Details

Time bar (total: 4.0s)

sample33.0ms

Algorithm
intervals
Results
13.0ms278×body80valid
4.0ms109×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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: 30.0b

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
4.4b
(* (* x y) z)
11.2b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
26.8b
(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)
9.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
3.0ms
(sqrt (- (* z z) (* t a)))

series198.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
81.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify56.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0346584
11863515
25002510

prune230.0ms

Filtered
88 candidates to 60 candidates (68.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
1.0b
(- (* z z) (* t a))
3.7b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
26.8b
(sqrt (- (* z z) (* t a)))

rewrite28.0ms

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

series226.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ z (sqrt (- (* z z) (* t a))))
33.0ms
(- (* z z) (* t a))
84.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
60.0ms
(sqrt (- (* z z) (* t a)))

simplify65.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
04311015
12166912
25002893

prune290.0ms

Filtered
124 candidates to 81 candidates (65.3%)
Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.8b

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
1.7b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
2.2b
(* y (/ z (sqrt (- (* z z) (* t a)))))
26.8b
(sqrt (- (* z z) (* t a)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
25×associate-*r*
20×add-cube-cbrt *-un-lft-identity times-frac
18×add-exp-log add-cbrt-cube
13×sqrt-prod
12×pow1
7×prod-exp cbrt-unprod
6×associate-*l* add-log-exp
4×sqrt-div pow-prod-down
3×flip3-- associate-*r/ flip-- unswap-sqr
2×cbrt-undiv div-exp associate-/r/ *-commutative
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-inv
Counts
4 → 92
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
10.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
14.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series232.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* z z) (* t a))
83.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
58.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
58.0ms
(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0403775
11781676
25001667

prune251.0ms

Filtered
104 candidates to 69 candidates (66.3%)
Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.8b

localize13.0ms

Local error

Found 4 expressions with local error:

1.7b
(* x (* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
6.6b
(* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
26.8b
(sqrt (- (* z z) (* t a)))
26.8b
(sqrt (- (* z z) (* t a)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
103×add-sqr-sqrt
84×sqrt-prod
78×times-frac
45×add-cube-cbrt *-un-lft-identity
36×associate-*l*
34×add-exp-log associate-*r* add-cbrt-cube
16×unswap-sqr
13×pow1 prod-exp cbrt-unprod
12×sqrt-div
8×cbrt-undiv div-exp
5×associate-*r/
4×flip3-- pow-prod-down associate-/r/ flip-- add-log-exp
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ *-commutative div-inv
Counts
4 → 159
Calls
4 calls:
18.0ms
(* x (* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
35.0ms
(* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series261.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(* x (* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
58.0ms
(* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
57.0ms
(sqrt (- (* z z) (* t a)))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify80.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06692587
129382289
250022195

prune436.0ms

Filtered
171 candidates to 107 candidates (62.6%)
Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.8b

regimes430.0ms

Accuracy

86.7% (2.7b remaining)

Error of 6.1b against oracle of 3.3b and baseline of 23.9b

bsearch143.0ms

Steps
ItersRangePoint
6
4.497160141224824e+62
5.412561749290906e+63
5.138627507566571e+63
5
7.526030467558641e-222
1.9735030148980284e-221
9.371590452656194e-222
10
-3.9685742971637917e-205
-3.1994036708994665e-216
-1.2244468886524224e-206
3
-9.592993846745733e+148
-7.22911386769367e+148
-7.96782636114744e+148

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04832
16632
26632

end0.0ms

sample822.0ms

Algorithm
intervals
Results
350.0ms8897×body80valid
107.0ms3023×body80nan