Details

Time bar (total: 4.9s)

sample19.0ms

Algorithm
intervals
Results
9.0ms256×body80valid

simplify18.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0167
1277
2337
3347
4347

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.9b

localize11.0ms

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)
37.0b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
19×times-frac
13×sqrt-prod
11×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u fma-def sum-log log1p-expm1-u
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 → 90
Calls
4 calls:
14.0ms
(+ (+ (* x x) (* y y)) (* z z))
3.0ms
(+ (* x x) (* y y))
36.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
16.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series354.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(+ (+ (* x x) (* y y)) (* z z))
33.0ms
(+ (* x x) (* y y))
65.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
204.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify51.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0345853
11445759
25001739

prune367.0ms

Filtered
102 candidates to 84 candidates (82.4%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.5b

localize14.0ms

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))
36.9b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.9b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
37.0b
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
41×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×expm1-log1p-u frac-times sqrt-pow1 associate-*l/ log1p-expm1-u add-log-exp
3×pow1/2
2×rem-sqrt-square associate-*r/ pow-prod-down prod-exp cbrt-unprod hypot-def
1×cbrt-undiv div-exp *-commutative div-inv
Counts
4 → 108
Calls
4 calls:
68.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
19.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
15.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
21.0ms
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

series533.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
129.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
131.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
205.0ms
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

simplify65.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
03441625
115051406
250011336

prune390.0ms

Filtered
120 candidates to 89 candidates (74.2%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 19.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
0.3b
(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
36.9b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.9b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
102×sqrt-prod
75×add-sqr-sqrt
44×times-frac
36×add-cube-cbrt *-un-lft-identity
25×associate-*r*
16×sqrt-div
12×unswap-sqr
11×pow1
9×associate-*l*
6×add-exp-log add-cbrt-cube
5×rem-sqrt-square sqrt-pow1 pow1/2
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u add-log-exp
3×pow-prod-down
2×frac-times associate-*l/ hypot-def div-inv
1×sqrt-unprod associate-*r/ prod-exp *-commutative cbrt-unprod
Counts
4 → 140
Calls
4 calls:
20.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
76.0ms
(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
19.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
16.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series666.0ms

Counts
4 → 12
Calls
4 calls:
196.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
216.0ms
(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
127.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
127.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify64.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
03562269
112372174
250022154

prune489.0ms

Filtered
152 candidates to 105 candidates (69.1%)
Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 19.5b

localize4.0ms

Local error

Found 1 expressions with local error:

0.2b
(* x (sqrt 0.3333333333333333))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×associate-*r*
4×add-cube-cbrt *-un-lft-identity sqrt-prod
3×pow1 add-exp-log associate-*l* add-cbrt-cube
2×unswap-sqr
1×expm1-log1p-u pow-prod-down prod-exp *-commutative cbrt-unprod log1p-expm1-u add-log-exp
Counts
1 → 24
Calls
1 calls:
5.0ms
(* x (sqrt 0.3333333333333333))

series49.0ms

Counts
1 → 3
Calls
1 calls:
49.0ms
(* x (sqrt 0.3333333333333333))

simplify72.0ms

Algorithm
egg-herbie
Counts
27 → 27
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
07190
124786
257184
389584
4201284
5500184

prune47.0ms

Filtered
27 candidates to 16 candidates (59.3%)
Pruning

14 alts after pruning (10 fresh and 4 done)

Merged error: 19.4b

regimes741.0ms

Accuracy

63.1% (7.2b remaining)

Error of 25.5b against oracle of 18.3b and baseline of 37.8b

bsearch110.0ms

Steps
ItersRangePoint
8
3.4079781488170856e+86
1.0026163978470942e+90
1.332425947371264e+89
11
-9.916277796985818e+165
-4.657848749767963e+130
-7.973789795621918e+148

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03020
13620
23620

end0.0ms

sample450.0ms

Algorithm
intervals
Results
273.0ms8000×body80valid