Details

Time bar (total: 4.2s)

sample30.0ms

Algorithm
intervals
Results
10.0ms275×body80valid
3.0ms96×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
5.0b
(* (* x y) z)
10.8b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.1b
(sqrt (- (* z z) (* t a)))

rewrite23.0ms

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))
5.0ms
(* (* x y) z)
9.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
3.0ms
(sqrt (- (* z z) (* t a)))

series199.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* z z) (* t a))
27.0ms
(* (* x y) z)
81.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
57.0ms
(sqrt (- (* z z) (* t a)))

simplify51.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0346584
11863515
25002510

prune221.0ms

Filtered
88 candidates to 60 candidates (68.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.8b
(- (* z z) (* t a))
3.1b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
25.1b
(sqrt (- (* z z) (* t a)))

rewrite28.0ms

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))))
3.0ms
(- (* z z) (* t a))
11.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series224.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(/ z (sqrt (- (* z z) (* t a))))
32.0ms
(- (* z z) (* t a))
83.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
64.0ms
(sqrt (- (* z z) (* t a)))

simplify63.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04311015
12166912
25002893

prune295.0ms

Filtered
124 candidates to 83 candidates (66.9%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
2.2b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
2.3b
(* y (/ z (sqrt (- (* z z) (* t a)))))
25.1b
(sqrt (- (* z z) (* t a)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
25×associate-*r*
20×add-cube-cbrt *-un-lft-identity times-frac
18×add-exp-log add-cbrt-cube
13×sqrt-prod
12×pow1
7×prod-exp cbrt-unprod
6×associate-*l* add-log-exp
4×sqrt-div pow-prod-down
3×flip3-- associate-*r/ flip-- unswap-sqr
2×cbrt-undiv div-exp associate-/r/ *-commutative
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-inv
Counts
4 → 92
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
13.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
11.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series230.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* z z) (* t a))
81.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
59.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
57.0ms
(sqrt (- (* z z) (* t a)))

simplify49.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0403775
11781676
25001667

prune247.0ms

Filtered
104 candidates to 70 candidates (67.3%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
0.8b
(- (* z z) (* t a))
3.1b
(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
25.1b
(sqrt (- (* z z) (* t a)))

rewrite51.0ms

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))
7.0ms
(- (* z z) (* t a))
19.0ms
(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
4.0ms
(sqrt (- (* z z) (* t a)))

series419.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
232.0ms
(- (* z z) (* t a))
77.0ms
(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm
egg-herbie
Counts
255 → 255
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09652684
150012341

prune516.0ms

Filtered
255 candidates to 142 candidates (55.7%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

regimes361.0ms

Accuracy

82.3% (3.5b remaining)

Error of 6.9b against oracle of 3.4b and baseline of 23.0b

bsearch185.0ms

Steps
ItersRangePoint
10
3.0886519766275007e+106
5.320008399497423e+116
1.3932528023672181e+110
9
5.1450817042009143e-194
2.3248318113166536e-186
1.1968985287902123e-192
11
-1.9460222259464434e-224
-1.69044388403838e-245
-1.4763620082139605e-232
1
-3.2219348736708655e+167
-3.0290001935999287e+167
-3.077233863617663e+167

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04728
16728
26728

end0.0ms

sample878.0ms

Algorithm
intervals
Results
357.0ms8852×body80valid
119.0ms3042×body80nan