Details

Time bar (total: 5.0s)

sample30.0ms

Algorithm
intervals
Results
11.0ms283×body80valid
3.0ms89×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0227
1467
2727
3997
41207
51207

prune3.0ms

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)))

rewrite26.0ms

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:
4.0ms
(- (* z z) (* t a))
5.0ms
(* (* x y) z)
10.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series203.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
83.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify55.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0368630
11941560
25001551

prune263.0ms

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:
6.0ms
(/ (sqrt (- (* z z) (* t a))) z)
4.0ms
(- (* z z) (* t a))
10.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
4.0ms
(sqrt (- (* z z) (* t a)))

series250.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(/ (sqrt (- (* z z) (* t a))) z)
33.0ms
(- (* z z) (* t a))
84.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify69.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05431379
124481281
250011260

prune389.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.1b

localize19.0ms

Local error

Found 4 expressions with local error:

1.8b
(/ (* x y) (/ (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))) (* (cbrt z) (cbrt z))))
26.5b
(sqrt (- (* z z) (* t a)))
26.5b
(sqrt (- (* z z) (* t a)))
26.5b
(sqrt (- (* z z) (* t a)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log
29×add-cbrt-cube
18×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
12×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity sqrt-prod
7×pow1 times-frac
6×sqrt-div
5×associate-/r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip-- div-inv
1×frac-2neg clear-num associate-/r/ associate-/l*
Counts
4 → 95
Calls
4 calls:
19.0ms
(/ (* x y) (/ (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))) (* (cbrt z) (cbrt z))))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series351.0ms

Counts
4 → 12
Calls
4 calls:
169.0ms
(/ (* x y) (/ (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))) (* (cbrt z) (cbrt z))))
60.0ms
(sqrt (- (* z z) (* t a)))
63.0ms
(sqrt (- (* z z) (* t a)))
59.0ms
(sqrt (- (* z z) (* t a)))

simplify65.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
04541381
124261099
250021008

prune375.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.1b

localize12.0ms

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)))

rewrite104.0ms

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)))))
4.0ms
(- (* z z) (* t a))
35.0ms
(/ (* x y) (/ (sqrt 1) (/ z (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))

series259.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ (sqrt 1) (/ z (sqrt (- (* z z) (* t a)))))
38.0ms
(- (* z z) (* t a))
87.0ms
(/ (* x y) (/ (sqrt 1) (/ z (sqrt (- (* z z) (* t a))))))
58.0ms
(sqrt (- (* z z) (* t a)))

simplify99.0ms

Algorithm
egg-herbie
Counts
560 → 560
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
016368357
150016994

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.1b

regimes319.0ms

Accuracy

85% (3.0b remaining)

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

bsearch108.0ms

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

sample826.0ms

Algorithm
intervals
Results
343.0ms8901×body80valid
107.0ms2959×body80nan