Details

Time bar (total: 3.8s)

sample29.0ms

Algorithm
intervals
Results
10.0ms277×body80valid
3.0ms101×body80nan

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
4.8b
(* (* x y) z)
8.9b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.4b
(sqrt (- (* z z) (* t a)))

rewrite29.0ms

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))
9.0ms
(* (* x y) z)
11.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series194.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
81.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
56.0ms
(sqrt (- (* z z) (* t a)))

simplify50.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0346584
11863515
25002510

prune223.0ms

Filtered
88 candidates to 60 candidates (68.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.2b
(- (* z z) (* t a))
2.3b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
23.4b
(sqrt (- (* z z) (* t a)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
24×associate-*r* sqrt-prod
18×add-exp-log add-cbrt-cube
10×pow1
6×sqrt-div prod-exp associate-/r* cbrt-unprod add-log-exp
4×flip3-- associate-/r/ flip--
3×cbrt-undiv div-exp pow-prod-down associate-/l*
2×div-inv
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ associate-*l* clear-num *-commutative
Counts
4 → 112
Calls
4 calls:
6.0ms
(/ z (sqrt (- (* z z) (* t a))))
3.0ms
(- (* z z) (* t a))
21.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ z (sqrt (- (* z z) (* t a))))
35.0ms
(- (* z z) (* t a))
81.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify61.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
04311015
12166912
25002893

prune298.0ms

Filtered
124 candidates to 82 candidates (66.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.2b
(- (* z z) (* t a))
2.4b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
23.4b
(sqrt (- (* z z) (* t a)))

rewrite31.0ms

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:
10.0ms
(/ (sqrt (- (* z z) (* t a))) z)
2.0ms
(- (* z z) (* t a))
10.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
4.0ms
(sqrt (- (* z z) (* t a)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(/ (sqrt (- (* z z) (* t a))) z)
34.0ms
(- (* z z) (* t a))
82.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
57.0ms
(sqrt (- (* z z) (* t a)))

simplify65.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05191327
123801230
250011214

prune338.0ms

Filtered
144 candidates to 98 candidates (68.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.3b

localize12.0ms

Local error

Found 4 expressions with local error:

2.4b
(/ (* x y) (/ (sqrt (* (sqrt (- (* z z) (* t a))) (sqrt (- (* z z) (* t a))))) z))
23.4b
(sqrt (* (sqrt (- (* z z) (* t a))) (sqrt (- (* z z) (* t a)))))
23.4b
(sqrt (- (* z z) (* t a)))
23.4b
(sqrt (- (* z z) (* t a)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
24×add-sqr-sqrt sqrt-pow1 sqrt-div
22×pow1 add-cube-cbrt *-un-lft-identity
16×add-exp-log associate-/r* add-cbrt-cube
13×sqrt-prod
11×pow1/2
8×flip3-- flip--
6×cbrt-undiv div-exp
5×pow-prod-up
4×frac-times add-log-exp
3×rem-sqrt-square pow-prod-down pow-sqr div-inv
2×associate-*r/ associate-*l/ prod-exp cbrt-unprod
1×pow2 frac-2neg pow-plus clear-num associate-/r/ associate-/l*
Counts
4 → 114
Calls
4 calls:
18.0ms
(/ (* x y) (/ (sqrt (* (sqrt (- (* z z) (* t a))) (sqrt (- (* z z) (* t a))))) z))
12.0ms
(sqrt (* (sqrt (- (* z z) (* t a))) (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series285.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(/ (* x y) (/ (sqrt (* (sqrt (- (* z z) (* t a))) (sqrt (- (* z z) (* t a))))) z))
59.0ms
(sqrt (* (sqrt (- (* z z) (* t a))) (sqrt (- (* z z) (* t a)))))
56.0ms
(sqrt (- (* z z) (* t a)))
88.0ms
(sqrt (- (* z z) (* t a)))

simplify64.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05081338
121871102
250021089

prune314.0ms

Filtered
126 candidates to 89 candidates (70.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.3b

regimes391.0ms

Accuracy

84.8% (2.9b remaining)

Error of 6.2b against oracle of 3.2b and baseline of 22.6b

bsearch65.0ms

Steps
ItersRangePoint
3
4.1175183293486755e+113
5.454825581884215e+113
4.368263439199089e+113
9
-7.721518663878112e+154
-1.486644691915056e+146
-1.3273676981364367e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02616
13216
23216

end0.0ms

sample789.0ms

Algorithm
intervals
Results
332.0ms8868×body80valid
99.0ms2917×body80nan