Details

Time bar (total: 4.8s)

sample48.0ms

Algorithm
intervals
Results
24.0ms285×body80valid
7.0ms105×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: 22.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
3.9b
(* (* x y) z)
8.0b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
20.8b
(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:
2.0ms
(- (* 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)))

series197.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
80.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0346584
11863515
25002510

prune224.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.6b
(- (* z z) (* t a))
3.9b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
20.8b
(sqrt (- (* z z) (* t a)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
47×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
33×sqrt-prod
25×associate-/r*
18×add-exp-log add-cbrt-cube
7×cbrt-undiv div-exp associate-/l*
6×add-log-exp
5×pow1
4×sqrt-div div-inv
3×flip3-- flip--
2×frac-2neg prod-exp clear-num cbrt-unprod associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/r/
Counts
4 → 132
Calls
4 calls:
7.0ms
(/ (sqrt (- (* z z) (* t a))) z)
2.0ms
(- (* z z) (* t a))
9.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
4.0ms
(sqrt (- (* z z) (* t a)))

series239.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(/ (sqrt (- (* z z) (* t a))) z)
32.0ms
(- (* z z) (* t a))
79.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
59.0ms
(sqrt (- (* z z) (* t a)))

simplify61.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05191327
123801230
250011214

prune359.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
0.6b
(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
3.9b
(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
20.8b
(sqrt (- (* z z) (* t a)))

rewrite62.0ms

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:
2.0ms
(- (* z z) (* t a))
10.0ms
(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
33.0ms
(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
4.0ms
(sqrt (- (* z z) (* t a)))

series224.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* z z) (* t a))
45.0ms
(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
81.0ms
(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
64.0ms
(sqrt (- (* z z) (* t a)))

simplify46.0ms

Algorithm
egg-herbie
Counts
255 → 255
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09652684
150012341

prune513.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (/ (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))) z))
3.9b
(* (* x y) (/ 1 (/ (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))) z)))
20.8b
(sqrt (- (* z z) (* t a)))
20.8b
(sqrt (- (* z z) (* t a)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
99×add-exp-log
63×times-frac
45×add-cbrt-cube
39×prod-exp
38×add-sqr-sqrt
36×add-cube-cbrt *-un-lft-identity div-exp
26×associate-*r*
15×cbrt-undiv cbrt-unprod
12×pow1
9×rec-exp 1-exp div-inv
7×associate-/r*
6×sqrt-prod
4×sqrt-div add-log-exp
3×pow-prod-down associate-/l*
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-/r/ flip--
1×pow-flip frac-2neg associate-*r/ associate-*l* clear-num un-div-inv *-commutative inv-pow
Counts
4 → 153
Calls
4 calls:
21.0ms
(/ 1 (/ (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))) z))
69.0ms
(* (* x y) (/ 1 (/ (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))) z)))
3.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series251.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ 1 (/ (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))) z))
81.0ms
(* (* x y) (/ 1 (/ (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))) z)))
61.0ms
(sqrt (- (* z z) (* t a)))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify80.0ms

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
06602196
133871629
250011540

prune369.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.5b

regimes404.0ms

Accuracy

80.5% (3.7b remaining)

Error of 7.1b against oracle of 3.4b and baseline of 22.4b

bsearch175.0ms

Steps
ItersRangePoint
6
6.6223722196249e+100
8.029854166877476e+101
1.2636554807731635e+101
10
-2.550968469978379e-179
-2.0858349132470847e-190
-1.1528738359290673e-189
9
-2.9927016332090275e+150
-2.351439734919327e+144
-1.1613085318430635e+146

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03117
13217
23817
33817

end0.0ms

sample1.3s

Algorithm
intervals
Results
710.0ms8900×body80valid
218.0ms3015×body80nan