Details

Time bar (total: 3.8s)

sample31.0ms

Algorithm
intervals
Results
10.0ms277×body80valid
6.0ms116×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune2.0ms

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: 23.6b

Counts
2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
3.8b
(* (* x y) z)
10.5b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.1b
(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))
4.0ms
(* (* x y) z)
9.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
3.0ms
(sqrt (- (* z z) (* t a)))

series194.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
80.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
60.0ms
(sqrt (- (* z z) (* t a)))

simplify51.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0346584
11863515
25002510

prune220.0ms

Filtered
88 candidates to 60 candidates (68.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New781088
Fresh000
Picked101
Done000
Total791089

Merged error: 3.9b

Counts
89 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.2b
(- (* z z) (* t a))
3.2b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
24.1b
(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:
52.0ms
(/ z (sqrt (- (* z z) (* t a))))
33.0ms
(- (* z z) (* t a))
82.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify63.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04311015
12166912
25002893

prune286.0ms

Filtered
124 candidates to 81 candidates (65.3%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1195124
Fresh549
Picked101
Done000
Total1259134

Merged error: 3.9b

Counts
134 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

4.5b
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
24.1b
(sqrt (- (* z z) (* t a)))
24.1b
(sqrt (- (* z z) (* t a)))
24.1b
(sqrt (- (* z z) (* t a)))

rewrite22.0ms

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

series307.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
62.0ms
(sqrt (- (* z z) (* t a)))
61.0ms
(sqrt (- (* z z) (* t a)))
57.0ms
(sqrt (- (* z z) (* t a)))

simplify85.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 3 (76.0ms)

IterNodesCost
0272814
1803789
23018774
35001771

prune351.0ms

Filtered
90 candidates to 72 candidates (80.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New90090
Fresh088
Picked011
Done000
Total90999

Merged error: 3.9b

Counts
99 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
1.6b
(* y (/ z (sqrt (- (* z z) (* t a)))))
1.7b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
24.1b
(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:
3.0ms
(- (* z z) (* t a))
11.0ms
(* 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))
56.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
80.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify55.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0403775
11781676
25001667

prune238.0ms

Filtered
104 candidates to 70 candidates (67.3%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1031104
Fresh167
Picked011
Done011
Total1049113

Merged error: 3.9b

Counts
113 → 9

regimes342.0ms

Accuracy

81.2% (3.7b remaining)

Error of 6.7b against oracle of 3.0b and baseline of 22.6b

bsearch93.0ms

Steps
ItersRangePoint
8
6.3736077767258876e+97
2.771218538638004e+101
1.1534159093312974e+100
9
-2.0153199407633189e+124
-1.9189580122017433e+117
-2.4660126757819895e+117

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03118
13618
24718
34718

end0.0ms

sample824.0ms

Algorithm
intervals
Results
362.0ms8834×body80valid
107.0ms2807×body80nan