Details

Time bar (total: 2.6s)

sample21.0ms

Algorithm
intervals
Results
9.0ms273×body80valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
08211
18211

prune9.0ms

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: 7.0b

Counts
2 → 2

localize7.0ms

Local error

Found 2 expressions with local error:

3.5b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
4.5b
(* y (+ 1.0 (* z z)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
20×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
16×add-exp-log add-cbrt-cube
13×associate-/l*
6×cbrt-undiv div-exp
4×pow1 associate-*r/
3×associate-*r* associate-*l* prod-exp cbrt-unprod div-inv
2×flip3-+ associate-/r/ flip-+ add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num associate-/r* *-commutative associate-/l/ unswap-sqr
Counts
2 → 70
Calls
2 calls:
7.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
5.0ms
(* y (+ 1.0 (* z z)))

series29.0ms

Counts
2 → 6
Calls
2 calls:
19.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
9.0ms
(* y (+ 1.0 (* z z)))

simplify45.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
05002885

prune117.0ms

Filtered
56 candidates to 76 candidates (-35.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New69776
Fresh011
Picked101
Done000
Total70878

Merged error: 6.2b

Counts
78 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
3.5b
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
18.8b
(sqrt (+ 1.0 (* z z)))
18.8b
(sqrt (+ 1.0 (* z z)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
30×add-exp-log add-cbrt-cube
28×sqrt-div
24×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
16×associate-*r/
14×flip3-+ flip-+
13×associate-/l*
11×pow1
9×cbrt-undiv div-exp prod-exp sqrt-prod cbrt-unprod
8×frac-times associate-/r/
6×associate-*r*
4×associate-*l/ add-log-exp
3×pow-prod-down div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-2neg associate-*l* clear-num associate-/r* *-commutative associate-/l/
Counts
4 → 117
Calls
4 calls:
10.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
13.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
2.0ms
(sqrt (+ 1.0 (* z z)))
2.0ms
(sqrt (+ 1.0 (* z z)))

series37.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
17.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
4.0ms
(sqrt (+ 1.0 (* z z)))
6.0ms
(sqrt (+ 1.0 (* z z)))

simplify33.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
051111716

prune198.0ms

Filtered
94 candidates to 129 candidates (-37.2%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1281129
Fresh257
Picked011
Done000
Total1307137

Merged error: 6.2b

Counts
137 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1.0 (* (sqrt (+ 1.0 (* z z))) x))
1.9b
(* (/ 1 (* (sqrt (+ 1.0 (* z z))) y)) (/ 1.0 (* (sqrt (+ 1.0 (* z z))) x)))
18.8b
(sqrt (+ 1.0 (* z z)))
18.8b
(sqrt (+ 1.0 (* z z)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
87×add-exp-log
45×add-cbrt-cube
38×prod-exp
28×div-exp
16×add-sqr-sqrt cbrt-unprod
14×cbrt-undiv
12×add-cube-cbrt *-un-lft-identity
10×sqrt-div
9×times-frac associate-*r* associate-*l*
8×pow1
7×associate-*l/
6×rec-exp 1-exp sqrt-prod associate-/r/
5×flip3-+ flip-+
4×add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down clear-num associate-/r* *-commutative unswap-sqr
Counts
4 → 114
Calls
4 calls:
6.0ms
(/ 1.0 (* (sqrt (+ 1.0 (* z z))) x))
15.0ms
(* (/ 1 (* (sqrt (+ 1.0 (* z z))) y)) (/ 1.0 (* (sqrt (+ 1.0 (* z z))) x)))
2.0ms
(sqrt (+ 1.0 (* z z)))
2.0ms
(sqrt (+ 1.0 (* z z)))

series31.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(/ 1.0 (* (sqrt (+ 1.0 (* z z))) x))
11.0ms
(* (/ 1 (* (sqrt (+ 1.0 (* z z))) y)) (/ 1.0 (* (sqrt (+ 1.0 (* z z))) x)))
3.0ms
(sqrt (+ 1.0 (* z z)))
4.0ms
(sqrt (+ 1.0 (* z z)))

simplify270.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
049661576
149661576

prune190.0ms

Filtered
82 candidates to 126 candidates (-53.7%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1242126
Fresh055
Picked101
Done011
Total1258133

Merged error: 6.2b

Counts
133 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1.0 (* (sqrt (+ 1.0 (* z z))) y))
2.1b
(/ (/ 1.0 (* (sqrt (+ 1.0 (* z z))) y)) (* (sqrt (+ 1.0 (* z z))) x))
18.8b
(sqrt (+ 1.0 (* z z)))
18.8b
(sqrt (+ 1.0 (* z z)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
30×add-exp-log add-cbrt-cube
18×times-frac
14×add-sqr-sqrt
12×cbrt-undiv add-cube-cbrt *-un-lft-identity sqrt-div div-exp associate-/l*
8×associate-*l/ associate-/r/
6×pow1 flip3-+ prod-exp sqrt-prod cbrt-unprod flip-+
4×div-inv add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/r*
1×associate-/l/
Counts
4 → 97
Calls
4 calls:
6.0ms
(/ 1.0 (* (sqrt (+ 1.0 (* z z))) y))
12.0ms
(/ (/ 1.0 (* (sqrt (+ 1.0 (* z z))) y)) (* (sqrt (+ 1.0 (* z z))) x))
2.0ms
(sqrt (+ 1.0 (* z z)))
2.0ms
(sqrt (+ 1.0 (* z z)))

series34.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(/ 1.0 (* (sqrt (+ 1.0 (* z z))) y))
14.0ms
(/ (/ 1.0 (* (sqrt (+ 1.0 (* z z))) y)) (* (sqrt (+ 1.0 (* z z))) x))
3.0ms
(sqrt (+ 1.0 (* z z)))
4.0ms
(sqrt (+ 1.0 (* z z)))

simplify68.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
049721428
149721428

prune161.0ms

Filtered
83 candidates to 109 candidates (-31.3%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1072109
Fresh246
Picked011
Done011
Total1098117

Merged error: 2.3b

Counts
117 → 8

regimes600.0ms

Accuracy

92.8% (0.3b remaining)

Error of 2.4b against oracle of 2.1b and baseline of 6.5b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03859
13859

end0.0ms

sample615.0ms

Algorithm
intervals
Results
313.0ms8653×body80valid

Profiling

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