Details

Time bar (total: 2.5m)

sample58.0ms

Algorithm
intervals
Results
20.0ms293×body80valid
10.0ms100×body80nan

simplify17.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune5.0ms

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: 22.2b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
3.0b
(* (* x y) z)
7.3b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
21.2b
(sqrt (- (* z z) (* t a)))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
940×add-sqr-sqrt
440×times-frac
430×associate-*l*
408×sqrt-prod
360×*-un-lft-identity
263×unswap-sqr
250×difference-of-squares
160×add-cube-cbrt
132×associate-*r*
100×distribute-lft-out--
94×*-commutative
50×swap-sqr
22×associate-/l*
20×associate-/r*
18×add-exp-log add-cbrt-cube
10×pow1
6×prod-exp cbrt-unprod add-log-exp
4×sqrt-div
3×cbrt-undiv flip3-- div-exp pow-prod-down flip--
2×associate-/r/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log clear-num div-inv
Counts
4 → 586
Calls
4 calls:
15.0ms
(- (* z z) (* t a))
7.0ms
(* (* x y) z)
39.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
15.0ms
(sqrt (- (* z z) (* t a)))

series211.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* z z) (* t a))
24.0ms
(* (* x y) z)
85.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
67.0ms
(sqrt (- (* z z) (* t a)))

simplify107.0ms

Algorithm
egg-herbie
Counts
598 → 598
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
012957635
150017555

prune815.0ms

Filtered
598 candidates to 262 candidates (43.8%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New58513598
Fresh000
Picked101
Done000
Total58613599

Merged error: 2.9b

Counts
599 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y)
1.8b
(* (* x (* (cbrt y) (cbrt y))) (/ (* (cbrt y) z) (sqrt (- (* z z) (* t a)))))
3.0b
(/ (* (cbrt y) z) (sqrt (- (* z z) (* t a))))
21.2b
(sqrt (- (* z z) (* t a)))

rewrite394.0ms

Algorithm
rewrite-expression-head
Rules
1659×add-sqr-sqrt
700×times-frac
625×sqrt-prod
547×unswap-sqr
536×*-un-lft-identity
485×associate-*r*
446×associate-*l*
350×difference-of-squares
255×cbrt-prod
254×add-cube-cbrt
140×distribute-lft-out--
123×*-commutative
103×add-cbrt-cube
92×swap-sqr
74×cbrt-unprod
45×add-exp-log
40×associate-/r*
39×associate-*r/
34×associate-/l*
22×prod-exp
21×cbrt-undiv
14×pow1
8×div-exp
6×sqrt-div pow-prod-down
4×associate-/r/ add-log-exp
3×flip3-- clear-num un-div-inv flip--
2×frac-2neg div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 939
Calls
4 calls:
1.0ms
(cbrt y)
255.0ms
(* (* x (* (cbrt y) (cbrt y))) (/ (* (cbrt y) z) (sqrt (- (* z z) (* t a)))))
30.0ms
(/ (* (cbrt y) z) (sqrt (- (* z z) (* t a))))
19.0ms
(sqrt (- (* z z) (* t a)))

series488.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(cbrt y)
116.0ms
(* (* x (* (cbrt y) (cbrt y))) (/ (* (cbrt y) z) (sqrt (- (* z z) (* t a)))))
122.0ms
(/ (* (cbrt y) z) (sqrt (- (* z z) (* t a))))
68.0ms
(sqrt (- (* z z) (* t a)))

simplify165.0ms

Algorithm
egg-herbie
Counts
951 → 951
Iterations

Useful iterations: 1 (47.0ms)

IterNodesCost
0245413759
1500212825

prune1.8s

Filtered
951 candidates to 463 candidates (48.7%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New9492951
Fresh01212
Picked011
Done000
Total94915964

