Details

Time bar (total: 3.8s)

sample28.0ms

Algorithm
intervals
Results
10.0ms284×body80valid
3.0ms95×body80nan

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
6.7b
(* (* x y) z)
8.2b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
26.1b
(sqrt (- (* z z) (* t a)))

rewrite29.0ms

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:
3.0ms
(- (* z z) (* t a))
6.0ms
(* (* x y) z)
14.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series201.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* z z) (* t a))
29.0ms
(* (* x y) z)
84.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
57.0ms
(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0346584
11863515
25002510

prune233.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.4b
(- (* z z) (* t a))
3.5b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
26.1b
(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×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:
6.0ms
(/ z (sqrt (- (* z z) (* t a))))
2.0ms
(- (* z z) (* t a))
19.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series224.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ z (sqrt (- (* z z) (* t a))))
32.0ms
(- (* z z) (* t a))
83.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify66.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
04311015
12166912
25002893

prune299.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
3.5b
(* (* x y) (* (/ 1 (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
26.1b
(sqrt (- (* z z) (* t a)))
26.1b
(sqrt (- (* z z) (* t a)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
77×add-exp-log
45×add-cbrt-cube
43×prod-exp
23×cbrt-unprod
18×pow1
16×div-exp
8×cbrt-undiv add-sqr-sqrt pow-prod-down
6×add-cube-cbrt *-un-lft-identity sqrt-prod add-log-exp
4×rec-exp sqrt-div 1-exp associate-*r/
3×flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times sub-neg diff-log associate-*r* associate-*l* associate-*l/ *-commutative
Counts
4 → 87
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
59.0ms
(* (* x y) (* (/ 1 (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)))

series243.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* z z) (* t a))
84.0ms
(* (* x y) (* (/ 1 (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
64.0ms
(sqrt (- (* z z) (* t a)))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify60.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
04871261
12291929
25001739

prune258.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.7b

localize13.0ms

Local error

Found 4 expressions with local error:

3.0b
(/ (* x (* y (/ z (sqrt (sqrt (- (* z z) (* t a))))))) (sqrt (sqrt (- (* z z) (* t a)))))
3.9b
(* x (* y (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
26.1b
(sqrt (- (* z z) (* t a)))
26.1b
(sqrt (- (* z z) (* t a)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
27×add-exp-log add-cbrt-cube
24×sqrt-prod
15×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
11×pow1
10×prod-exp cbrt-unprod
9×times-frac associate-/r*
8×sqrt-div
6×cbrt-undiv div-exp
4×associate-*r/ add-log-exp
3×flip3-- associate-*l* pow-prod-down flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×frac-2neg associate-*r* clear-num *-commutative div-inv associate-/l/ associate-/l*
Counts
4 → 91
Calls
4 calls:
30.0ms
(/ (* x (* y (/ z (sqrt (sqrt (- (* z z) (* t a))))))) (sqrt (sqrt (- (* z z) (* t a)))))
24.0ms
(* x (* y (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series314.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(/ (* x (* y (/ z (sqrt (sqrt (- (* z z) (* t a))))))) (sqrt (sqrt (- (* z z) (* t a)))))
111.0ms
(* x (* y (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
62.0ms
(sqrt (- (* z z) (* t a)))
58.0ms
(sqrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04151228
119531002
25002986

prune283.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.7b

regimes345.0ms

Accuracy

79.8% (4.2b remaining)

Error of 7.6b against oracle of 3.4b and baseline of 24.0b

bsearch104.0ms

Steps
ItersRangePoint
8
1.415354163576236e+117
8.302175042271763e+120
1.507591943378104e+117
8
-335813708160.4535
-59376144.544019125
-329128518468.4069

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04025
15625
25625

end0.0ms

sample770.0ms

Algorithm
intervals
Results
329.0ms8874×body80valid
102.0ms2927×body80nan