Details

Time bar (total: 5.3s)

sample52.0ms

Algorithm
intervals
Results
26.0ms294×body80valid
8.0ms111×body80nan

simplify17.0ms

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: 25.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
4.4b
(* (* x y) z)
11.0b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.3b
(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:
3.0ms
(- (* 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)))

series265.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(- (* z z) (* t a))
29.0ms
(* (* x y) z)
113.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
82.0ms
(sqrt (- (* z z) (* t a)))

simplify61.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0346584
11863515
25002510

prune278.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.6b
(- (* z z) (* t a))
2.2b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
24.3b
(sqrt (- (* z z) (* t a)))

rewrite36.0ms

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)))

series292.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(/ z (sqrt (- (* z z) (* t a))))
41.0ms
(- (* z z) (* t a))
109.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
78.0ms
(sqrt (- (* z z) (* t a)))

simplify74.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
04311015
12166912
25002893

prune361.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
0.7b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
1.0b
(* y (/ z (sqrt (- (* z z) (* t a)))))
24.3b
(sqrt (- (* z z) (* t a)))

rewrite50.0ms

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))
20.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
20.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series305.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* z z) (* t a))
109.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
70.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
79.0ms
(sqrt (- (* z z) (* t a)))

simplify61.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0403776
11775676
25002667

prune295.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.4b

localize15.0ms

Local error

Found 4 expressions with local error:

1.3b
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
3.8b
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
24.3b
(sqrt (- (* z z) (* t a)))
24.3b
(sqrt (- (* z z) (* t a)))

rewrite75.0ms

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)))))
53.0ms
(* (/ (* x 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)))

series390.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
111.0ms
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
78.0ms
(sqrt (- (* z z) (* t a)))
80.0ms
(sqrt (- (* z z) (* t a)))

simplify100.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
06291951
133621738
250011614

prune727.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.4b

regimes400.0ms

Accuracy

86.2% (2.6b remaining)

Error of 6.3b against oracle of 3.6b and baseline of 22.7b

bsearch141.0ms

Steps
ItersRangePoint
9
2.0864676433609674e+119
1.1678228820445103e+126
5.324503325682955e+121
10
-5.301064106295175e+157
-2.1363922009711632e+141
-3.6721891600828564e+151

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02710
13310
23310

end0.0ms

sample1.3s

Algorithm
intervals
Results
696.0ms8835×body80valid
205.0ms2909×body80nan