Details

Time bar (total: 4.4s)

sample32.0ms

Algorithm
intervals
Results
10.0ms289×body80valid
3.0ms110×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: 28.2b

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
4.0b
(* (* x y) z)
11.2b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
27.9b
(sqrt (- (* z z) (* t a)))

rewrite69.0ms

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:
8.0ms
(- (* z z) (* t a))
20.0ms
(* (* x y) z)
29.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
10.0ms
(sqrt (- (* z z) (* t a)))

series191.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* z z) (* t a))
21.0ms
(* (* x y) z)
81.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
54.0ms
(sqrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0346585
11857515
25001510

prune227.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
1.0b
(- (* z z) (* t a))
2.5b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
27.9b
(sqrt (- (* z z) (* t a)))

rewrite81.0ms

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:
14.0ms
(/ z (sqrt (- (* z z) (* t a))))
8.0ms
(- (* z z) (* t a))
46.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
9.0ms
(sqrt (- (* z z) (* t a)))

series212.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ z (sqrt (- (* z z) (* t a))))
29.0ms
(- (* z z) (* t a))
79.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
56.0ms
(sqrt (- (* z z) (* t a)))

simplify63.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04311015
12166912
25002893

prune285.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.9b

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
1.9b
(* y (/ z (sqrt (- (* z z) (* t a)))))
2.2b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
27.9b
(sqrt (- (* z z) (* t a)))

rewrite108.0ms

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:
8.0ms
(- (* z z) (* t a))
41.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
47.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
9.0ms
(sqrt (- (* z z) (* t a)))

series215.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(- (* z z) (* t a))
54.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
74.0ms
(* 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

prune242.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.9b

localize15.0ms

Local error

Found 4 expressions with local error:

2.2b
(* x (* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
8.2b
(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
28.8b
(cbrt (- (* z z) (* t a)))
28.8b
(cbrt (- (* z z) (* t a)))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
46×times-frac
34×add-exp-log associate-*r* add-cbrt-cube
33×add-cube-cbrt *-un-lft-identity
22×sqrt-prod
17×cbrt-prod
16×associate-*l*
13×prod-exp cbrt-unprod
11×pow1
8×cbrt-undiv div-exp unswap-sqr
6×cbrt-div
5×associate-*r/
4×pow-prod-down add-log-exp
3×flip3-- flip--
2×frac-times pow1/3 sqrt-div associate-*l/ associate-/r/ *-commutative div-inv
Counts
4 → 127
Calls
4 calls:
58.0ms
(* x (* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
60.0ms
(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
6.0ms
(cbrt (- (* z z) (* t a)))
6.0ms
(cbrt (- (* z z) (* t a)))

series488.0ms

Counts
4 → 12
Calls
4 calls:
194.0ms
(* x (* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
135.0ms
(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
79.0ms
(cbrt (- (* z z) (* t a)))
80.0ms
(cbrt (- (* z z) (* t a)))

simplify85.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
07442169
133561869
250011859

prune457.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.9b

regimes419.0ms

Accuracy

83.3% (3.3b remaining)

Error of 6.4b against oracle of 3.1b and baseline of 22.8b

bsearch39.0ms

Steps
ItersRangePoint
0
1.281024336404866e+68
1.3038645461094304e+68
1.292444441257148e+68
9
-2.1605719851212306e+156
-8.864743291636389e+150
-1.1315032243066199e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02710
12810
23110
33110

end0.0ms

sample867.0ms

Algorithm
intervals
Results
315.0ms8880×body80valid
94.0ms3095×body80nan