Details

Time bar (total: 16.0s)

analyze2.1s

Algorithm
search

sample45.0ms

Algorithm
intervals
Results
25.0ms256×body80valid
3.0ms35×body80invalid

simplify64.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05518
111618
232918
393518
4287618
5500118

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.7b

Counts
2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z)
0.1b
(* (+ (* z 3.13060547623) 11.1667541262) z)
2.7b
(* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b))
27.5b
(/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×add-exp-log add-cbrt-cube
12×add-cube-cbrt *-un-lft-identity
10×pow1
9×associate-*r* associate-*l*
5×flip3-+ flip-+
4×associate-*r/ associate-*l/ prod-exp cbrt-unprod add-log-exp
3×times-frac pow-prod-down associate-/r* *-commutative unswap-sqr
2×cbrt-undiv div-exp associate-/r/ associate-/l/
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num div-inv associate-/l*
Counts
4 → 87
Calls
4 calls:
11.0ms
(* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z)
6.0ms
(* (+ (* z 3.13060547623) 11.1667541262) z)
16.0ms
(* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b))
25.0ms
(/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))

series218.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z)
5.0ms
(* (+ (* z 3.13060547623) 11.1667541262) z)
48.0ms
(* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b))
159.0ms
(/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))

simplify75.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
05811221
128201048
250011048

prune220.0ms

Filtered
72 candidates to 99 candidates (-37.5%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New91899
Fresh000
Picked101
Done000
Total928100

Merged error: 2.9b

Counts
100 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

10.5b
(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
10.5b
(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
19.4b
(* (/ y (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))) (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))
23.2b
(/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
66×times-frac
47×add-cube-cbrt *-un-lft-identity
42×sqrt-prod
24×associate-*r* associate-*l*
18×add-exp-log add-cbrt-cube
10×sqrt-div
9×unswap-sqr
8×pow1
6×flip3-+ associate-/r* associate-/r/ flip-+
5×cbrt-undiv div-exp
4×prod-exp cbrt-unprod add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 150
Calls
4 calls:
11.0ms
(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
11.0ms
(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
44.0ms
(* (/ y (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))) (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))
28.0ms
(/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))

series215.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
6.0ms
(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
134.0ms
(* (/ y (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))) (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))
69.0ms
(/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))

simplify92.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
06734328
128913955
250013822

prune561.0ms

Filtered
112 candidates to 162 candidates (-44.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1611162
Fresh167
Picked011
Done000
Total1628170

Merged error: 2.9b

Counts
170 → 8

localize33.0ms

Local error

Found 4 expressions with local error:

10.5b
(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
13.8b
(sqrt (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))
13.8b
(sqrt (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))
19.4b
(* (/ y (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))) (/ (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))) (sqrt (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))))

rewrite255.0ms

Algorithm
rewrite-expression-head
Rules
648×sqrt-prod
647×times-frac
465×add-sqr-sqrt
303×associate-*r*
293×add-cube-cbrt *-un-lft-identity
52×sqrt-div
39×unswap-sqr
25×add-exp-log add-cbrt-cube
24×associate-*l*
22×associate-/r/
14×flip3-+ flip-+
11×pow1 div-inv
9×cbrt-undiv sqrt-pow1 div-exp
6×prod-exp cbrt-unprod
5×rem-sqrt-square pow1/2
4×add-log-exp
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 447
Calls
4 calls:
11.0ms
(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
12.0ms
(sqrt (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))
12.0ms
(sqrt (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))
179.0ms
(* (/ y (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))) (/ (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))) (sqrt (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))))

series176.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
10.0ms
(sqrt (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))
10.0ms
(sqrt (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))
150.0ms
(* (/ y (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))) (/ (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))) (sqrt (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))))

simplify198.0ms

Algorithm
egg-herbie
Counts
459 → 459
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
0214718124
1500217155

prune2.4s

Filtered
191 candidates to 459 candidates (-140.3%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New4590459
Fresh066
Picked011
Done011
Total4598467

Merged error: 2.9b

Counts
467 → 8

localize36.0ms

Local error

Found 4 expressions with local error:

17.6b
(cbrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
17.6b
(cbrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
17.6b
(cbrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
24.3b
(* (/ y (* (cbrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)) (cbrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))) (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (cbrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
28×times-frac
25×add-exp-log
24×associate-*r*
22×add-cube-cbrt *-un-lft-identity
20×cbrt-prod cbrt-div
18×add-cbrt-cube
15×associate-*l*
10×flip3-+ associate-/r/ flip-+
8×prod-exp cbrt-unprod
7×cbrt-undiv div-exp
6×pow1 unswap-sqr
5×frac-times
4×add-log-exp
3×pow1/3 associate-*r/ associate-*l/
2×div-inv
1×pow-prod-down *-commutative
Counts
4 → 108
Calls
4 calls:
12.0ms
(cbrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
12.0ms
(cbrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
12.0ms
(cbrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
66.0ms
(* (/ y (* (cbrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)) (cbrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))) (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (cbrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))

series171.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(cbrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
10.0ms
(cbrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
10.0ms
(cbrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
140.0ms
(* (/ y (* (cbrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)) (cbrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))) (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (cbrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))

simplify102.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
07023922
131903425
250013222

prune586.0ms

Filtered
100 candidates to 120 candidates (-20.0%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1200120
Fresh055
Picked011
Done022
Total1208128

Merged error: 2.9b

Counts
128 → 8

regimes850.0ms

Accuracy

94.1% (1.4b remaining)

Error of 4.8b against oracle of 3.3b and baseline of 27.9b

bsearch4.4s

Steps
ItersRangePoint
9
4.3901966315328686e+39
1.8350013024382465e+48
6.050948453672537e+45
5
-1.548780779927515e+73
-5.612436248354682e+72
-5.695669122738708e+72

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07648
17648

end0.0ms

analyze1.9s

Algorithm
search

sample1.0s

Algorithm
intervals
Results
675.0ms8000×body80valid
77.0ms913×body80invalid

Profiling

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