Details

Time bar (total: 5.0s)

sample32.0ms

Algorithm
intervals
Results
12.0ms277×body80valid
2.0ms65×body80nan

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0227
1467
2727
3997
41207
51207

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
4.7b
(* (* x y) z)
8.5b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
26.5b
(sqrt (- (* z z) (* t a)))

rewrite67.0ms

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:
8.0ms
(- (* z z) (* t a))
18.0ms
(* (* x y) z)
28.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
10.0ms
(sqrt (- (* z z) (* t a)))

series186.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(- (* z z) (* t a))
25.0ms
(* (* x y) z)
73.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
58.0ms
(sqrt (- (* z z) (* t a)))

simplify56.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0368630
11941560
25001551

prune262.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.4b
(- (* z z) (* t a))
1.2b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
26.5b
(sqrt (- (* z z) (* t a)))

rewrite82.0ms

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:
13.0ms
(/ z (sqrt (- (* z z) (* t a))))
8.0ms
(- (* z z) (* t a))
43.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
11.0ms
(sqrt (- (* z z) (* t a)))

series208.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ z (sqrt (- (* z z) (* t a))))
29.0ms
(- (* z z) (* t a))
77.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
54.0ms
(sqrt (- (* z z) (* t a)))

simplify63.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04531067
12239963
25001942

prune327.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
0.4b
(- (* z z) (* t a))
1.2b
(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
26.5b
(sqrt (- (* z z) (* t a)))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
48×add-exp-log
32×add-sqr-sqrt
30×add-cbrt-cube
27×prod-exp
25×associate-*r*
22×times-frac
21×*-un-lft-identity
19×pow1 add-cube-cbrt
15×cbrt-unprod
14×sqrt-prod
9×pow-prod-down
6×div-exp add-log-exp
5×unswap-sqr
4×expm1-log1p-u sqrt-div associate-*r/ associate-*l* log1p-expm1-u
3×cbrt-undiv rec-exp flip3-- 1-exp flip--
2×associate-/r/ un-div-inv *-commutative
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff div-inv
Counts
4 → 118
Calls
4 calls:
40.0ms
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
8.0ms
(- (* z z) (* t a))
60.0ms
(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
11.0ms
(sqrt (- (* z z) (* t a)))

series213.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
31.0ms
(- (* z z) (* t a))
78.0ms
(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
56.0ms
(sqrt (- (* z z) (* t a)))

simplify63.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05011017
12458840
25002802

prune293.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.7b

localize15.0ms

Local error

Found 4 expressions with local error:

3.1b
(/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z))
3.1b
(/ (/ (* 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)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
413×times-frac
157×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
114×sqrt-prod
63×cbrt-prod
34×add-exp-log add-cbrt-cube
24×div-inv
22×associate-/r*
19×associate-/l*
17×cbrt-undiv div-exp
13×associate-/r/
6×cbrt-div
4×pow1 expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×flip3-- flip--
2×frac-2neg pow1/3 sqrt-div clear-num
1×associate-/l/
Counts
4 → 292
Calls
4 calls:
13.0ms
(/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z))
34.0ms
(/ (/ (* x 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)))

series424.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z))
197.0ms
(/ (/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z)) (sqrt (cbrt (- (* z z) (* t a)))))
81.0ms
(cbrt (- (* z z) (* t a)))
82.0ms
(cbrt (- (* z z) (* t a)))

simplify83.0ms

Algorithm
egg-herbie
Counts
304 → 304
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012736567
150016234

prune1.0s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.7b

regimes402.0ms

Accuracy

85.2% (2.9b remaining)

Error of 6.2b against oracle of 3.3b and baseline of 23.0b

bsearch53.0ms

Steps
ItersRangePoint
5
2.0444512156611406e+70
5.0533976637557934e+70
4.762366900384719e+70
6
-3.1180314797754244e+138
-6.80629099292568e+137
-1.783459363067828e+138

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02410
12510
23110
33110

end0.0ms

sample871.0ms

Algorithm
intervals
Results
315.0ms8812×body80valid
88.0ms2761×body80nan