Details

Time bar (total: 4.1s)

sample30.0ms

Algorithm
intervals
Results
9.0ms278×body80valid
3.0ms90×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: 24.9b

localize10.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* z z) (* t a))
5.4b
(* (* x y) z)
8.9b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.3b
(sqrt (- (* z z) (* t a)))

rewrite64.0ms

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:
7.0ms
(- (* z z) (* t a))
16.0ms
(* (* x y) z)
30.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
8.0ms
(sqrt (- (* z z) (* t a)))

series180.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(- (* z z) (* t a))
20.0ms
(* (* x y) z)
76.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
54.0ms
(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0346584
11863515
25002510

prune205.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
1.2b
(- (* z z) (* t a))
3.2b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
22.3b
(sqrt (- (* z z) (* t a)))

rewrite73.0ms

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:
13.0ms
(/ z (sqrt (- (* z z) (* t a))))
7.0ms
(- (* z z) (* t a))
41.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
8.0ms
(sqrt (- (* z z) (* t a)))

series199.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(/ z (sqrt (- (* z z) (* t a))))
32.0ms
(- (* z z) (* t a))
72.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
55.0ms
(sqrt (- (* z z) (* t a)))

simplify60.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04311015
12166912
25002893

prune316.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.8b

localize10.0ms

Local error

Found 4 expressions with local error:

1.2b
(* y (/ z (sqrt (- (* z z) (* t a)))))
1.2b
(- (* z z) (* t a))
2.2b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
22.3b
(sqrt (- (* z z) (* t a)))

rewrite102.0ms

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:
37.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
7.0ms
(- (* z z) (* t a))
44.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
8.0ms
(sqrt (- (* z z) (* t a)))

series214.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
29.0ms
(- (* z z) (* t a))
79.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
53.0ms
(sqrt (- (* z z) (* t a)))

simplify51.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0403775
11781676
25001667

prune224.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.8b

localize19.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* z z) (* t a))
3.2b
(* (* x y) (* (/ 1 (* (fabs (cbrt (- (* z z) (* t a)))) 1)) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
23.1b
(cbrt (- (* z z) (* t a)))
23.1b
(cbrt (- (* z z) (* t a)))

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
193×add-exp-log
127×prod-exp
69×add-cbrt-cube
44×div-exp
37×cbrt-unprod
24×1-exp
16×pow1
14×cbrt-undiv
12×rec-exp
8×pow-prod-down
6×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-log-exp
4×cbrt-div associate-*r/
3×flip3-- flip--
2×pow1/3
1×frac-times sub-neg diff-log associate-*r* associate-*l* associate-*l/ *-commutative
Counts
4 → 111
Calls
4 calls:
11.0ms
(- (* z z) (* t a))
135.0ms
(* (* x y) (* (/ 1 (* (fabs (cbrt (- (* z z) (* t a)))) 1)) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
5.0ms
(cbrt (- (* z z) (* t a)))
6.0ms
(cbrt (- (* z z) (* t a)))

series388.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(- (* z z) (* t a))
203.0ms
(* (* x y) (* (/ 1 (* (fabs (cbrt (- (* z z) (* t a)))) 1)) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
77.0ms
(cbrt (- (* z z) (* t a)))
80.0ms
(cbrt (- (* z z) (* t a)))

simplify69.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
08061975
129881463
250011457

prune274.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 2.8b

regimes431.0ms

Accuracy

85.1% (2.9b remaining)

Error of 6.3b against oracle of 3.3b and baseline of 23.1b

bsearch76.0ms

Steps
ItersRangePoint
9
3.0311955630322647e+63
3.022532828458784e+71
1.5571214549086307e+71
10
-4.429048610702511e+99
-1.948993049043845e+84
-4.129387480874186e+99

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02910
13010
23310
33310

end0.0ms

sample868.0ms

Algorithm
intervals
Results
300.0ms8837×body80valid
93.0ms3018×body80nan