Details

Time bar (total: 4.1s)

sample35.0ms

Algorithm
intervals
Results
10.0ms287×body80valid
6.0ms99×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
5.1b
(* (* x y) z)
10.5b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.6b
(sqrt (- (* z z) (* t a)))

rewrite67.0ms

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:
8.0ms
(- (* z z) (* t a))
19.0ms
(* (* x y) z)
28.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
9.0ms
(sqrt (- (* z z) (* t a)))

series214.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* z z) (* t a))
28.0ms
(* (* x y) z)
86.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0346584
11863515
25002510

prune228.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.6b
(- (* z z) (* t a))
3.2b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
24.6b
(sqrt (- (* z z) (* t a)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
24×associate-*r* sqrt-prod
18×add-exp-log add-cbrt-cube
10×pow1
6×sqrt-div prod-exp associate-/r* cbrt-unprod add-log-exp
4×flip3-- associate-/r/ flip--
3×cbrt-undiv div-exp pow-prod-down associate-/l*
2×div-inv
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ associate-*l* clear-num *-commutative
Counts
4 → 112
Calls
4 calls:
14.0ms
(/ z (sqrt (- (* z z) (* t a))))
10.0ms
(- (* z z) (* t a))
41.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
9.0ms
(sqrt (- (* z z) (* t a)))

series239.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ z (sqrt (- (* z z) (* t a))))
37.0ms
(- (* z z) (* t a))
91.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify63.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
04311015
12166912
25002893

prune295.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
1.3b
(* y (/ z (sqrt (- (* z z) (* t a)))))
2.0b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
24.6b
(sqrt (- (* z z) (* t a)))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
25×associate-*r*
20×add-cube-cbrt *-un-lft-identity times-frac
18×add-exp-log add-cbrt-cube
13×sqrt-prod
12×pow1
7×prod-exp cbrt-unprod
6×associate-*l* add-log-exp
4×sqrt-div pow-prod-down
3×flip3-- associate-*r/ flip-- unswap-sqr
2×cbrt-undiv div-exp associate-/r/ *-commutative
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-inv
Counts
4 → 92
Calls
4 calls:
9.0ms
(- (* z z) (* t a))
38.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
45.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
9.0ms
(sqrt (- (* z z) (* t a)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* z z) (* t a))
62.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
91.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify50.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0403775
11781676
25001667

prune243.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.0b

localize14.0ms

Local error

Found 4 expressions with local error:

3.2b
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
24.6b
(sqrt (- (* z z) (* t a)))
24.6b
(sqrt (- (* z z) (* t a)))
24.6b
(sqrt (- (* z z) (* t a)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod
23×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
8×sqrt-div
7×pow1
4×add-exp-log flip3-- add-cbrt-cube flip-- add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×associate-/r/
1×cbrt-div pow1/3 div-inv
Counts
4 → 78
Calls
4 calls:
8.0ms
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
9.0ms
(sqrt (- (* z z) (* t a)))
9.0ms
(sqrt (- (* z z) (* t a)))
9.0ms
(sqrt (- (* z z) (* t a)))

series318.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
60.0ms
(sqrt (- (* z z) (* t a)))
63.0ms
(sqrt (- (* z z) (* t a)))
64.0ms
(sqrt (- (* z z) (* t a)))

simplify78.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 3 (70.0ms)

IterNodesCost
0272817
1797789
22990774
35001771

prune317.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.0b

regimes380.0ms

Accuracy

78% (4.2b remaining)

Error of 7.1b against oracle of 2.9b and baseline of 22.2b

bsearch153.0ms

Steps
ItersRangePoint
4
4.774247135773842e+113
7.50002489248219e+113
6.344623429916867e+113
8
5.33924979008046e-170
8.410459962733418e-167
5.408002280660189e-170
10
8.70971164655884e-238
6.532280200382943e-228
6.447720564522469e-228
9
-2.3132843735365205e+104
-2.0509244193021767e+98
-5.841072424480833e+103

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03518
13918
24818
34818

end0.0ms

sample866.0ms

Algorithm
intervals
Results
305.0ms8828×body80valid
95.0ms2971×body80nan