Details

Time bar (total: 4.6s)

sample29.0ms

Algorithm
intervals
Results
11.0ms283×body80valid
3.0ms89×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
3.3b
(* (* x y) z)
10.3b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
26.5b
(sqrt (- (* z z) (* t a)))

rewrite23.0ms

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))
5.0ms
(* (* x y) z)
10.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series203.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
81.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify55.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0346584
11863515
25002510

prune231.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.6b
(- (* z z) (* t a))
3.5b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
26.5b
(sqrt (- (* z z) (* t a)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
47×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
33×sqrt-prod
25×associate-/r*
18×add-exp-log add-cbrt-cube
7×cbrt-undiv div-exp associate-/l*
6×add-log-exp
5×pow1
4×sqrt-div div-inv
3×flip3-- flip--
2×frac-2neg prod-exp clear-num cbrt-unprod associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/r/
Counts
4 → 132
Calls
4 calls:
6.0ms
(/ (sqrt (- (* z z) (* t a))) z)
4.0ms
(- (* z z) (* t a))
10.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
4.0ms
(sqrt (- (* z z) (* t a)))

series257.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(/ (sqrt (- (* z z) (* t a))) z)
33.0ms
(- (* z z) (* t a))
85.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
64.0ms
(sqrt (- (* z z) (* t a)))

simplify70.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
05191327
123801230
250011214

prune364.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (/ z (sqrt (- (* z z) (* t a)))))
0.6b
(- (* z z) (* t a))
3.5b
(/ (* x y) (/ 1 (/ z (sqrt (- (* z z) (* t a))))))
26.5b
(sqrt (- (* z z) (* t a)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
473×times-frac
211×add-sqr-sqrt
210×add-cube-cbrt *-un-lft-identity
101×associate-/r*
93×sqrt-prod
60×add-exp-log
35×div-exp
30×add-cbrt-cube
24×associate-/r/
22×sqrt-div
15×cbrt-undiv
14×div-inv
12×flip3-- flip--
7×prod-exp
6×pow1 rec-exp 1-exp add-log-exp
4×associate-/l*
3×cbrt-unprod
2×frac-2neg clear-num
1×sub-neg rem-sqrt-square pow-flip sqrt-pow1 pow1/2 diff-log inv-pow
Counts
4 → 333
Calls
4 calls:
11.0ms
(/ 1 (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(- (* z z) (* t a))
20.0ms
(/ (* x y) (/ 1 (/ z (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))

series257.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(/ 1 (/ z (sqrt (- (* z z) (* t a)))))
33.0ms
(- (* z z) (* t a))
84.0ms
(/ (* x y) (/ 1 (/ z (sqrt (- (* z z) (* t a))))))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify71.0ms

Algorithm
egg-herbie
Counts
345 → 345
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
012224333
150023768

prune757.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
3.5b
(/ (* x y) (/ 1 (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))))
26.5b
(sqrt (- (* z z) (* t a)))
26.5b
(sqrt (- (* z z) (* t a)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
158×times-frac
148×sqrt-div
78×add-exp-log
52×add-sqr-sqrt
51×associate-/r/
50×add-cube-cbrt *-un-lft-identity associate-/r*
44×div-exp
39×flip3-- flip--
36×add-cbrt-cube
24×frac-times
18×cbrt-undiv
16×prod-exp
12×associate-*r/ associate-*l/
9×div-inv
6×pow1 rec-exp 1-exp sqrt-prod cbrt-unprod add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg frac-2neg diff-log clear-num associate-/l*
Counts
4 → 182
Calls
4 calls:
4.0ms
(- (* z z) (* t a))
27.0ms
(/ (* x y) (/ 1 (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series243.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* z z) (* t a))
86.0ms
(/ (* x y) (/ 1 (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))))
64.0ms
(sqrt (- (* z z) (* t a)))
59.0ms
(sqrt (- (* z z) (* t a)))

simplify56.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010623325
150012661

prune591.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 3.1b

regimes304.0ms

Accuracy

85% (3.0b remaining)

Error of 6.6b against oracle of 3.6b and baseline of 23.4b

bsearch110.0ms

Steps
ItersRangePoint
11
3.7831286906685055e+99
5.0015180444029904e+126
2.71648771019888e+115
10
-1.3628973842616926e+158
-1.1041089689887482e+148
-5.666550928011494e+151

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02410
13010
23010

end0.0ms

sample807.0ms

Algorithm
intervals
Results
347.0ms8901×body80valid
107.0ms2959×body80nan