Details

Time bar (total: 14.8s)

analyze1.9s

Algorithm
search
Search
TrueOtherFalseIter
0%99.7%0.3%0
0%99.7%0.3%1
0%99.7%0.3%2
0%99.7%0.3%3
0%99.7%0.3%4
0%99.7%0.3%5
0%99.7%0.3%6
0%99.7%0.3%7
0%99.7%0.3%8
0%99.7%0.3%9
0%99.7%0.3%10
0%99.7%0.3%11
0%99.7%0.3%12
0.8%98.9%0.3%13
1.2%98.5%0.3%14

sample40.0ms

Algorithm
intervals
Results
22.0ms256×body80valid
3.0ms33×body80invalid

simplify63.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
0491437
1491437

prune18.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 27.7b

Counts
2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(* z (+ (* z 3.13060547623) 11.1667541262))
0.1b
(* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
0.1b
(* y (/ (+ (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a)) b) (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771)))
26.8b
(/ (+ (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a)) b) (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity
21×associate-*r*
19×times-frac
15×add-exp-log add-cbrt-cube
10×pow1
9×associate-*l*
5×flip3-+ associate-*r/ flip-+
4×prod-exp associate-/r/ cbrt-unprod add-log-exp unswap-sqr
3×pow-prod-down associate-/r* *-commutative associate-/l*
2×cbrt-undiv distribute-rgt-in distribute-lft-in div-exp div-inv associate-/l/
1×frac-2neg clear-num
Counts
4 → 109
Calls
4 calls:
8.0ms
(* z (+ (* z 3.13060547623) 11.1667541262))
12.0ms
(* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
25.0ms
(* y (/ (+ (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a)) b) (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771)))
25.0ms
(/ (+ (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a)) b) (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771))

series387.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(* z (+ (* z 3.13060547623) 11.1667541262))
11.0ms
(* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
322.0ms
(* y (/ (+ (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a)) b) (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771)))
48.0ms
(/ (+ (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a)) b) (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771))

simplify71.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049753425
149753425

prune332.0ms

Filtered
92 candidates to 121 candidates (-31.5%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1147121
Fresh011
Picked101
Done000
Total1158123

Merged error: 0.2b

Counts
123 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 3.13060547623 (- (/ t (* z z)) (/ 36.527041698806414 z)))
0.0b
(- (/ t (* z z)) (/ 36.527041698806414 z))
2.7b
(* y (+ 3.13060547623 (- (/ t (* z z)) (/ 36.527041698806414 z))))
10.9b
(/ t (* z z))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt *-un-lft-identity
11×add-exp-log add-cbrt-cube add-log-exp
8×add-cube-cbrt
7×times-frac
6×pow1
5×associate-*r*
4×distribute-lft-out difference-of-squares
3×associate-*l* associate-/l* distribute-lft-out--
2×cbrt-undiv sub-neg flip3-+ diff-log associate-*r/ div-exp prod-exp sum-log cbrt-unprod flip-+
1×+-commutative distribute-rgt-in associate-+r- associate-+r+ flip3-- frac-2neg distribute-lft-in pow-prod-down clear-num associate-/r* *-commutative frac-sub flip-- div-inv unswap-sqr
Counts
4 → 78
Calls
4 calls:
13.0ms
(+ 3.13060547623 (- (/ t (* z z)) (/ 36.527041698806414 z)))
10.0ms
(- (/ t (* z z)) (/ 36.527041698806414 z))
15.0ms
(* y (+ 3.13060547623 (- (/ t (* z z)) (/ 36.527041698806414 z))))
5.0ms
(/ t (* z z))

series33.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(+ 3.13060547623 (- (/ t (* z z)) (/ 36.527041698806414 z)))
7.0ms
(- (/ t (* z z)) (/ 36.527041698806414 z))
15.0ms
(* y (+ 3.13060547623 (- (/ t (* z z)) (/ 36.527041698806414 z))))
5.0ms
(/ t (* z z))

simplify43.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
052021075

prune127.0ms

Filtered
63 candidates to 90 candidates (-42.9%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New90090
Fresh077
Picked011
Done000
Total90898

