Details

Time bar (total: 4.0s)

sample53.0ms

Algorithm
intervals
Results
20.0ms275×body80valid
7.0ms96×body80nan

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
5.0b
(* (* x y) z)
10.8b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.1b
(sqrt (- (* z z) (* t a)))

rewrite22.0ms

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:
3.0ms
(- (* z z) (* t a))
5.0ms
(* (* x y) z)
9.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
3.0ms
(sqrt (- (* z z) (* t a)))

series206.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* z z) (* t a))
26.0ms
(* (* x y) z)
83.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
65.0ms
(sqrt (- (* z z) (* t a)))

simplify50.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0346584
11863515
25002510

prune228.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.8b
(- (* z z) (* t a))
3.1b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
25.1b
(sqrt (- (* z z) (* t a)))

rewrite28.0ms

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:
6.0ms
(/ z (sqrt (- (* z z) (* t a))))
4.0ms
(- (* z z) (* t a))
11.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
3.0ms
(sqrt (- (* z z) (* t a)))

series226.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ z (sqrt (- (* z z) (* t a))))
33.0ms
(- (* z z) (* t a))
84.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify63.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04311015
12166912
25002893

prune298.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
2.2b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
2.3b
(* y (/ z (sqrt (- (* z z) (* t a)))))
25.1b
(sqrt (- (* z z) (* t a)))

rewrite35.0ms

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:
3.0ms
(- (* z z) (* t a))
10.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
15.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series237.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* z z) (* t a))
85.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
58.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
60.0ms
(sqrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0403775
11781676
25001667

prune245.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.3b

localize20.0ms

Local error

Found 4 expressions with local error:

2.2b
(* x (* (* y (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))))
25.1b
(sqrt (- (* z z) (* t a)))
25.1b
(sqrt (- (* z z) (* t a)))
25.1b
(sqrt (- (* z z) (* t a)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
74×add-exp-log
46×add-cbrt-cube
43×prod-exp cbrt-unprod
16×pow1
14×cbrt-undiv div-exp
11×add-sqr-sqrt
9×sqrt-prod
8×add-cube-cbrt *-un-lft-identity
6×sqrt-div associate-*r/ pow-prod-down
4×add-log-exp
3×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*l* flip--
1×frac-times associate-*r* associate-*l/ *-commutative
Counts
4 → 89
Calls
4 calls:
32.0ms
(* x (* (* y (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series290.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(* x (* (* y (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))))
60.0ms
(sqrt (- (* z z) (* t a)))
61.0ms
(sqrt (- (* z z) (* t a)))
58.0ms
(sqrt (- (* z z) (* t a)))

simplify79.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
06261848
130701240
25001903

prune324.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.3b

regimes449.0ms

Accuracy

83% (3.3b remaining)

Error of 6.7b against oracle of 3.4b and baseline of 22.7b

bsearch187.0ms

Steps
ItersRangePoint
10
3.0886519766275007e+106
5.320008399497423e+116
2.3705720990957475e+108
8
3.519603425790599e-88
1.4418182004301454e-84
6.189477390780605e-86
10
-1.0492185689179587e-302
5.524529284580325e-298
6.1289396716952e-310
1
-3.2219348736708655e+167
-3.0290001935999287e+167
-3.077233863617663e+167

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05345
15945
25945

end0.0ms

sample839.0ms

Algorithm
intervals
Results
375.0ms8852×body80valid
122.0ms3042×body80nan