Details

Time bar (total: 5.3s)

sample29.0ms

Algorithm
intervals
Results
10.0ms281×body80valid
3.0ms95×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
4.0b
(* (* x y) z)
6.3b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.3b
(sqrt (- (* z z) (* t a)))

rewrite27.0ms

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

series201.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* z z) (* t a))
26.0ms
(* (* x y) z)
80.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify51.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0346584
11863515
25002510

prune215.0ms

Filtered
88 candidates to 60 candidates (68.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.7b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
63×sqrt-prod
48×add-sqr-sqrt times-frac
35×add-cube-cbrt *-un-lft-identity
33×associate-*r*
30×add-exp-log add-cbrt-cube
16×sqrt-div
15×associate-*l*
9×cbrt-undiv div-exp prod-exp associate-/r* cbrt-unprod
8×pow1
6×associate-/r/
5×flip3-- flip--
4×add-log-exp unswap-sqr
3×div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 141
Calls
4 calls:
8.0ms
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
48.0ms
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series300.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
86.0ms
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
61.0ms
(sqrt (- (* z z) (* t a)))
59.0ms
(sqrt (- (* z z) (* t a)))

simplify87.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
06291951
133621738
250011614

prune416.0ms

Filtered
153 candidates to 100 candidates (65.4%)
Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.6b

localize14.0ms

Local error

Found 4 expressions with local error:

2.9b
(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
7.9b
(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
23.0b
(cbrt (- (* z z) (* t a)))
23.0b
(cbrt (- (* z z) (* t a)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
189×times-frac
147×add-sqr-sqrt
102×add-cube-cbrt *-un-lft-identity
44×associate-*l*
33×associate-*r*
30×add-exp-log add-cbrt-cube
24×sqrt-prod
18×cbrt-prod
13×associate-/r*
12×cbrt-undiv div-exp unswap-sqr
10×div-inv
6×pow1 cbrt-div prod-exp cbrt-unprod
4×associate-/r/ add-log-exp
3×flip3-- flip-- associate-/l*
2×pow1/3 sqrt-div
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 209
Calls
4 calls:
5.0ms
(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
54.0ms
(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
2.0ms
(cbrt (- (* z z) (* t a)))
2.0ms
(cbrt (- (* z z) (* t a)))

series526.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
300.0ms
(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
82.0ms
(cbrt (- (* z z) (* t a)))
84.0ms
(cbrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm
egg-herbie
Counts
221 → 221
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010813457
150013199

prune776.0ms

Filtered
221 candidates to 182 candidates (82.4%)
Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 3.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b
(* y (/ z (sqrt (cbrt (- (* z z) (* t a))))))
10.3b
(* (/ x (fabs (cbrt (- (* z z) (* t a))))) (* y (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
23.0b
(cbrt (- (* z z) (* t a)))
23.0b
(cbrt (- (* z z) (* t a)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
39×times-frac
34×associate-*r*
33×add-cube-cbrt *-un-lft-identity
30×add-exp-log add-cbrt-cube
20×sqrt-prod
16×cbrt-prod associate-*l*
12×prod-exp cbrt-unprod
11×pow1
6×cbrt-undiv cbrt-div div-exp
4×associate-*r/ pow-prod-down add-log-exp unswap-sqr
3×flip3-- flip--
2×pow1/3 sqrt-div associate-/r/ *-commutative div-inv
1×frac-times associate-*l/
Counts
4 → 119
Calls
4 calls:
23.0ms
(* y (/ z (sqrt (cbrt (- (* z z) (* t a))))))
27.0ms
(* (/ x (fabs (cbrt (- (* z z) (* t a))))) (* y (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
2.0ms
(cbrt (- (* z z) (* t a)))
2.0ms
(cbrt (- (* z z) (* t a)))

series576.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(* y (/ z (sqrt (cbrt (- (* z z) (* t a))))))
327.0ms
(* (/ x (fabs (cbrt (- (* z z) (* t a))))) (* y (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
81.0ms
(cbrt (- (* z z) (* t a)))
81.0ms
(cbrt (- (* z z) (* t a)))

simplify73.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06471582
129761336
250011326

prune411.0ms

Filtered
131 candidates to 101 candidates (77.1%)
Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 3.6b

regimes371.0ms

Accuracy

82.6% (3.5b remaining)

Error of 6.7b against oracle of 3.2b and baseline of 23.5b

bsearch78.0ms

Steps
ItersRangePoint
8
4.443829456592018e+130
1.6495000632116558e+134
5.7646822522115484e+131
6
-8.786369008283137e+83
-9.386334716635728e+82
-1.1707719178549918e+83

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02717
13317
23317

end0.0ms

sample781.0ms

Algorithm
intervals
Results
333.0ms8820×body80valid
101.0ms3009×body80nan