Details

Time bar (total: 4.3s)

sample32.0ms

Algorithm
intervals
Results
13.0ms286×body80valid
3.0ms94×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: 25.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
7.0b
(* (* x y) z)
8.6b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.6b
(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)
11.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series201.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* z z) (* t a))
24.0ms
(* (* x y) z)
82.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify61.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0368630
11941560
25001551

prune267.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
6.0b
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
25.6b
(sqrt (- (* z z) (* t a)))
25.6b
(sqrt (- (* z z) (* t a)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
63×sqrt-prod
48×add-sqr-sqrt times-frac
35×add-cube-cbrt *-un-lft-identity
33×associate-*r*
30×add-exp-log add-cbrt-cube
16×sqrt-div
15×associate-*l*
9×cbrt-undiv div-exp prod-exp associate-/r* cbrt-unprod
8×pow1
6×associate-/r/
5×flip3-- flip--
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 149
Calls
4 calls:
8.0ms
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
51.0ms
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series303.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
85.0ms
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
65.0ms
(sqrt (- (* z z) (* t a)))
60.0ms
(sqrt (- (* z z) (* t a)))

simplify86.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
06432019
134021804
250011678

prune466.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.6b

localize14.0ms

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)))))
25.6b
(sqrt (- (* z z) (* t a)))

rewrite37.0ms

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)))))
5.0ms
(sqrt (- (* z z) (* t a)))

series236.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ z (sqrt (- (* z z) (* t a))))
33.0ms
(- (* z z) (* t a))
86.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
65.0ms
(sqrt (- (* z z) (* t a)))

simplify63.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
04531067
12239963
25001942

prune338.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b
(* y (/ z (sqrt (- (* z z) (* t a)))))
0.8b
(- (* z z) (* t a))
2.2b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
25.6b
(sqrt (- (* z z) (* t a)))

rewrite52.0ms

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:
22.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
3.0ms
(- (* z z) (* t a))
20.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
37.0ms
(- (* z z) (* t a))
87.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
59.0ms
(sqrt (- (* z z) (* t a)))

simplify56.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0425829
11848729
25001717

prune264.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.6b

regimes477.0ms

Accuracy

85.7% (2.8b remaining)

Error of 6.1b against oracle of 3.3b and baseline of 22.7b

bsearch174.0ms

Steps
ItersRangePoint
9
3.746727403856088e+106
3.7825834698094115e+111
2.966256665740778e+111
8
1.1153785941723318e-233
6.35612659283377e-229
1.8216614650284523e-230
9
-3.6939352897630696e-286
-3.8233550731978216e-294
-1.5634428196347479e-286
5
-3.761360877216288e+146
-1.6259263967015282e+146
-3.4871110320270968e+146

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04225
14525
25125
35125

end0.0ms

sample790.0ms

Algorithm
intervals
Results
332.0ms8857×body80valid
105.0ms3027×body80nan