Details

Time bar (total: 4.5s)

sample33.0ms

Algorithm
intervals
Results
10.0ms287×body80valid
3.0ms99×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: 26.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
5.1b
(* (* x y) z)
10.5b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.6b
(sqrt (- (* z z) (* t a)))

rewrite72.0ms

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:
9.0ms
(- (* z z) (* t a))
17.0ms
(* (* x y) z)
32.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
12.0ms
(sqrt (- (* z z) (* t a)))

series215.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(- (* z z) (* t a))
24.0ms
(* (* x y) z)
90.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify56.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0368630
11941560
25001551

prune278.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.6b
(- (* z z) (* t a))
3.2b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
24.6b
(sqrt (- (* z z) (* t a)))

rewrite85.0ms

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:
15.0ms
(/ z (sqrt (- (* z z) (* t a))))
9.0ms
(- (* z z) (* t a))
46.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
11.0ms
(sqrt (- (* z z) (* t a)))

series245.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ z (sqrt (- (* z z) (* t a))))
35.0ms
(- (* z z) (* t a))
92.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
65.0ms
(sqrt (- (* z z) (* t a)))

simplify66.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
04531067
12239963
25001942

prune325.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
1.3b
(* y (/ z (sqrt (- (* z z) (* t a)))))
2.0b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
24.6b
(sqrt (- (* z z) (* t a)))

rewrite109.0ms

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×expm1-log1p-u sqrt-div pow-prod-down log1p-expm1-u
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 fma-neg diff-log prod-diff div-inv
Counts
4 → 102
Calls
4 calls:
10.0ms
(- (* z z) (* t a))
39.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
45.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
11.0ms
(sqrt (- (* z z) (* t a)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* z z) (* t a))
62.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
92.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0425829
11848729
25001717

prune284.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.0b

localize16.0ms

Local error

Found 4 expressions with local error:

3.2b
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
24.6b
(sqrt (- (* z z) (* t a)))
24.6b
(sqrt (- (* z z) (* t a)))
24.6b
(sqrt (- (* z z) (* t a)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod
23×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
8×sqrt-div
7×pow1
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×associate-/r/
1×cbrt-div pow1/3 div-inv
Counts
4 → 86
Calls
4 calls:
9.0ms
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
11.0ms
(sqrt (- (* z z) (* t a)))
12.0ms
(sqrt (- (* z z) (* t a)))
15.0ms
(sqrt (- (* z z) (* t a)))

series337.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
62.0ms
(sqrt (- (* z z) (* t a)))
60.0ms
(sqrt (- (* z z) (* t a)))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify92.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 3 (79.0ms)

IterNodesCost
0286857
1859832
23232817
35001814

prune401.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.0b

regimes386.0ms

Accuracy

78.1% (4.3b remaining)

Error of 7.1b against oracle of 2.9b and baseline of 22.3b

bsearch162.0ms

Steps
ItersRangePoint
4
4.774247135773842e+113
7.50002489248219e+113
6.344623429916867e+113
8
5.33924979008046e-170
8.410459962733418e-167
3.417452118825497e-169
10
8.70971164655884e-238
6.532280200382943e-228
6.447720564522469e-228
9
-2.3132843735365205e+104
-2.0509244193021767e+98
-5.841072424480833e+103

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04433
14533
24833
34833

end0.0ms

sample902.0ms

Algorithm
intervals
Results
319.0ms8828×body80valid
94.0ms2971×body80nan