Details

Time bar (total: 5.6s)

sample51.0ms

Algorithm
intervals
Results
28.0ms277×body80valid
8.0ms86×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: 26.4b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
4.3b
(* (* x y) z)
8.1b
(/ (* (* 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:
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)))

series199.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
81.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify57.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0368630
11941560
25001551

prune269.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
1.0b
(- (* z z) (* t a))
1.3b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
26.5b
(sqrt (- (* z z) (* t a)))

rewrite35.0ms

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)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series227.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ z (sqrt (- (* z z) (* t a))))
33.0ms
(- (* z z) (* t a))
83.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify63.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
04531067
12239963
25001942

prune322.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.9b

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
1.3b
(* (* x y) (/ (/ 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)))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
546×sqrt-prod
540×times-frac
303×associate-*r*
279×add-sqr-sqrt
277×add-cube-cbrt *-un-lft-identity
44×sqrt-div
25×add-exp-log add-cbrt-cube
20×associate-/r/
13×flip3-- flip--
11×pow1
10×div-inv
9×prod-exp cbrt-unprod
6×cbrt-undiv div-exp add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-prod-down
2×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg fma-neg diff-log associate-*r/ associate-*l* prod-diff *-commutative
Counts
4 → 379
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
87.0ms
(* (* x y) (/ (/ z (sqrt (sqrt (- (* z z) (* t a))))) (sqrt (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series241.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* z z) (* t a))
79.0ms
(* (* x y) (/ (/ z (sqrt (sqrt (- (* z z) (* t a))))) (sqrt (sqrt (- (* z z) (* t a))))))
61.0ms
(sqrt (- (* z z) (* t a)))
67.0ms
(sqrt (- (* z z) (* t a)))

simplify79.0ms

Algorithm
egg-herbie
Counts
391 → 391
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
018715745
150025157

prune899.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
1.0b
(- (* z z) (* t a))
1.3b
(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
26.5b
(sqrt (- (* z z) (* t a)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
258×times-frac
143×add-sqr-sqrt
142×add-cube-cbrt *-un-lft-identity
71×associate-*r*
66×sqrt-prod
60×add-exp-log
30×add-cbrt-cube
22×associate-/r*
21×div-exp prod-exp
11×pow1
9×cbrt-undiv cbrt-unprod div-inv
6×rec-exp 1-exp add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-prod-down associate-/l*
2×flip3-- sqrt-div associate-/r/ flip--
1×sub-neg rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*r/ associate-*l* prod-diff clear-num un-div-inv *-commutative inv-pow
Counts
4 → 253
Calls
4 calls:
9.0ms
(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
3.0ms
(- (* z z) (* t a))
34.0ms
(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
10.0ms
(sqrt (- (* z z) (* t a)))

series218.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
31.0ms
(- (* z z) (* t a))
78.0ms
(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
60.0ms
(sqrt (- (* z z) (* t a)))

simplify47.0ms

Algorithm
egg-herbie
Counts
265 → 265
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09872740
150012395

prune564.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.9b

regimes403.0ms

Accuracy

82.6% (3.4b remaining)

Error of 6.5b against oracle of 3.1b and baseline of 22.4b

bsearch93.0ms

Steps
ItersRangePoint
10
1.0719743660571042e+57
1.1805727329510681e+69
1.0963182012451444e+69
4
-1.1648502447702071e+144
-6.937240094948613e+143
-1.1125528044552557e+144

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03218
15018
25018

end0.0ms

sample1.6s

Algorithm
intervals
Results
912.0ms8821×body80valid
293.0ms3083×body80nan