body80valid
159.0ms931×body1280valid
95.0ms2854×body80nan
61.0ms471×body640valid
25.0ms101×body5120valid
24.0ms244×body320valid
7.0ms109×body160valid