Details

Time bar (total: 5.2s)

sample50.0ms

Algorithm
intervals
Results
28.0ms277×body80valid
7.0ms86×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.4b

localize10.0ms

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)))

rewrite25.0ms

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×sqrt-div
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 diff-log associate-*l* clear-num *-commutative div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
2.0ms
(- (* 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)))

series202.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
81.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
60.0ms
(sqrt (- (* z z) (* t a)))

simplify55.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0346584
11863515
25002510

prune219.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.9b

localize10.0ms

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)))

rewrite42.0ms

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×flip3-- associate-/r/ flip--
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 diff-log associate-*r/ associate-*l* clear-num *-commutative
Counts
4 → 112
Calls
4 calls:
8.0ms
(/ z (sqrt (- (* z z) (* t a))))
3.0ms
(- (* z z) (* t a))
21.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(/ z (sqrt (- (* z z) (* t a))))
36.0ms
(- (* z z) (* t a))
80.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
65.0ms
(sqrt (- (* z z) (* t a)))

simplify58.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
04311015
12166912
25002893

prune272.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.9b

localize12.0ms

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)))

rewrite127.0ms

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
3×pow-prod-down
2×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg diff-log associate-*r/ associate-*l* *-commutative
Counts
4 → 369
Calls
4 calls:
2.0ms
(- (* z z) (* t a))
84.0ms
(* (* x y) (/ (/ z (sqrt (sqrt (- (* z z) (* t a))))) (sqrt (sqrt (- (* z z) (* t a))))))
3.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series236.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* z z) (* t a))
81.0ms
(* (* x y) (/ (/ z (sqrt (sqrt (- (* z z) (* t a))))) (sqrt (sqrt (- (* z z) (* t a))))))
57.0ms
(sqrt (- (* z z) (* t a)))
64.0ms
(sqrt (- (* z z) (* t a)))

simplify83.0ms

Algorithm
egg-herbie
Counts
381 → 381
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
018515681
150015095

prune734.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.9b

localize14.0ms

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)))

rewrite58.0ms

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
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 diff-log associate-*r/ associate-*l* clear-num un-div-inv *-commutative inv-pow
Counts
4 → 243
Calls
4 calls:
9.0ms
(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
2.0ms
(- (* z z) (* t a))
30.0ms
(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
4.0ms
(sqrt (- (* z z) (* t a)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
32.0ms
(- (* z z) (* t a))
82.0ms
(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
60.0ms
(sqrt (- (* z z) (* t a)))

simplify48.0ms

Algorithm
egg-herbie
Counts
255 → 255
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09652684
150012341

prune529.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.9b

regimes410.0ms

Accuracy

82.6% (3.4b remaining)

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

bsearch89.0ms

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

sample1.5s

Algorithm
intervals
Results
837.0ms8821×body80valid
272.0ms3083×body80nan