Details

Time bar (total: 4.1s)

sample31.0ms

Algorithm
intervals
Results
12.0ms286×body80valid
3.0ms94×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
7.0b
(* (* x y) z)
8.6b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.6b
(sqrt (- (* z z) (* t a)))

rewrite25.0ms

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))
6.0ms
(* (* x y) z)
11.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series200.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* z z) (* t a))
24.0ms
(* (* x y) z)
82.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0346584
11863515
25002510

prune219.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
6.0b
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
25.6b
(sqrt (- (* z z) (* t a)))
25.6b
(sqrt (- (* z z) (* t a)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
63×sqrt-prod
48×add-sqr-sqrt times-frac
35×add-cube-cbrt *-un-lft-identity
33×associate-*r*
30×add-exp-log add-cbrt-cube
16×sqrt-div
15×associate-*l*
9×cbrt-undiv div-exp prod-exp associate-/r* cbrt-unprod
8×pow1
6×associate-/r/
5×flip3-- flip--
4×add-log-exp unswap-sqr
3×div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 141
Calls
4 calls:
8.0ms
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
48.0ms
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
3.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series296.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
83.0ms
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
58.0ms
(sqrt (- (* z z) (* t a)))
64.0ms
(sqrt (- (* z z) (* t a)))

simplify80.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
06291951
133621738
250011641

prune472.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.8b
(- (* z z) (* t a))
3.0b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
25.6b
(sqrt (- (* z z) (* t a)))

rewrite37.0ms

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))
18.0ms
(* (* 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))))
36.0ms
(- (* z z) (* t a))
84.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
58.0ms
(sqrt (- (* z z) (* t a)))

simplify61.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
04311016
12160912
25001893

prune296.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b
(* y (/ z (sqrt (- (* z z) (* t a)))))
0.8b
(- (* z z) (* t a))
2.2b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
25.6b
(sqrt (- (* z z) (* t a)))

rewrite49.0ms

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:
18.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
2.0ms
(- (* 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:
53.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
36.0ms
(- (* z z) (* t a))
83.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
58.0ms
(sqrt (- (* z z) (* t a)))

simplify50.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0403775
11781676
25001667

prune229.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.6b

regimes472.0ms

Accuracy

85.7% (2.8b remaining)

Error of 6.1b against oracle of 3.3b and baseline of 22.7b

bsearch171.0ms

Steps
ItersRangePoint
9
3.746727403856088e+106
3.7825834698094115e+111
2.966256665740778e+111
8
1.1153785941723318e-233
6.35612659283377e-229
1.8216614650284523e-230
9
-3.6939352897630696e-286
-3.8233550731978216e-294
-1.5634428196347479e-286
5
-3.761360877216288e+146
-1.6259263967015282e+146
-3.4871110320270968e+146

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03824
14424
24424

end0.0ms

sample784.0ms

Algorithm
intervals
Results
326.0ms8857×body80valid
96.0ms3027×body80nan