Merged error: 2.9b

Counts
964 → 15

localize26.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (* x (* (cbrt y) (cbrt y))) (* (/ (* (cbrt (cbrt y)) (cbrt (cbrt y))) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) (/ (* (cbrt (cbrt y)) z) (cbrt (sqrt (- (* z z) (* t a)))))))
21.2b
(sqrt (- (* z z) (* t a)))
21.2b
(sqrt (- (* z z) (* t a)))
21.2b
(sqrt (- (* z z) (* t a)))

rewrite45.8s

Algorithm
rewrite-expression-head
Rules
322908×add-sqr-sqrt
196860×cbrt-prod
187282×unswap-sqr
75350×times-frac
47407×sqrt-prod
32206×swap-sqr
15286×*-un-lft-identity
14740×associate-*l*
12950×associate-*r*
9757×*-commutative
8945×associate-/r*
7476×associate-*r/
7226×frac-times
6738×difference-of-squares
6141×cbrt-unprod
6037×add-cbrt-cube
5089×associate-/l*
4948×distribute-lft-out--
4684×add-cube-cbrt
1986×cbrt-undiv
310×add-exp-log
206×clear-num
205×frac-2neg
192×prod-exp
159×associate-*l/
66×div-exp
28×pow1
20×sqrt-div
15×pow-prod-down
14×cbrt-div
10×flip3-- associate-/r/ flip--
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 un-div-inv
2×div-inv
Counts
4 → 50453
Calls
4 calls:
29.7s
(* (* x (* (cbrt y) (cbrt y))) (* (/ (* (cbrt (cbrt y)) (cbrt (cbrt y))) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) (/ (* (cbrt (cbrt y)) z) (cbrt (sqrt (- (* z z) (* t a)))))))
15.0ms
(sqrt (- (* z z) (* t a)))
16.0ms
(sqrt (- (* z z) (* t a)))
16.0ms
(sqrt (- (* z z) (* t a)))

series314.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(* (* x (* (cbrt y) (cbrt y))) (* (/ (* (cbrt (cbrt y)) (cbrt (cbrt y))) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) (/ (* (cbrt (cbrt y)) z) (cbrt (sqrt (- (* z z) (* t a)))))))
66.0ms
(sqrt (- (* z z) (* t a)))
62.0ms
(sqrt (- (* z z) (* t a)))
70.0ms
(sqrt (- (* z z) (* t a)))

simplify23.7s

Algorithm
egg-herbie
Counts
50465 → 50465
Iterations

Useful iterations: 0 (412.0ms)

IterNodesCost
0171093096440

prune1.3m

Filtered
50465 candidates to 11163 candidates (22.1%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New50464150465
Fresh01313
Picked101
Done011
Total504651550480

Merged error: 2.9b

Counts
50480 → 15

localize18.0ms

Local error

Found 4 expressions with local error:

7.6b
(cbrt (* x y))
7.6b
(cbrt (* x y))
21.2b
(sqrt (- (* z z) (* t a)))
21.2b
(sqrt (- (* z z) (* t a)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
68×add-sqr-sqrt
34×sqrt-prod
28×*-un-lft-identity
24×cbrt-prod
20×difference-of-squares
16×unswap-sqr
14×associate-*l*
12×add-cube-cbrt
8×distribute-lft-out--
6×pow1 associate-*r* *-commutative
4×add-exp-log sqrt-div swap-sqr add-cbrt-cube add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 pow1/3 flip--
Counts
4 → 98
Calls
4 calls:
4.0ms
(cbrt (* x y))
4.0ms
(cbrt (* x y))
15.0ms
(sqrt (- (* z z) (* t a)))
18.0ms
(sqrt (- (* z z) (* t a)))

series270.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(cbrt (* x y))
69.0ms
(cbrt (* x y))
64.0ms
(sqrt (- (* z z) (* t a)))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify65.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 3 (56.0ms)

IterNodesCost
0269682
1711662
22176632
35001624

prune283.0ms

Filtered
110 candidates to 74 candidates (67.3%)
Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New1091110
Fresh11213
Picked011
Done011
Total11015125

Merged error: 2.9b

Counts
125 → 15

regimes575.0ms

Accuracy

84.7% (3.0b remaining)

Error of 6.2b against oracle of 3.2b and baseline of 22.7b

bsearch76.0ms

Steps
ItersRangePoint
8
1.2618041718263966e+72
6.888002027293982e+75
3.978479322381757e+75
6
-1.8994188819116795e+129
-2.225823687745991e+128
-2.852449342955382e+128

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03115
13715
23715

end0.0ms

sample759.0ms

Algorithm
intervals
Results
331.0ms8834×body80valid
97.0ms2843×body80nan