Details

Time bar (total: 3.6s)

sample29.0ms

Algorithm
intervals
Results
16.0ms465×body80valid

simplify76.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0237
1596
21116
32046
43696
58396
621686
750016

prune7.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma x x (- (* y y) (* z z)))
4.0b
(- (* y y) (* z z))
27.3b
(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

rewrite13.0ms

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:
0.0ms
(fma x x (- (* y y) (* z z)))
3.0ms
(- (* y y) (* z z))
6.0ms
(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

series193.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(fma x x (- (* y y) (* z z)))
39.0ms
(- (* y y) (* z z))
100.0ms
(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

simplify64.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
04661096
118811029
250011026

prune356.0ms

Filtered
108 candidates to 87 candidates (80.6%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ y (/ (pow x 2) y))
8.8b
(/ (pow z 2) y)
9.2b
(/ (pow x 2) y)

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
40×*-un-lft-identity
38×add-sqr-sqrt add-cube-cbrt
24×unpow-prod-down
16×associate-/l*
13×add-exp-log
8×unpow2 sqr-pow
7×add-cbrt-cube
6×div-exp associate-/r*
5×add-log-exp
3×pow1 expm1-log1p-u fma-def log1p-expm1-u
2×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
1×+-commutative flip3-+ sum-log flip-+ distribute-lft-out
Counts
3 → 119
Calls
3 calls:
15.0ms
(+ y (/ (pow x 2) y))
4.0ms
(/ (pow z 2) y)
4.0ms
(/ (pow x 2) y)

series73.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(+ y (/ (pow x 2) y))
20.0ms
(/ (pow z 2) y)
21.0ms
(/ (pow x 2) y)

simplify53.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0338574
11172513
25001507

prune358.0ms

Filtered
128 candidates to 85 candidates (66.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ y (/ (pow x (/ 2 2)) (/ y x)))
0.2b
(/ (pow x (/ 2 2)) (/ y x))
8.8b
(/ (pow z 2) y)

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
187×times-frac
107×*-un-lft-identity
105×add-sqr-sqrt add-cube-cbrt
54×unpow-prod-down
21×add-exp-log
18×sqr-pow
16×associate-/r*
15×associate-/l*
12×div-exp
10×add-cbrt-cube div-inv
5×add-log-exp
4×cbrt-undiv unpow2
3×pow1 expm1-log1p-u pow-to-exp fma-def pow-exp log1p-expm1-u
2×frac-2neg clear-num
1×+-commutative flip3-+ sum-log associate-/r/ flip-+ distribute-lft-out
Counts
3 → 200
Calls
3 calls:
32.0ms
(+ y (/ (pow x (/ 2 2)) (/ y x)))
8.0ms
(/ (pow x (/ 2 2)) (/ y x))
4.0ms
(/ (pow z 2) y)

series73.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(+ y (/ (pow x (/ 2 2)) (/ y x)))
21.0ms
(/ (pow x (/ 2 2)) (/ y x))
21.0ms
(/ (pow z 2) y)

simplify125.0ms

Algorithm
egg-herbie
Counts
209 → 209
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
07321301
134331108
250011103

prune484.0ms

Filtered
209 candidates to 114 candidates (54.5%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
173×times-frac
101×add-sqr-sqrt
98×*-un-lft-identity
96×add-cube-cbrt
42×unpow-prod-down
21×add-exp-log
14×sqr-pow
13×associate-*r* associate-/r* add-cbrt-cube
10×div-exp div-inv
7×associate-/l*
5×pow1 add-log-exp
4×cbrt-undiv
3×expm1-log1p-u fma-def associate-*l* log1p-expm1-u
2×pow-to-exp pow-exp prod-exp cbrt-unprod unswap-sqr
1×+-commutative frac-2neg flip3-+ associate-*r/ pow-prod-down clear-num sum-log associate-/r/ *-commutative flip-+ distribute-lft-out
Counts
3 → 183
Calls
3 calls:
34.0ms
(+ y (/ (pow x (/ 2 2)) (/ y x)))
7.0ms
(* (fabs z) (/ (fabs z) y))
8.0ms
(/ (pow x (/ 2 2)) (/ y x))

series83.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(+ y (/ (pow x (/ 2 2)) (/ y x)))
22.0ms
(* (fabs z) (/ (fabs z) y))
22.0ms
(/ (pow x (/ 2 2)) (/ y x))

simplify131.0ms

Algorithm
egg-herbie
Counts
192 → 192
Iterations

Useful iterations: 2 (112.0ms)

IterNodesCost
07441272
136861079
250021074

prune456.0ms

Filtered
192 candidates to 106 candidates (55.2%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

regimes114.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02418
12418

end0.0ms

sample747.0ms

Algorithm
intervals
Results
470.0ms13764×body80valid