Details

Time bar (total: 4.5s)

sample31.0ms

Algorithm
intervals
Results
11.0ms281×body80valid
4.0ms107×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: 23.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
5.6b
(* (* x y) z)
8.3b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.3b
(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))
6.0ms
(* (* x y) z)
12.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series202.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
82.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify57.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0368630
11941560
25001551

prune273.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.8b
(- (* z z) (* t a))
3.0b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
22.3b
(sqrt (- (* z z) (* t a)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
47×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
33×sqrt-prod
25×associate-/r*
18×add-exp-log add-cbrt-cube
7×cbrt-undiv div-exp associate-/l*
6×add-log-exp
5×pow1
4×expm1-log1p-u sqrt-div log1p-expm1-u div-inv
3×flip3-- flip--
2×frac-2neg prod-exp clear-num cbrt-unprod associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff associate-/r/
Counts
4 → 142
Calls
4 calls:
8.0ms
(/ (sqrt (- (* z z) (* t a))) z)
3.0ms
(- (* z z) (* t a))
10.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
4.0ms
(sqrt (- (* z z) (* t a)))

series254.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(/ (sqrt (- (* z z) (* t a))) z)
33.0ms
(- (* z z) (* t a))
82.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
65.0ms
(sqrt (- (* z z) (* t a)))

simplify68.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05431379
124481281
250011260

prune410.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
1.5b
(/ y (/ (sqrt (- (* z z) (* t a))) z))
2.0b
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
22.3b
(sqrt (- (* z z) (* t a)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
263×times-frac
157×add-sqr-sqrt
143×add-cube-cbrt *-un-lft-identity
71×associate-*r*
67×sqrt-prod
22×associate-/r*
18×add-exp-log add-cbrt-cube
9×div-inv
7×pow1
6×cbrt-undiv div-exp add-log-exp
4×expm1-log1p-u log1p-expm1-u unswap-sqr
3×associate-*l* prod-exp cbrt-unprod associate-/l*
2×flip3-- sqrt-div associate-/r/ flip--
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*r/ prod-diff pow-prod-down clear-num *-commutative
Counts
4 → 237
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
9.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
34.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
7.0ms
(sqrt (- (* z z) (* t a)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* z z) (* t a))
58.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
84.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
65.0ms
(sqrt (- (* z z) (* t a)))

simplify106.0ms

Algorithm
egg-herbie
Counts
249 → 249
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
08392556
140712400
250022396

prune673.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.8b
(- (* z z) (* t a))
3.0b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
22.3b
(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×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))
19.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series239.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(/ z (sqrt (- (* z z) (* t a))))
33.0ms
(- (* z z) (* t a))
82.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify87.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
04531067
12239963
25001942

prune334.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 2.9b

regimes446.0ms

Accuracy

85.9% (2.7b remaining)

Error of 6.1b against oracle of 3.3b and baseline of 22.8b

bsearch99.0ms

Steps
ItersRangePoint
11
6.7885585141402705e+103
1.0680580568755772e+124
2.63678430171191e+123
9
-5.753239068835225e+150
-4.934060275160021e+145
-3.0286624309368284e+146

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03111
14711
24711

end0.0ms

sample789.0ms

Algorithm
intervals
Results
349.0ms8843×body80valid
106.0ms2918×body80nan