Details

Time bar (total: 4.0s)

sample29.0ms

Algorithm
intervals
Results
11.0ms289×body80valid
3.0ms94×body80nan

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize16.0ms

Local error

Found 3 expressions with local error:

4.6b
(* (* x y) z)
8.0b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.6b
(sqrt (- (* z z) (* t a)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
17×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
6×times-frac prod-exp associate-/r* cbrt-unprod
4×sqrt-div
3×cbrt-undiv div-exp associate-*r* pow-prod-down add-log-exp
2×flip3-- associate-/r/ flip--
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*l* clear-num *-commutative div-inv associate-/l*
Counts
3 → 64
Calls
3 calls:
6.0ms
(* (* x y) z)
12.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series173.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(* (* x y) z)
80.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0327503
11810442
25001437

prune183.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.7b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
1.4b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
22.6b
(sqrt (- (* z z) (* t a)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
46×add-sqr-sqrt
45×add-cube-cbrt *-un-lft-identity
33×sqrt-prod
25×associate-/r*
17×add-exp-log add-cbrt-cube
7×cbrt-undiv div-exp associate-/l*
4×pow1 sqrt-div div-inv
3×add-log-exp
2×flip3-- frac-2neg prod-exp clear-num flip-- cbrt-unprod associate-/l/
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
Counts
3 → 120
Calls
3 calls:
7.0ms
(/ (sqrt (- (* z z) (* t a))) z)
9.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
4.0ms
(sqrt (- (* z z) (* t a)))

series210.0ms

Counts
3 → 9
Calls
3 calls:
67.0ms
(/ (sqrt (- (* z z) (* t a))) z)
81.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify64.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05001246
123201157
250011141

prune529.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))
1.4b
(/ (* x y) (/ (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))) z))
22.6b
(sqrt (- (* z z) (* t a)))
22.6b
(sqrt (- (* z z) (* t a)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
54×add-sqr-sqrt
34×sqrt-pow1
29×pow1
28×sqrt-div
27×add-exp-log add-cbrt-cube
22×add-cube-cbrt *-un-lft-identity
18×pow1/2
15×swap-sqr
13×times-frac
10×cbrt-undiv div-exp
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
8×flip3-- flip--
7×associate-/r*
6×prod-exp cbrt-unprod
5×pow-prod-down pow-sqr
4×frac-times add-log-exp
3×div-inv
2×rem-sqrt-square associate-*r/ associate-*l/
1×pow2 frac-2neg pow-plus sqrt-unprod clear-num rem-square-sqrt associate-/r/ *-commutative associate-/l*
Counts
4 → 151
Calls
4 calls:
28.0ms
(* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))
14.0ms
(/ (* x y) (/ (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))) z))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series270.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))
85.0ms
(/ (* x y) (/ (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))) z))
61.0ms
(sqrt (- (* z z) (* t a)))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify82.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
04821582
124901312
250011296

prune337.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (sqrt (- (* z z) (* t a))))
0.2b
(* (/ 1 (sqrt (- (* z z) (* t a)))) z)
1.3b
(* (* x y) (* (/ 1 (sqrt (- (* z z) (* t a)))) z))
22.6b
(sqrt (- (* z z) (* t a)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
52×add-exp-log
47×add-sqr-sqrt
40×times-frac
36×*-un-lft-identity
34×add-cube-cbrt
32×add-cbrt-cube
27×prod-exp
26×sqrt-prod
25×associate-*l*
21×pow1
15×cbrt-unprod
9×pow-prod-down
8×div-exp
6×sqrt-div associate-/r*
5×unswap-sqr
4×cbrt-undiv rec-exp 1-exp associate-*r* associate-/r/ add-log-exp
3×flip3-- pow-flip flip-- associate-/l*
2×sqrt-pow1 pow1/2 associate-*l/ *-commutative div-inv
1×rem-sqrt-square frac-2neg associate-*r/ clear-num inv-pow
Counts
4 → 141
Calls
4 calls:
7.0ms
(/ 1 (sqrt (- (* z z) (* t a))))
20.0ms
(* (/ 1 (sqrt (- (* z z) (* t a)))) z)
30.0ms
(* (* x y) (* (/ 1 (sqrt (- (* z z) (* t a)))) z))
4.0ms
(sqrt (- (* z z) (* t a)))

series239.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(/ 1 (sqrt (- (* z z) (* t a))))
45.0ms
(* (/ 1 (sqrt (- (* z z) (* t a)))) z)
79.0ms
(* (* x y) (* (/ 1 (sqrt (- (* z z) (* t a)))) z))
59.0ms
(sqrt (- (* z z) (* t a)))

simplify60.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
04721301
121811091
250021052

prune300.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.7b

regimes340.0ms

Accuracy

84.4% (3.1b remaining)

Error of 6.5b against oracle of 3.4b and baseline of 23.3b

bsearch94.0ms

Steps
ItersRangePoint
9
6.851992818311858e+130
4.847494362921101e+138
1.893724912731755e+137
9
-2.3467190644739184e+107
-3.2019781887028674e+101
-2.6550496665863674e+104

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03011
13611
23611

end0.0ms

sample798.0ms

Algorithm
intervals
Results
342.0ms8863×body80valid
114.0ms3074×body80nan