Details

Time bar (total: 4.6s)

sample27.0ms

Algorithm
intervals
Results
10.0ms275×body80valid
3.0ms79×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0227
1467
2727
3997
41207
51207

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)))

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×expm1-log1p-u sqrt-div log1p-expm1-u
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 fma-neg diff-log associate-*l* prod-diff clear-num *-commutative div-inv associate-/l*
Counts
4 → 86
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
7.0ms
(* (* x y) z)
11.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series204.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
83.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0368630
11941560
25001551

prune281.0ms

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)))

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×expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u
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 fma-neg diff-log associate-*r/ associate-*l* prod-diff clear-num *-commutative
Counts
4 → 122
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)))

series236.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ z (sqrt (- (* z z) (* t a))))
33.0ms
(- (* z z) (* t a))
87.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
64.0ms
(sqrt (- (* z z) (* t a)))

simplify63.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
04531067
12239963
25001942

prune504.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.9b

localize14.0ms

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)))

rewrite46.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 123
Calls
4 calls:
3.0ms
(/ (* x y) (fabs (cbrt (- (* z z) (* t a)))))
33.0ms
(* (/ (* x y) (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
2.0ms
(cbrt (- (* z z) (* t a)))
2.0ms
(cbrt (- (* z z) (* t a)))

series408.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(/ (* x y) (fabs (cbrt (- (* z z) (* t a)))))
196.0ms
(* (/ (* x y) (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
82.0ms
(cbrt (- (* z z) (* t a)))
84.0ms
(cbrt (- (* z z) (* t a)))

simplify85.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
06911891
136871645
250021635

prune478.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.9b

localize18.0ms

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)))

rewrite10.0ms

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 expm1-log1p-u flip3-- pow1/3 add-cbrt-cube flip-- log1p-expm1-u add-log-exp
Counts
4 → 60
Calls
4 calls:
2.0ms
(cbrt (- (* z z) (* t a)))
2.0ms
(cbrt (- (* z z) (* t a)))
2.0ms
(cbrt (- (* z z) (* t a)))
2.0ms
(cbrt (- (* z z) (* t a)))

series333.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(cbrt (- (* z z) (* t a)))
83.0ms
(cbrt (- (* z z) (* t a)))
83.0ms
(cbrt (- (* z z) (* t a)))
83.0ms
(cbrt (- (* z z) (* t a)))

simplify128.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0153576
1477540
21474532
34623532
45001532

prune374.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.9b

regimes360.0ms

Accuracy

81.8% (3.5b remaining)

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

bsearch99.0ms

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
02817
13417
23417

end0.0ms

sample786.0ms

Algorithm
intervals
Results
338.0ms8866×body80valid
100.0ms2998×body80nan