Details

Time bar (total: 4.2s)

sample46.0ms

Algorithm
intervals
Results
13.0ms286×body80valid
5.0ms109×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: 24.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
4.6b
(* (* x y) z)
9.3b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.2b
(sqrt (- (* z z) (* t a)))

rewrite70.0ms

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)
33.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
9.0ms
(sqrt (- (* z z) (* t a)))

series216.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* z z) (* t a))
25.0ms
(* (* x y) z)
91.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
64.0ms
(sqrt (- (* z z) (* t a)))

simplify56.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0346584
11863515
25002510

prune218.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.6b
(- (* z z) (* t a))
1.4b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
24.2b
(sqrt (- (* z z) (* t a)))

rewrite80.0ms

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))))
8.0ms
(- (* z z) (* t a))
45.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
9.0ms
(sqrt (- (* z z) (* t a)))

series246.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ z (sqrt (- (* z z) (* t a))))
34.0ms
(- (* z z) (* t a))
94.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify62.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04311015
12166912
25002893

prune288.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
0.6b
(- (* z z) (* t a))
1.4b
(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
24.2b
(sqrt (- (* z z) (* t a)))

rewrite107.0ms

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:
20.0ms
(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
8.0ms
(- (* z z) (* t a))
55.0ms
(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
9.0ms
(sqrt (- (* z z) (* t a)))

series246.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
35.0ms
(- (* z z) (* t a))
92.0ms
(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
68.0ms
(sqrt (- (* z z) (* t a)))

simplify51.0ms

Algorithm
egg-herbie
Counts
255 → 255
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09652685
150012341

prune523.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
1.4b
(* (* x y) (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
24.2b
(sqrt (- (* z z) (* t a)))
24.2b
(sqrt (- (* z z) (* t a)))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
28×sqrt-div
25×add-exp-log add-cbrt-cube
15×associate-*r*
11×pow1 prod-exp cbrt-unprod
10×add-sqr-sqrt
9×flip3-- flip--
8×add-cube-cbrt *-un-lft-identity associate-/r/
6×sqrt-prod add-log-exp
4×cbrt-undiv frac-times div-exp
3×times-frac associate-*r/ pow-prod-down
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/
1×sub-neg diff-log associate-*l* *-commutative div-inv
Counts
4 → 81
Calls
4 calls:
8.0ms
(- (* z z) (* t a))
115.0ms
(* (* x y) (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
9.0ms
(sqrt (- (* z z) (* t a)))
9.0ms
(sqrt (- (* z z) (* t a)))

series259.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(- (* z z) (* t a))
94.0ms
(* (* x y) (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
61.0ms
(sqrt (- (* z z) (* t a)))
65.0ms
(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0431935
11953723
25002717

prune266.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.1b

regimes299.0ms

Accuracy

86% (2.7b remaining)

Error of 6.3b against oracle of 3.6b and baseline of 23.2b

bsearch77.0ms

Steps
ItersRangePoint
8
5.629384986291813e+133
2.372085431100728e+138
8.769862591561265e+136
8
-1.1755015533027564e+157
-4.376466409121207e+153
-1.3250618426451895e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03112
14912
24912

end0.0ms

sample875.0ms

Algorithm
intervals
Results
303.0ms8844×body80valid
91.0ms3040×body80nan