Details

Time bar (total: 5.1s)

sample27.0ms

Algorithm
intervals
Results
10.0ms283×body80valid
3.0ms89×body80nan

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.8b

localize10.0ms

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)))

rewrite26.0ms

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:
2.0ms
(- (* z z) (* t a))
7.0ms
(* (* x y) z)
11.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series202.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
82.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0346584
11863515
25002510

prune217.0ms

Filtered
88 candidates to 60 candidates (68.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.1b

localize10.0ms

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:
7.0ms
(/ (sqrt (- (* z z) (* t a))) z)
3.0ms
(- (* z z) (* t a))
10.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
4.0ms
(sqrt (- (* z z) (* t a)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(/ (sqrt (- (* z z) (* t a))) z)
32.0ms
(- (* z z) (* t a))
84.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify64.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05191327
123801230
250011214

prune349.0ms

Filtered
144 candidates to 99 candidates (68.8%)
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
(/ (sqrt 1) (/ z (sqrt (- (* z z) (* t a)))))
0.6b
(- (* z z) (* t a))
3.5b
(/ (* x y) (/ (sqrt 1) (/ z (sqrt (- (* z z) (* t a))))))
26.5b
(sqrt (- (* z z) (* t a)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
923×times-frac
401×add-sqr-sqrt
400×add-cube-cbrt *-un-lft-identity
393×sqrt-prod
173×associate-/r*
42×associate-/r/
40×sqrt-div
30×add-exp-log add-cbrt-cube
23×div-inv
21×flip3-- flip--
15×cbrt-undiv div-exp
7×associate-/l*
6×add-log-exp
5×pow1
3×prod-exp cbrt-unprod
2×frac-2neg clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 538
Calls
4 calls:
14.0ms
(/ (sqrt 1) (/ z (sqrt (- (* z z) (* t a)))))
3.0ms
(- (* z z) (* t a))
37.0ms
(/ (* x y) (/ (sqrt 1) (/ z (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))

series254.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(/ (sqrt 1) (/ z (sqrt (- (* z z) (* t a)))))
32.0ms
(- (* z z) (* t a))
85.0ms
(/ (* x y) (/ (sqrt 1) (/ z (sqrt (- (* z z) (* t a))))))
65.0ms
(sqrt (- (* z z) (* t a)))

simplify102.0ms

Algorithm
egg-herbie
Counts
550 → 550
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
016128297
150016872

prune993.0ms

Filtered
550 candidates to 247 candidates (44.9%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.1b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
311×times-frac
292×sqrt-div
99×associate-/r/
96×sqrt-prod
95×associate-/r*
94×add-sqr-sqrt
92×add-cube-cbrt *-un-lft-identity
75×flip3-- flip--
48×frac-times
36×add-exp-log add-cbrt-cube
24×associate-*r/ associate-*l/
18×cbrt-undiv div-exp
15×div-inv
6×pow1 prod-exp 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 → 260
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
38.0ms
(/ (* x y) (/ (sqrt 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)))

series238.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* z z) (* t a))
86.0ms
(/ (* x y) (/ (sqrt 1) (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))))
61.0ms
(sqrt (- (* z z) (* t a)))
58.0ms
(sqrt (- (* z z) (* t a)))

simplify72.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
013155542
150014874

prune901.0ms

Filtered
272 candidates to 187 candidates (68.8%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 3.1b

regimes268.0ms

Accuracy

85% (3.0b remaining)

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

bsearch98.0ms

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

sample763.0ms

Algorithm
intervals
Results
324.0ms8901×body80valid
102.0ms2959×body80nan