Details

Time bar (total: 3.8s)

sample28.0ms

Algorithm
intervals
Results
10.0ms271×body80valid
3.0ms98×body80nan

simplify12.0ms

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: 25.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
3.8b
(* (* x y) z)
9.8b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
26.3b
(sqrt (- (* z z) (* t a)))

rewrite27.0ms

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))))
7.0ms
(sqrt (- (* z z) (* t a)))

series204.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* z z) (* t a))
29.0ms
(* (* x y) z)
84.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
58.0ms
(sqrt (- (* z z) (* t a)))

simplify55.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0346584
11863515
25002510

prune231.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.6b
(- (* z z) (* t a))
3.3b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
26.3b
(sqrt (- (* z z) (* t a)))

rewrite34.0ms

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))))
3.0ms
(- (* z z) (* t a))
17.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series234.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ z (sqrt (- (* z z) (* t a))))
39.0ms
(- (* z z) (* t a))
88.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
59.0ms
(sqrt (- (* z z) (* t a)))

simplify62.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04311015
12166912
25002893

prune299.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
2.0b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
2.3b
(* y (/ z (sqrt (- (* z z) (* t a)))))
26.3b
(sqrt (- (* z z) (* t a)))

rewrite31.0ms

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:
4.0ms
(- (* z z) (* t a))
10.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
11.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series239.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(- (* z z) (* t a))
85.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
53.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0403776
11775676
25002667

prune246.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.0b

localize20.0ms

Local error

Found 4 expressions with local error:

5.7b
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
26.3b
(sqrt (- (* z z) (* t a)))
26.3b
(sqrt (- (* z z) (* t a)))
26.3b
(sqrt (- (* z z) (* t a)))

rewrite20.0ms

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:
6.0ms
(cbrt (/ z (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)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
66.0ms
(sqrt (- (* z z) (* t a)))
65.0ms
(sqrt (- (* z z) (* t a)))
58.0ms
(sqrt (- (* z z) (* t a)))

simplify82.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 3 (74.0ms)

IterNodesCost
0272814
1803789
23018774
35001771

prune330.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.0b

regimes397.0ms

Accuracy

78.6% (4.1b remaining)

Error of 7.5b against oracle of 3.4b and baseline of 22.7b

bsearch78.0ms

Steps
ItersRangePoint
6
2.01645319072261e+30
2.864590415848179e+31
1.6894597162167635e+31
9
-8.13895866141384e+30
-1.7311009141305664e+23
-1.1453877187877288e+27

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02910
13010
23310
33310

end0.0ms

sample777.0ms

Algorithm
intervals
Results
334.0ms8888×body80valid
99.0ms2944×body80nan