Details

Time bar (total: 3.8s)

sample34.0ms

Algorithm
intervals
Results
12.0ms286×body80valid
5.0ms111×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
4.2b
(* (* x y) z)
8.7b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.1b
(sqrt (- (* z z) (* t a)))

rewrite24.0ms

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)
10.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series209.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* z z) (* t a))
24.0ms
(* (* x y) z)
85.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0346584
11863515
25002510

prune233.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.2b
(- (* z z) (* t a))
3.9b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
23.1b
(sqrt (- (* z z) (* t a)))

rewrite31.0ms

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))))
4.0ms
(- (* z z) (* t a))
13.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series236.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ z (sqrt (- (* z z) (* t a))))
34.0ms
(- (* z z) (* t a))
85.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
64.0ms
(sqrt (- (* z z) (* t a)))

simplify65.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
04311015
12166912
25002893

prune314.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
1.2b
(* y (/ z (sqrt (- (* z z) (* t a)))))
2.4b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
23.1b
(sqrt (- (* z z) (* t a)))

rewrite33.0ms

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:
4.0ms
(- (* z z) (* t a))
12.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
11.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))

series242.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* z z) (* t a))
55.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
87.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
64.0ms
(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0403775
11781676
25001667

prune256.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

localize17.0ms

Local error

Found 4 expressions with local error:

1.2b
(* y (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
2.4b
(* x (* y (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))))
23.1b
(sqrt (- (* z z) (* t a)))
23.1b
(sqrt (- (* z z) (* t a)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
28×sqrt-div
27×add-exp-log add-cbrt-cube
16×add-sqr-sqrt associate-*r*
13×pow1
12×prod-exp cbrt-unprod
10×add-cube-cbrt *-un-lft-identity
8×flip3-- associate-/r/ flip--
6×associate-*l* sqrt-prod
5×associate-*r/
4×cbrt-undiv frac-times times-frac div-exp pow-prod-down add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ *-commutative unswap-sqr
1×div-inv
Counts
4 → 89
Calls
4 calls:
19.0ms
(* y (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
19.0ms
(* x (* y (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series268.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* y (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
84.0ms
(* x (* y (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))))
60.0ms
(sqrt (- (* z z) (* t a)))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify49.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04131119
11692857
25001830

prune297.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.2b

regimes350.0ms

Accuracy

81% (3.7b remaining)

Error of 7.2b against oracle of 3.5b and baseline of 22.8b

bsearch97.0ms

Steps
ItersRangePoint
6
6.533440019736163e+126
9.198944834822479e+127
8.001380975877731e+126
10
-1.5217146184155857e+89
-7.696003816443151e+76
-1.1055887578016406e+87

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03222
13822
23822

end0.0ms

sample885.0ms

Algorithm
intervals
Results
400.0ms8853×body80valid
125.0ms3007×body80nan