Details

Time bar (total: 3.8s)

sample28.0ms

Algorithm
intervals
Results
10.0ms281×body80valid
3.0ms82×body80nan

simplify12.0ms

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: 25.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
4.7b
(* (* x y) z)
8.5b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.1b
(sqrt (- (* z z) (* t a)))

rewrite27.0ms

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))
6.0ms
(* (* x y) z)
12.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series207.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
84.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify55.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0346584
11863515
25002510

prune232.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.6b
(- (* z z) (* t a))
2.9b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
23.1b
(sqrt (- (* z z) (* t a)))

rewrite38.0ms

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))
19.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series230.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ z (sqrt (- (* z z) (* t a))))
37.0ms
(- (* z z) (* t a))
87.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
58.0ms
(sqrt (- (* z z) (* t a)))

simplify65.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
04311015
12166912
25002893

prune310.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
1.3b
(* y (/ z (sqrt (- (* z z) (* t a)))))
2.6b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
23.1b
(sqrt (- (* z z) (* t a)))

rewrite48.0ms

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))
19.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
19.0ms
(* x (* y (/ z (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))
58.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
85.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0403775
11781676
25001667

prune261.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.6b
(- (* z z) (* t a))
3.0b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
23.1b
(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)))

series252.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(/ (sqrt (- (* z z) (* t a))) z)
32.0ms
(- (* z z) (* t a))
83.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify66.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05191327
123801230
250011214

prune354.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.6b

regimes411.0ms

Accuracy

85.3% (2.8b remaining)

Error of 6.1b against oracle of 3.2b and baseline of 22.4b

bsearch88.0ms

Steps
ItersRangePoint
9
4.73660966086644e+91
1.92650848024315e+99
1.4676500402789059e+97
7
-1.135288498988565e+59
-4.458473145575816e+57
-4.76490929390757e+58

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03623
15223
25223

end0.0ms

sample792.0ms

Algorithm
intervals
Results
345.0ms8939×body80valid
98.0ms3034×body80nan