Details

Time bar (total: 4.5s)

sample44.0ms

Algorithm
intervals
Results
23.0ms285×body80valid
5.0ms79×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
4.5b
(* (* x y) z)
7.7b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.9b
(sqrt (- (* z z) (* t a)))

rewrite25.0ms

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))
6.0ms
(* (* x y) z)
11.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series198.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
83.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0346584
11863515
25002510

prune207.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.2b
(- (* z z) (* t a))
3.0b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
23.9b
(sqrt (- (* z z) (* t a)))

rewrite33.0ms

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))))
2.0ms
(- (* z z) (* t a))
18.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series224.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ z (sqrt (- (* z z) (* t a))))
33.0ms
(- (* z z) (* t a))
82.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
60.0ms
(sqrt (- (* z z) (* t a)))

simplify65.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
04311015
12166912
25002893

prune273.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.2b

localize23.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (* x y) (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))
23.9b
(sqrt (- (* z z) (* t a)))
23.9b
(sqrt (- (* z z) (* t a)))
23.9b
(sqrt (- (* z z) (* t a)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log
29×add-cbrt-cube
23×prod-exp cbrt-unprod
18×sqrt-div
13×associate-*r*
12×pow1 cbrt-div
11×add-sqr-sqrt
9×flip3-- sqrt-prod flip--
8×cbrt-undiv add-cube-cbrt *-un-lft-identity div-exp associate-/r/
4×frac-times add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down
2×associate-*l/
1×times-frac associate-*l* *-commutative div-inv
Counts
4 → 90
Calls
4 calls:
45.0ms
(* (* x y) (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series354.0ms

Counts
4 → 12
Calls
4 calls:
169.0ms
(* (* x y) (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))
60.0ms
(sqrt (- (* z z) (* t a)))
62.0ms
(sqrt (- (* z z) (* t a)))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify71.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
05031320
125701047
25001953

prune343.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 2.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
0.7b
(* y (/ z (sqrt (- (* z z) (* t a)))))
1.8b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
23.9b
(sqrt (- (* z z) (* t a)))

rewrite45.0ms

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:
2.0ms
(- (* z z) (* t a))
18.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
18.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))

series238.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* z z) (* t a))
51.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
91.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
60.0ms
(sqrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0403775
11781676
25001667

prune247.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 2.1b

regimes407.0ms

Accuracy

86.2% (2.6b remaining)

Error of 6.0b against oracle of 3.4b and baseline of 22.4b

bsearch112.0ms

Steps
ItersRangePoint
10
1.0894270704813426e+95
1.5741303840168087e+105
6.7193907563449e+103
7
-1.5931363873182533e+155
-1.016503209116054e+153
-8.778173507641342e+153

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03929
14429
25229
35229

end0.0ms

sample1.4s

Algorithm
intervals
Results
742.0ms8879×body80valid
231.0ms2979×body80nan