Details

Time bar (total: 5.6s)

sample20.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0157
1227
2247
3247

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.0b
(+ (* x x) (* y y))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.4b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity times-frac
13×sqrt-prod
11×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1
4×sum-log
3×flip3-+ associate-/r* flip-+ associate-/l*
2×+-commutative rem-sqrt-square div-inv associate-/l/
1×cbrt-undiv associate-+l+ frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
4 → 78
Calls
4 calls:
14.0ms
(+ (+ (* x x) (* y y)) (* z z))
2.0ms
(+ (* x x) (* y y))
29.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
14.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series266.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(+ (+ (* x x) (* y y)) (* z z))
25.0ms
(+ (* x x) (* y y))
49.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
155.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify37.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0325828
11345761
25001755

prune232.0ms

Filtered
90 candidates to 71 candidates (78.9%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
35.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.4b
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
24×sqrt-prod
22×times-frac associate-*r*
21×add-cube-cbrt *-un-lft-identity
17×sqrt-div
11×pow1
9×add-exp-log add-cbrt-cube
6×flip3-+ associate-*l* flip-+ unswap-sqr
4×frac-times sqrt-pow1 associate-*l/ add-log-exp
3×pow1/2
2×rem-sqrt-square associate-*r/ pow-prod-down prod-exp cbrt-unprod
1×cbrt-undiv div-exp *-commutative div-inv
Counts
4 → 98
Calls
4 calls:
64.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
18.0ms
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

series399.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
99.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
94.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
157.0ms
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

simplify51.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
03321540
114551341
250011274

prune285.0ms

Filtered
110 candidates to 77 candidates (70.0%)
Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 18.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.2b
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
0.4b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
35.4b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
75×times-frac sqrt-prod
53×*-un-lft-identity
49×add-cube-cbrt
35×cbrt-prod
25×associate-*r*
16×unswap-sqr
10×associate-*l*
9×pow1
8×add-exp-log
7×add-cbrt-cube
6×associate-/r* add-log-exp
5×sqrt-div
4×div-inv
3×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-/l*
2×flip3-+ flip-+ associate-/l/
1×cbrt-undiv +-commutative frac-times frac-2neg sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num sum-log *-commutative cbrt-unprod
Counts
4 → 155
Calls
4 calls:
3.0ms
(+ (* x x) (* y y))
50.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
65.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
18.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series813.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (* x x) (* y y))
138.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
316.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
326.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify60.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04672452
117972356
250022337

prune554.0ms

Filtered
167 candidates to 131 candidates (78.4%)
Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 18.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ 1 (cbrt 3.0))))
0.5b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
1.0b
(/ 1 (cbrt 3.0))
35.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite221.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
45×sqrt-prod
43×times-frac
41×*-un-lft-identity
39×add-cube-cbrt
31×associate-*r*
29×sqrt-div
21×cbrt-prod
18×pow1
15×add-exp-log
12×add-cbrt-cube
11×frac-times associate-*l*
10×pow-prod-down
8×associate-*l/ unswap-sqr
7×flip3-+ associate-*r/ flip-+
6×sqrt-pow1 pow1/2 associate-/r*
4×prod-exp cbrt-unprod add-log-exp
3×sqrt-unprod div-inv associate-/l*
2×pow-flip div-exp *-commutative
1×cbrt-undiv rem-sqrt-square rec-exp frac-2neg pow1/3 1-exp clear-num inv-pow
Counts
4 → 156
Calls
4 calls:
141.0ms
(* (* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ 1 (cbrt 3.0))))
58.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
3.0ms
(/ 1 (cbrt 3.0))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series655.0ms

Counts
4 → 10
Calls
4 calls:
332.0ms
(* (* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ 1 (cbrt 3.0))))
226.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
0.0ms
(/ 1 (cbrt 3.0))
97.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify59.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
04962082
121501932
250011814

prune483.0ms

Filtered
166 candidates to 112 candidates (67.5%)
Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 18.5b

regimes571.0ms

Accuracy

62.3% (7.3b remaining)

Error of 25.6b against oracle of 18.3b and baseline of 37.7b

bsearch87.0ms

Steps
ItersRangePoint
10
3.94458661202886e+76
9.884633136253305e+89
1.3871413343689093e+89
9
-7.212657878859726e+147
-7.178555249598632e+141
-8.292015359329398e+144

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04328
14928
24928

end0.0ms

sample424.0ms

Algorithm
intervals
Results
265.0ms8000×body80valid