Details

Time bar (total: 4.2s)

sample39.0ms

Algorithm
intervals
Results
16.0ms286×body80valid
5.0ms113×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 26.2b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* z z) (* t a))
5.0b
(* (* x y) z)
9.6b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.5b
(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)))

series199.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
82.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify61.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0346584
11863515
25002510

prune205.0ms

Filtered
88 candidates to 60 candidates (68.2%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New80888
Fresh000
Picked011
Done000
Total80989

Merged error: 5.4b

Counts
89 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
1.2b
(- (* z z) (* t a))
3.8b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
25.5b
(sqrt (- (* z z) (* t a)))

rewrite27.0ms

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

series228.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ z (sqrt (- (* z z) (* t a))))
32.0ms
(- (* z z) (* t a))
82.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify65.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
04311015
12166912
25002893

prune259.0ms

Filtered
124 candidates to 80 candidates (64.5%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1222124
Fresh167
Picked101
Done011
Total1249133

Merged error: 4.9b

Counts
133 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* z z) (* t a))
2.4b
(* y (/ z (sqrt (- (* z z) (* t a)))))
3.6b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
25.5b
(sqrt (- (* z z) (* t a)))

rewrite37.0ms

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))
17.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
10.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))

series230.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* z z) (* t a))
57.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
84.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
57.0ms
(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0403775
11781676
25001667

prune224.0ms

Filtered
104 candidates to 68 candidates (65.4%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1022104
Fresh077
Picked011
Done011
Total10211113

Merged error: 4.7b

Counts
113 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

3.6b
(* 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)))))))
25.5b
(sqrt (- (* z z) (* t a)))
25.5b
(sqrt (- (* z z) (* t a)))
25.5b
(sqrt (- (* z z) (* t a)))

rewrite49.0ms

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:
34.0ms
(* 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)))

series291.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(* 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)))))))
63.0ms
(sqrt (- (* z z) (* t a)))
64.0ms
(sqrt (- (* z z) (* t a)))
58.0ms
(sqrt (- (* z z) (* t a)))

simplify87.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
06261848
130701240
25001903

prune282.0ms

Filtered
101 candidates to 65 candidates (64.4%)
Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New1001101
Fresh088
Picked011
Done022
Total10012112

Merged error: 4.7b

Counts
112 → 12

regimes554.0ms

Accuracy

78.8% (4.1b remaining)

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

bsearch101.0ms

Steps
ItersRangePoint
8
9.865387479601035e+48
1.0433903392957286e+52
9.375790730632526e+51
9
-1.628339896851984e+59
-1.0205942138599043e+52
-5.070658730829399e+58

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02717
13317
23317

end0.0ms

sample1.2s

Algorithm
intervals
Results
455.0ms8847×body80valid
340.0ms2949×body80nan

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