Details

Time bar (total: 3.9s)

sample17.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.9b

localize12.0ms

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))

rewrite26.0ms

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:
6.0ms
(+ (+ (* x x) (* y y)) (* z z))
4.0ms
(+ (* x x) (* y y))
9.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
6.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series274.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(+ (+ (* x x) (* y y)) (* z z))
29.0ms
(+ (* x x) (* y y))
48.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
163.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify41.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0325828
11345761
25001755

prune248.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.5b

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))
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)))

rewrite46.0ms

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:
20.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
12.0ms
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

series451.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
98.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
136.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
163.0ms
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

simplify53.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
03321540
114551341
250011274

prune296.0ms

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))) 1)) (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)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
152×sqrt-prod
122×add-sqr-sqrt
84×times-frac
55×*-un-lft-identity
47×add-cube-cbrt
25×associate-*r* associate-*l*
24×unswap-sqr
11×pow1
9×sqrt-div
6×add-exp-log add-cbrt-cube
5×rem-sqrt-square sqrt-pow1 pow1/2
4×add-log-exp
3×pow-prod-down div-inv
2×flip3-+ flip-+
1×frac-times sqrt-unprod associate-*r/ associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 156
Calls
4 calls:
7.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
28.0ms
(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
6.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series524.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
172.0ms
(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
101.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
104.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify67.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03912969
113182831
250022779

prune454.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 19.5b

localize3.0ms

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×pow-prod-down prod-exp *-commutative cbrt-unprod add-log-exp
Counts
1 → 22
Calls
1 calls:
5.0ms
(* x (sqrt 0.3333333333333333))

series43.0ms

Counts
1 → 3
Calls
1 calls:
43.0ms
(* x (sqrt 0.3333333333333333))

simplify60.0ms

Algorithm
egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
06984
124580
256978
389378
4200178
5500178

prune31.0ms

Pruning

13 alts after pruning (9 fresh and 4 done)

Merged error: 19.4b

regimes593.0ms

Accuracy

63.1% (7.2b remaining)

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

bsearch87.0ms

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

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02712
13312
23312

end0.0ms

sample433.0ms

Algorithm
intervals
Results
267.0ms8000×body80valid