Details

Time bar (total: 4.3s)

sample27.0ms

Algorithm
intervals
Results
10.0ms275×body80valid
2.0ms79×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: 25.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
4.0b
(* (* x y) z)
7.8b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
26.4b
(sqrt (- (* z z) (* t a)))

rewrite28.0ms

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))
7.0ms
(* (* x y) z)
12.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series211.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* z z) (* t a))
25.0ms
(* (* x y) z)
88.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0346584
11863515
25002510

prune231.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.4b
(- (* z z) (* t a))
3.9b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
26.4b
(sqrt (- (* z z) (* t a)))

rewrite39.0ms

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:
7.0ms
(/ z (sqrt (- (* z z) (* t a))))
3.0ms
(- (* z z) (* t a))
21.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series235.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ z (sqrt (- (* z z) (* t a))))
33.0ms
(- (* z z) (* t a))
87.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
65.0ms
(sqrt (- (* z z) (* t a)))

simplify60.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04311015
12166912
25002893

prune281.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.9b

localize17.0ms

Local error

Found 4 expressions with local error:

1.6b
(/ (* x y) (fabs (cbrt (- (* z z) (* t a)))))
7.1b
(* (/ (* x y) (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
27.2b
(cbrt (- (* z z) (* t a)))
27.2b
(cbrt (- (* z z) (* t a)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
36×times-frac
33×associate-*r*
30×add-exp-log add-cbrt-cube
29×add-cube-cbrt *-un-lft-identity
20×sqrt-prod
16×cbrt-prod
9×cbrt-undiv div-exp prod-exp cbrt-unprod
7×associate-*l*
6×pow1 cbrt-div
4×add-log-exp unswap-sqr
3×flip3-- associate-/r* flip-- div-inv
2×pow1/3 sqrt-div associate-/r/
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 115
Calls
4 calls:
3.0ms
(/ (* x y) (fabs (cbrt (- (* z z) (* t a)))))
34.0ms
(* (/ (* x y) (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
2.0ms
(cbrt (- (* z z) (* t a)))
3.0ms
(cbrt (- (* z z) (* t a)))

series450.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ (* x y) (fabs (cbrt (- (* z z) (* t a)))))
215.0ms
(* (/ (* x y) (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
89.0ms
(cbrt (- (* z z) (* t a)))
91.0ms
(cbrt (- (* z z) (* t a)))

simplify85.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
06791825
136441579
250011569

prune446.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.9b

localize22.0ms

Local error

Found 4 expressions with local error:

27.2b
(cbrt (- (* z z) (* t a)))
27.2b
(cbrt (- (* z z) (* t a)))
27.2b
(cbrt (- (* z z) (* t a)))
27.2b
(cbrt (- (* z z) (* t a)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt cbrt-div *-un-lft-identity
4×pow1 add-exp-log flip3-- pow1/3 add-cbrt-cube flip-- add-log-exp
Counts
4 → 52
Calls
4 calls:
2.0ms
(cbrt (- (* z z) (* t a)))
2.0ms
(cbrt (- (* z z) (* t a)))
2.0ms
(cbrt (- (* z z) (* t a)))
3.0ms
(cbrt (- (* z z) (* t a)))

series357.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(cbrt (- (* z z) (* t a)))
90.0ms
(cbrt (- (* z z) (* t a)))
89.0ms
(cbrt (- (* z z) (* t a)))
90.0ms
(cbrt (- (* z z) (* t a)))

simplify129.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 4 (123.0ms)

IterNodesCost
0145536
1439500
21301492
34135492
45001488

prune320.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.9b

regimes357.0ms

Accuracy

81.8% (3.5b remaining)

Error of 7.1b against oracle of 3.7b and baseline of 22.7b

bsearch92.0ms

Steps
ItersRangePoint
8
1.809966974149678e+110
2.6911721134682347e+113
4.518132542240334e+112
9
-1.2707248800969787e+89
-6.309199235252727e+80
-2.1890101961612443e+88

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03218
13718
24818
34818

end0.0ms

sample767.0ms

Algorithm
intervals
Results
329.0ms8866×body80valid
94.0ms2998×body80nan