Details

Time bar (total: 3.7s)

sample33.0ms

Algorithm
intervals
Results
16.0ms523×body80valid

simplify126.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 9 (107.0ms)

IterNodesCost
0216
1526
21716
34016
48296
510906
616106
719566
822526
923675
1023675

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(- t (* z z))
0.0b
(fma x x (* (* y 4.0) (- t (* z z))))
5.7b
(* (* y 4.0) (- t (* z z)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×prod-diff
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
5×distribute-rgt-in distribute-lft-in add-log-exp
4×associate-*r*
3×expm1-log1p-u sub-neg fma-neg pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
2×flip3-- associate-*r/ flip-- difference-of-squares
1×diff-log associate-*l* *-commutative fma-udef
Counts
3 → 64
Calls
3 calls:
2.0ms
(- t (* z z))
0.0ms
(fma x x (* (* y 4.0) (- t (* z z))))
11.0ms
(* (* y 4.0) (- t (* z z)))

series256.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(- t (* z z))
109.0ms
(fma x x (* (* y 4.0) (- t (* z z))))
98.0ms
(* (* y 4.0) (- t (* z z)))

simplify56.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0279440
11253374
25002367

prune216.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.7b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(- t (* z z))
0.0b
(fma x x (* y (* 4.0 (- t (* z z)))))
5.4b
(* y (* 4.0 (- t (* z z))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
20×distribute-rgt-in distribute-lft-in
15×prod-diff
11×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
8×pow1 add-exp-log add-cbrt-cube
5×sub-neg add-log-exp
4×associate-*r/
3×expm1-log1p-u fma-neg associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
2×flip3-- flip--
1×diff-log associate-*r* *-commutative fma-udef difference-of-squares
Counts
3 → 73
Calls
3 calls:
2.0ms
(- t (* z z))
0.0ms
(fma x x (* y (* 4.0 (- t (* z z)))))
13.0ms
(* y (* 4.0 (- t (* z z))))

series253.0ms

Counts
3 → 9
Calls
3 calls:
43.0ms
(- t (* z z))
113.0ms
(fma x x (* y (* 4.0 (- t (* z z)))))
97.0ms
(* y (* 4.0 (- t (* z z))))

simplify143.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0301529
11000455
24648454
35001454

prune209.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(- t (* z z))
0.0b
(+ (pow x 2) (* y (* 4.0 (- t (* z z)))))
5.4b
(* y (* 4.0 (- t (* z z))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
40×distribute-rgt-in distribute-lft-in
27×prod-diff
20×associate-+r+
17×add-sqr-sqrt
16×add-cube-cbrt *-un-lft-identity
9×sub-neg
8×pow1 add-exp-log fma-def add-cbrt-cube
7×add-log-exp
4×associate-*r/
3×expm1-log1p-u unpow-prod-down fma-neg associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
2×flip3-- flip--
1×+-commutative flip3-+ diff-log associate-*r* sum-log *-commutative flip-+ unpow2 difference-of-squares sqr-pow
Counts
3 → 104
Calls
3 calls:
2.0ms
(- t (* z z))
11.0ms
(+ (pow x 2) (* y (* 4.0 (- t (* z z)))))
17.0ms
(* y (* 4.0 (- t (* z z))))

series227.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(- t (* z z))
98.0ms
(+ (pow x 2) (* y (* 4.0 (- t (* z z)))))
90.0ms
(* y (* 4.0 (- t (* z z))))

simplify57.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0387717
11331612
25001608

prune324.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.6b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(- t (pow z 2))
5.7b
(fma (* y 4.0) (- t (pow z 2)) (pow x 2))
40.7b
(fma (- z) z (* z z))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt prod-diff
20×*-un-lft-identity
18×add-cube-cbrt
10×unpow-prod-down
5×add-log-exp
4×unpow2 difference-of-squares sqr-pow
3×pow1 add-exp-log expm1-log1p-u fma-neg add-cbrt-cube log1p-expm1-u
2×fma-udef
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
3 → 66
Calls
3 calls:
6.0ms
(- t (pow z 2))
0.0ms
(fma (* y 4.0) (- t (pow z 2)) (pow x 2))
0.0ms
(fma (- z) z (* z z))

series231.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(- t (pow z 2))
123.0ms
(fma (* y 4.0) (- t (pow z 2)) (pow x 2))
65.0ms
(fma (- z) z (* z z))

simplify48.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0278589
1813395
25001388

prune222.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.6b

regimes248.0ms

Accuracy

81.8% (0.6b remaining)

Error of 3.2b against oracle of 2.6b and baseline of 6.0b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03320
13320

end0.0ms

sample881.0ms

Algorithm
intervals
Results
489.0ms15798×body80valid