Details

Time bar (total: 5.9s)

sample19.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0157
1227
2247
3247

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.3b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
34.5b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite143.0ms

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:
8.0ms
(+ (* x x) (* y y))
30.0ms
(+ (+ (* x x) (* y y)) (* z z))
74.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
29.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series263.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(+ (* x x) (* y y))
38.0ms
(+ (+ (* x x) (* y y)) (* z z))
46.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
155.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify38.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0325828
11345761
25001755

prune242.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 19.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
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))))
34.8b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite256.0ms

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 add-log-exp
8×add-exp-log
7×add-cbrt-cube
6×associate-/r*
5×sqrt-div
4×div-inv
3×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down sum-log associate-/l*
2×flip3-+ flip-+ associate-/l/
1×cbrt-undiv +-commutative frac-times associate-+l+ frac-2neg sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num *-commutative cbrt-unprod
Counts
4 → 157
Calls
4 calls:
28.0ms
(+ (+ (* x x) (* y y)) (* z z))
73.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
114.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
33.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series776.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (+ (* x x) (* y y)) (* z z))
115.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
306.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
321.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify61.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04332503
115792407
250012388

prune534.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 19.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 (cbrt 3.0))))
0.4b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 (cbrt 3.0)))))
1.0b
(/ 1 (cbrt 3.0))
34.7b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite267.0ms

Algorithm
rewrite-expression-head
Rules
68×add-sqr-sqrt
51×sqrt-prod
47×times-frac
43×*-un-lft-identity
39×add-cube-cbrt
29×sqrt-div
26×associate-*r*
25×cbrt-prod
18×pow1
16×associate-*l*
15×add-exp-log
12×add-cbrt-cube unswap-sqr
11×frac-times
10×pow-prod-down
8×associate-*r/
7×flip3-+ associate-*l/ 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 → 160
Calls
4 calls:
83.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 (cbrt 3.0))))
141.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 (cbrt 3.0)))))
6.0ms
(/ 1 (cbrt 3.0))
31.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series738.0ms

Counts
4 → 10
Calls
4 calls:
333.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 (cbrt 3.0))))
312.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 (cbrt 3.0)))))
0.0ms
(/ 1 (cbrt 3.0))
92.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify56.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04592025
116441869
250011762

prune484.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 19.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b
(* x (sqrt (/ 1 (cbrt 3.0))))
0.5b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (* x (sqrt (/ 1 (cbrt 3.0)))))
1.0b
(/ 1 (cbrt 3.0))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
43×times-frac
38×*-un-lft-identity
36×add-cube-cbrt
34×sqrt-prod
26×associate-*r*
23×cbrt-prod
14×add-exp-log
13×associate-*l*
11×pow1 add-cbrt-cube
6×associate-/r* unswap-sqr
5×sqrt-div
4×associate-*r/ pow-prod-down prod-exp cbrt-unprod
3×div-inv associate-/l* add-log-exp
2×pow-flip div-exp *-commutative
1×cbrt-undiv frac-times rec-exp frac-2neg pow1/3 1-exp associate-*l/ clear-num inv-pow
Counts
3 → 118
Calls
3 calls:
22.0ms
(* x (sqrt (/ 1 (cbrt 3.0))))
80.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (* x (sqrt (/ 1 (cbrt 3.0)))))
6.0ms
(/ 1 (cbrt 3.0))

series247.0ms

Counts
3 → 7
Calls
3 calls:
105.0ms
(* x (sqrt (/ 1 (cbrt 3.0))))
142.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (* x (sqrt (/ 1 (cbrt 3.0)))))
0.0ms
(/ 1 (cbrt 3.0))

simplify94.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0306845
11112740
24940652
35002652

prune239.0ms

Pruning

15 alts after pruning (11 fresh and 4 done)

Merged error: 19.2b

regimes707.0ms

Accuracy

60.2% (7.7b remaining)

Error of 25.9b against oracle of 18.2b and baseline of 37.6b

bsearch80.0ms

Steps
ItersRangePoint
8
2.277912944090519e+87
3.551748340418938e+90
3.509581298916955e+90
10
-2.2536194562167577e+79
-3.066737593147216e+67
-2.225117955444305e+79

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03828
14828
25228
35228

end0.0ms

sample488.0ms

Algorithm
intervals
Results
253.0ms8000×body80valid