Details

Time bar (total: 5.8s)

sample34.0ms

Algorithm
intervals
Results
11.0ms294×body80valid
3.0ms91×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
5.5b
(* (* x y) z)
9.3b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.9b
(sqrt (- (* z z) (* t a)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
11×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
9×sqrt-prod
6×times-frac prod-exp associate-/r* cbrt-unprod add-log-exp
4×sqrt-div
3×cbrt-undiv flip3-- div-exp associate-*r* pow-prod-down flip--
2×associate-/r/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*l* clear-num *-commutative div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
9.0ms
(- (* z z) (* t a))
18.0ms
(* (* x y) z)
34.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
10.0ms
(sqrt (- (* z z) (* t a)))

series210.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
89.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
65.0ms
(sqrt (- (* z z) (* t a)))

simplify61.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0346584
11863515
25002510

prune261.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.8b
(- (* z z) (* t a))
3.4b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
23.9b
(sqrt (- (* z z) (* t a)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
47×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
33×sqrt-prod
25×associate-/r*
18×add-exp-log add-cbrt-cube
7×cbrt-undiv div-exp associate-/l*
6×add-log-exp
5×pow1
4×sqrt-div div-inv
3×flip3-- flip--
2×frac-2neg prod-exp clear-num cbrt-unprod associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/r/
Counts
4 → 132
Calls
4 calls:
18.0ms
(/ (sqrt (- (* z z) (* t a))) z)
11.0ms
(- (* z z) (* t a))
22.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
10.0ms
(sqrt (- (* z z) (* t a)))

series265.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(/ (sqrt (- (* z z) (* t a))) z)
37.0ms
(- (* z z) (* t a))
88.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
65.0ms
(sqrt (- (* z z) (* t a)))

simplify66.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05191327
123801230
250011214

prune404.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
2.0b
(/ y (/ (sqrt (- (* z z) (* t a))) z))
2.1b
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
23.9b
(sqrt (- (* z z) (* t a)))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
263×times-frac
157×add-sqr-sqrt
143×add-cube-cbrt *-un-lft-identity
71×associate-*r*
67×sqrt-prod
22×associate-/r*
18×add-exp-log add-cbrt-cube
9×div-inv
7×pow1
6×cbrt-undiv div-exp add-log-exp
4×unswap-sqr
3×associate-*l* prod-exp cbrt-unprod associate-/l*
2×flip3-- sqrt-div associate-/r/ flip--
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down clear-num *-commutative
Counts
4 → 227
Calls
4 calls:
9.0ms
(- (* z z) (* t a))
21.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
52.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
13.0ms
(sqrt (- (* z z) (* t a)))

series252.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(- (* z z) (* t a))
58.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
89.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify117.0ms

Algorithm
egg-herbie
Counts
239 → 239
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
08172502
140052347
250022347

prune669.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
1.9b
(/ (/ (sqrt (- (* z z) (* t a))) z) y)
2.1b
(* x (/ 1 (/ (/ (sqrt (- (* z z) (* t a))) z) y)))
23.9b
(sqrt (- (* z z) (* t a)))

rewrite198.0ms

Algorithm
rewrite-expression-head
Rules
726×times-frac
371×add-sqr-sqrt
342×*-un-lft-identity
338×add-cube-cbrt
215×associate-*r*
122×sqrt-prod
41×add-exp-log
23×add-cbrt-cube
22×associate-/l*
18×div-exp div-inv
10×prod-exp
9×cbrt-undiv unswap-sqr
7×pow1
6×add-log-exp
4×cbrt-unprod
3×rec-exp 1-exp associate-*l* associate-/r*
2×flip3-- sqrt-div flip--
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down clear-num associate-/r/ un-div-inv *-commutative associate-/l/
Counts
4 → 385
Calls
4 calls:
9.0ms
(- (* z z) (* t a))
26.0ms
(/ (/ (sqrt (- (* z z) (* t a))) z) y)
115.0ms
(* x (/ 1 (/ (/ (sqrt (- (* z z) (* t a))) z) y)))
13.0ms
(sqrt (- (* z z) (* t a)))

series260.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* z z) (* t a))
74.0ms
(/ (/ (sqrt (- (* z z) (* t a))) z) y)
90.0ms
(* x (/ 1 (/ (/ (sqrt (- (* z z) (* t a))) z) y)))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify91.0ms

Algorithm
egg-herbie
Counts
397 → 397
Iterations

Useful iterations: 1 (46.0ms)

IterNodesCost
018254530
150024184

prune1.1s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.2b

regimes492.0ms

Accuracy

85% (3.0b remaining)

Error of 6.4b against oracle of 3.4b and baseline of 23.1b

bsearch54.0ms

Steps
ItersRangePoint
6
6.554426983178909e+120
6.504069070328982e+121
1.5848429024938848e+121
6
-1.176493073943078e+144
-9.600945552693004e+142
-1.0685989201997895e+144

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02410
13010
23010

end0.0ms

sample894.0ms

Algorithm
intervals
Results
317.0ms8892×body80valid
98.0ms2907×body80nan