Details

Time bar (total: 5.7s)

sample30.0ms

Algorithm
intervals
Results
11.0ms283×body80valid
3.0ms89×body80nan

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0227
1467
2727
3997
41207
51207

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
3.3b
(* (* x y) z)
10.3b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
26.5b
(sqrt (- (* z z) (* t a)))

rewrite32.0ms

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)
12.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
5.0ms
(sqrt (- (* z z) (* t a)))

series207.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
85.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify56.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0368630
11941560
25001551

prune267.0ms

Filtered
98 candidates to 71 candidates (72.4%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.6b
(- (* z z) (* t a))
3.5b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
26.5b
(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))
5.0ms
(sqrt (- (* z z) (* t a)))

series259.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(/ (sqrt (- (* z z) (* t a))) z)
34.0ms
(- (* z z) (* t a))
87.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
64.0ms
(sqrt (- (* z z) (* t a)))

simplify68.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05431379
124481281
250011260

prune396.0ms

Filtered
154 candidates to 110 candidates (71.4%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt 1) (/ z (sqrt (- (* z z) (* t a)))))
0.6b
(- (* z z) (* t a))
3.5b
(/ (* x y) (/ (sqrt 1) (/ z (sqrt (- (* z z) (* t a))))))
26.5b
(sqrt (- (* z z) (* t a)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
923×times-frac
401×add-sqr-sqrt
400×add-cube-cbrt *-un-lft-identity
393×sqrt-prod
173×associate-/r*
42×associate-/r/
40×sqrt-div
30×add-exp-log add-cbrt-cube
23×div-inv
21×flip3-- flip--
15×cbrt-undiv div-exp
7×associate-/l*
6×add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×prod-exp cbrt-unprod
2×frac-2neg clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 548
Calls
4 calls:
14.0ms
(/ (sqrt 1) (/ z (sqrt (- (* z z) (* t a)))))
3.0ms
(- (* z z) (* t a))
33.0ms
(/ (* x y) (/ (sqrt 1) (/ z (sqrt (- (* z z) (* t a))))))
5.0ms
(sqrt (- (* z z) (* t a)))

series267.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(/ (sqrt 1) (/ z (sqrt (- (* z z) (* t a)))))
34.0ms
(- (* z z) (* t a))
87.0ms
(/ (* x y) (/ (sqrt 1) (/ z (sqrt (- (* z z) (* t a))))))
68.0ms
(sqrt (- (* z z) (* t a)))

simplify108.0ms

Algorithm
egg-herbie
Counts
560 → 560
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
016368357
150016994

prune1.1s

Filtered
560 candidates to 258 candidates (46.1%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
3.5b
(/ (* x y) (/ (sqrt 1) (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))))
26.5b
(sqrt (- (* z z) (* t a)))
26.5b
(sqrt (- (* z z) (* t a)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
311×times-frac
292×sqrt-div
99×associate-/r/
96×sqrt-prod
95×associate-/r*
94×add-sqr-sqrt
92×add-cube-cbrt *-un-lft-identity
75×flip3-- flip--
48×frac-times
36×add-exp-log add-cbrt-cube
24×associate-*r/ associate-*l/
18×cbrt-undiv div-exp
15×div-inv
6×pow1 prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u log1p-expm1-u
2×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg frac-2neg fma-neg diff-log prod-diff clear-num associate-/l*
Counts
4 → 270
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
42.0ms
(/ (* x y) (/ (sqrt 1) (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))))
5.0ms
(sqrt (- (* z z) (* t a)))
5.0ms
(sqrt (- (* z z) (* t a)))

series257.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(- (* z z) (* t a))
89.0ms
(/ (* x y) (/ (sqrt 1) (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))))
62.0ms
(sqrt (- (* z z) (* t a)))
68.0ms
(sqrt (- (* z z) (* t a)))

simplify71.0ms

Algorithm
egg-herbie
Counts
282 → 282
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013355610
150014940

prune1.1s

Filtered
282 candidates to 197 candidates (69.9%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 3.1b

regimes292.0ms

Accuracy

85% (3.0b remaining)

Error of 6.6b against oracle of 3.6b and baseline of 23.4b

bsearch113.0ms

Steps
ItersRangePoint
11
3.7831286906685055e+99
5.0015180444029904e+126
2.71648771019888e+115
10
-1.3628973842616926e+158
-1.1041089689887482e+148
-5.666550928011494e+151

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02410
13010
23010

end0.0ms

sample802.0ms

Algorithm
intervals
Results
335.0ms8901×body80valid
103.0ms2959×body80nan