Details

Time bar (total: 4.3s)

sample51.0ms

Algorithm
intervals
Results
27.0ms284×body80valid
8.0ms92×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: 23.7b

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* z z) (* t a))
6.2b
(* (* x y) z)
8.4b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.5b
(sqrt (- (* z z) (* t a)))

rewrite30.0ms

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))
8.0ms
(* (* x y) z)
12.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
5.0ms
(sqrt (- (* z z) (* t a)))

series207.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
86.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0346584
11863515
25002510

prune227.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
1.2b
(- (* z z) (* t a))
2.9b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
24.5b
(sqrt (- (* z z) (* t a)))

rewrite37.0ms

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))
21.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series232.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ z (sqrt (- (* z z) (* t a))))
33.0ms
(- (* z z) (* t a))
84.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify68.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
04311015
12166912
25002893

prune315.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
1.2b
(- (* z z) (* t a))
2.4b
(* y (/ z (sqrt (- (* z z) (* t a)))))
24.5b
(sqrt (- (* z z) (* t a)))

rewrite50.0ms

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:
20.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
3.0ms
(- (* z z) (* t a))
20.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
34.0ms
(- (* z z) (* t a))
59.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify55.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0403775
11781676
25001667

prune247.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.1b

localize19.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* z z) (* t a))
24.5b
(sqrt (- (* z z) (* t a)))
24.5b
(sqrt (- (* z z) (* t a)))
24.5b
(sqrt (- (* z z) (* t a)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div add-log-exp
4×add-exp-log flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg diff-log
Counts
4 → 57
Calls
4 calls:
3.0ms
(- (* 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)))

series214.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* z z) (* t a))
63.0ms
(sqrt (- (* z z) (* t a)))
57.0ms
(sqrt (- (* z z) (* t a)))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify61.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (49.0ms)

IterNodesCost
0142423
1469403
21500397
35001394

prune276.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.1b

regimes345.0ms

Accuracy

85.7% (2.8b remaining)

Error of 6.2b against oracle of 3.4b and baseline of 22.8b

bsearch122.0ms

Steps
ItersRangePoint
8
1.6906878989450038e+108
1.9687550893258914e+111
3.210515607801375e+110
9
-3.4624365171705646e+156
-2.2826144912851317e+150
-1.3632525312502413e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03428
14028
24028

end0.0ms

sample1.4s

Algorithm
intervals
Results
769.0ms8873×body80valid
236.0ms2989×body80nan