Merged error: 0.2b

Counts
98 → 8

localize33.0ms

Local error

Found 4 expressions with local error:

17.9b
(cbrt (+ (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a)) b))
17.9b
(cbrt (+ (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a)) b))
18.0b
(/ (cbrt (+ (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a)) b)) (sqrt (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771)))
18.0b
(/ (cbrt (+ (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a)) b)) (sqrt (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
72×times-frac
62×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
48×cbrt-prod
42×sqrt-prod
12×associate-/r* associate-/l*
8×add-exp-log cbrt-div
6×flip3-+ add-cbrt-cube flip-+
4×pow1 sqrt-div associate-/r/ associate-/l/ add-log-exp
2×cbrt-undiv frac-2neg pow1/3 div-exp clear-num div-inv
Counts
4 → 154
Calls
4 calls:
12.0ms
(cbrt (+ (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a)) b))
12.0ms
(cbrt (+ (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a)) b))
31.0ms
(/ (cbrt (+ (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a)) b)) (sqrt (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771)))
26.0ms
(/ (cbrt (+ (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a)) b)) (sqrt (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771)))

series300.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(cbrt (+ (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a)) b))
46.0ms
(cbrt (+ (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a)) b))
104.0ms
(/ (cbrt (+ (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a)) b)) (sqrt (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771)))
106.0ms
(/ (cbrt (+ (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a)) b)) (sqrt (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771)))

simplify87.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
055048208

prune971.0ms

Filtered
116 candidates to 166 candidates (-43.1%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1660166
Fresh066
Picked011
Done011
Total1668174

Merged error: 0.2b

Counts
174 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

16.8b
(cbrt (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771))
16.8b
(cbrt (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771))
16.8b
(cbrt (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771))
25.1b
(* (/ y (* (cbrt (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771)) (cbrt (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771)))) (/ (+ (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a)) b) (cbrt (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771))))

rewrite95.0ms

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:
11.0ms
(cbrt (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771))
11.0ms
(cbrt (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771))
11.0ms
(cbrt (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771))
58.0ms
(* (/ y (* (cbrt (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771)) (cbrt (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771)))) (/ (+ (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a)) b) (cbrt (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771))))

series171.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(cbrt (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771))
10.0ms
(cbrt (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771))
10.0ms
(cbrt (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771))
141.0ms
(* (/ y (* (cbrt (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771)) (cbrt (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771)))) (/ (+ (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a)) b) (cbrt (+ (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721)) 0.607771387771))))

simplify56.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
050745877

prune583.0ms

Filtered
102 candidates to 120 candidates (-17.6%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1200120
Fresh055
Picked011
Done022
Total1208128

Merged error: 0.2b

Counts
128 → 8

regimes1.1s

Accuracy

97.3% (0.7b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 28.0b

bsearch5.2s

Steps
ItersRangePoint
8
7.136175227329974e+33
2.332333158153084e+38
1.3818885668958042e+37
8
-4.931173504271819e+28
-1.548510954776926e+26
-1.1564103734550455e+28

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07064
17064

end0.0ms

analyze1.9s

Algorithm
search
Search
TrueOtherFalseIter
0%99.7%0.3%0
0%99.7%0.3%1
0%99.7%0.3%2
0%99.7%0.3%3
0%99.7%0.3%4
0%99.7%0.3%5
0%99.7%0.3%6
0%99.7%0.3%7
0%99.7%0.3%8
0%99.7%0.3%9
0%99.7%0.3%10
0%99.7%0.3%11
0%99.7%0.3%12
0.8%98.9%0.3%13
1.2%98.5%0.3%14

sample1.1s

Algorithm
intervals
Results
689.0ms8000×body80valid
80.0ms936×body80invalid

Profiling

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