Details

Time bar (total: 5.9s)

sample29.0ms

Algorithm
intervals
Results
15.0ms453×body80valid

simplify84.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0237
1596
21116
32046
43696
58396
621686
750016

prune6.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 26.3b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.5b
(fma x x (- (* y y) (* z z)))
4.7b
(- (* y y) (* z z))
24.4b
(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
45×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
13×associate-/l*
8×add-exp-log add-cbrt-cube
5×div-inv add-log-exp
3×pow1 cbrt-undiv expm1-log1p-u div-exp associate-/r* log1p-expm1-u
1×sub-neg flip3-- frac-2neg fma-neg diff-log prod-diff clear-num flip-- fma-udef associate-/l/ difference-of-squares
Counts
3 → 99
Calls
3 calls:
1.0ms
(fma x x (- (* y y) (* z z)))
8.0ms
(- (* y y) (* z z))
7.0ms
(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

series186.0ms

Counts
3 → 9
Calls
3 calls:
52.0ms
(fma x x (- (* y y) (* z z)))
34.0ms
(- (* y y) (* z z))
99.0ms
(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

simplify65.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04661096
118811029
250011026

prune348.0ms

Filtered
108 candidates to 87 candidates (80.6%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New999108
Fresh000
Picked101
Done000
Total1009109

Merged error: 10.6b

Counts
109 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ y (/ (pow x 2) y))
0.2b
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
7.9b
(/ (pow z 2) y)
8.0b
(/ (pow x 2) y)

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
336×*-un-lft-identity
244×times-frac
231×add-sqr-sqrt
224×prod-diff
217×add-cube-cbrt
115×distribute-rgt-in distribute-lft-in
97×unpow-prod-down
58×distribute-lft-out
33×unpow2 sqr-pow
16×add-exp-log associate-/l*
10×associate-*r* add-cbrt-cube div-inv
6×pow1 div-exp associate-/r* add-log-exp
5×difference-of-squares
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×fma-def associate-*l*
2×cbrt-undiv pow-to-exp sub-neg frac-2neg flip3-+ pow-exp associate--l+ clear-num frac-sub flip-+ distribute-lft-out--
1×+-commutative flip3-- pow-prod-down prod-exp sum-log *-commutative flip-- cbrt-unprod unswap-sqr
Counts
4 → 380
Calls
4 calls:
10.0ms
(+ y (/ (pow x 2) y))
35.0ms
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
5.0ms
(/ (pow z 2) y)
6.0ms
(/ (pow x 2) y)

series140.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(+ y (/ (pow x 2) y))
66.0ms
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
21.0ms
(/ (pow z 2) y)
22.0ms
(/ (pow x 2) y)

simplify180.0ms

Algorithm
egg-herbie
Counts
392 → 392
Iterations

Useful iterations: 2 (110.0ms)

IterNodesCost
012698538
148036226
250016222

prune557.0ms

Filtered
392 candidates to 129 candidates (32.9%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New3875392
Fresh628
Picked101
Done000
Total3947401

Merged error: 1.0b

Counts
401 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (+ y (/ (pow x 2) y)) (/ z (/ y z)))
0.1b
(/ z (/ y z))
0.2b
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ z (/ y z))))
8.0b
(/ (pow x 2) y)

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
897×times-frac
894×*-un-lft-identity
638×add-sqr-sqrt
618×add-cube-cbrt
528×prod-diff
179×distribute-rgt-in distribute-lft-in
135×distribute-lft-out
54×div-inv
16×add-exp-log associate-/r*
13×associate-/r/ add-cbrt-cube
12×unpow-prod-down
11×associate-/l*
9×add-log-exp
8×associate-*r*
6×pow1 div-exp difference-of-squares
4×cbrt-undiv expm1-log1p-u fma-neg associate-*r/ frac-sub log1p-expm1-u distribute-lft-out-- unpow2 sqr-pow
3×sub-neg associate-*l* associate--l+
2×flip3-- frac-2neg flip3-+ diff-log clear-num flip-- flip-+
1×pow-to-exp pow-prod-down pow-exp prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
Counts
4 → 713
Calls
4 calls:
31.0ms
(- (+ y (/ (pow x 2) y)) (/ z (/ y z)))
6.0ms
(/ z (/ y z))
48.0ms
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ z (/ y z))))
5.0ms
(/ (pow x 2) y)

series156.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (+ y (/ (pow x 2) y)) (/ z (/ y z)))
26.0ms
(/ z (/ y z))
63.0ms
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ z (/ y z))))
22.0ms
(/ (pow x 2) y)

simplify219.0ms

Algorithm
egg-herbie
Counts
725 → 725
Iterations

Useful iterations: 1 (53.0ms)

IterNodesCost
0191021928
1500217287

prune1.2s

Filtered
725 candidates to 272 candidates (37.5%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New7232725
Fresh336
Picked101
Done000
Total7275732

Merged error: 0.0b

Counts
732 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ y (/ (pow x (/ 2 2)) (/ y x)))
0.1b
(/ z (/ y z))
0.1b
(/ (pow x (/ 2 2)) (/ y x))
0.2b
(* 0.5 (- (+ y (/ (pow x (/ 2 2)) (/ y x))) (/ z (/ y z))))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
769×times-frac
684×*-un-lft-identity
512×add-sqr-sqrt
501×add-cube-cbrt
352×prod-diff
179×distribute-rgt-in distribute-lft-in
90×distribute-lft-out
46×div-inv
42×unpow-prod-down
26×associate-/r*
24×add-exp-log
16×add-cbrt-cube
14×sqr-pow
12×div-exp
10×associate-/r/ associate-/l*
8×associate-*r*
6×pow1 cbrt-undiv add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×fma-def associate-*l* difference-of-squares
2×pow-to-exp sub-neg frac-2neg flip3-+ pow-exp associate--l+ clear-num frac-sub flip-+ distribute-lft-out--
1×+-commutative flip3-- pow-prod-down prod-exp sum-log *-commutative flip-- cbrt-unprod unswap-sqr
Counts
4 → 608
Calls
4 calls:
24.0ms
(+ y (/ (pow x (/ 2 2)) (/ y x)))
6.0ms
(/ z (/ y z))
9.0ms
(/ (pow x (/ 2 2)) (/ y x))
62.0ms
(* 0.5 (- (+ y (/ (pow x (/ 2 2)) (/ y x))) (/ z (/ y z))))

series144.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(+ y (/ (pow x (/ 2 2)) (/ y x)))
21.0ms
(/ z (/ y z))
22.0ms
(/ (pow x (/ 2 2)) (/ y x))
71.0ms
(* 0.5 (- (+ y (/ (pow x (/ 2 2)) (/ y x))) (/ z (/ y z))))

simplify195.0ms

Algorithm
egg-herbie
Counts
620 → 620
Iterations

Useful iterations: 1 (52.0ms)

IterNodesCost
0225516471
1500114247

prune1.0s

Filtered
620 candidates to 241 candidates (38.9%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New6182620
Fresh224
Picked101
Done000
Total6214625

Merged error: 0.0b

Counts
625 → 4

regimes89.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0189
1189

end0.0ms

sample764.0ms

Algorithm
intervals
Results
475.0ms13684×body80valid