Details

Time bar (total: 4.0s)

sample65.0ms

Algorithm
intervals
Results
19.0ms289×body80valid
10.0ms117×body80nan

simplify19.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
3.3b
(* (* x y) z)
9.0b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
20.4b
(sqrt (- (* z z) (* t a)))

rewrite91.0ms

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:
8.0ms
(- (* z z) (* t a))
17.0ms
(* (* x y) z)
48.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
17.0ms
(sqrt (- (* z z) (* t a)))

series221.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* z z) (* t a))
26.0ms
(* (* x y) z)
93.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify56.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0346584
11863515
25002510

prune217.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.2b
(- (* z z) (* t a))
3.1b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
20.4b
(sqrt (- (* z z) (* t a)))

rewrite77.0ms

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:
14.0ms
(/ z (sqrt (- (* z z) (* t a))))
10.0ms
(- (* z z) (* t a))
41.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
9.0ms
(sqrt (- (* z z) (* t a)))

series246.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ z (sqrt (- (* z z) (* t a))))
39.0ms
(- (* z z) (* t a))
93.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify63.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04311015
12166912
25002908

prune311.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
0.5b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
2.2b
(* y (/ z (sqrt (- (* z z) (* t a)))))
20.4b
(sqrt (- (* z z) (* t a)))

rewrite103.0ms

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:
8.0ms
(- (* z z) (* t a))
43.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
40.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
9.0ms
(sqrt (- (* z z) (* t a)))

series253.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(- (* z z) (* t a))
91.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
60.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
65.0ms
(sqrt (- (* z z) (* t a)))

simplify50.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0403776
11775676
25002667

prune232.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
0.5b
(* x (* (* y z) (/ 1 (sqrt (- (* z z) (* t a))))))
10.1b
(* (* y z) (/ 1 (sqrt (- (* z z) (* t a)))))
20.4b
(sqrt (- (* z z) (* t a)))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
58×add-exp-log
34×add-cbrt-cube
33×prod-exp
25×associate-*r*
20×add-sqr-sqrt
19×pow1 add-cube-cbrt *-un-lft-identity
18×times-frac
17×cbrt-unprod
12×sqrt-prod
9×pow-prod-down
8×div-exp
6×add-log-exp
4×cbrt-undiv rec-exp sqrt-div 1-exp associate-*r/ associate-*l*
3×flip3-- flip--
2×associate-/r/ un-div-inv *-commutative
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-inv
Counts
4 → 107
Calls
4 calls:
8.0ms
(- (* z z) (* t a))
76.0ms
(* x (* (* y z) (/ 1 (sqrt (- (* z z) (* t a))))))
45.0ms
(* (* y z) (/ 1 (sqrt (- (* z z) (* t a)))))
9.0ms
(sqrt (- (* z z) (* t a)))

series253.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* z z) (* t a))
93.0ms
(* x (* (* y z) (/ 1 (sqrt (- (* z z) (* t a))))))
63.0ms
(* (* y z) (/ 1 (sqrt (- (* z z) (* t a)))))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify67.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
0528962
12744778
25001752

prune230.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.9b

regimes283.0ms

Accuracy

80.5% (3.7b remaining)

Error of 6.9b against oracle of 3.2b and baseline of 21.9b

bsearch76.0ms

Steps
ItersRangePoint
6
4.4132260206004296e+125
3.970733553694869e+126
5.834852428696667e+125
10
-2.642425440707785e+96
-3.1738050367834455e+84
-1.203020892426847e+85

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03111
13211
23811
33811

end0.0ms

sample891.0ms

Algorithm
intervals
Results
319.0ms8858×body80valid
95.0ms3022×body80nan