Details

Time bar (total: 5.3s)

sample29.0ms

Algorithm
intervals
Results
19.0ms256×body80valid

simplify17.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0167
1277
2337
3347
4347

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
32.9b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×times-frac
18×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1
3×expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv +-commutative fma-def frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num sum-log
Counts
3 → 72
Calls
3 calls:
3.0ms
(+ (* x x) (* y y))
30.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
16.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series286.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(+ (* x x) (* y y))
62.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
193.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify163.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0310729
11303650
24811634
35001634

prune303.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.2b

localize13.0ms

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))
32.9b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
32.9b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
32.9b
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

rewrite124.0ms

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:
69.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
15.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
15.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
20.0ms
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

series518.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
130.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
122.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
199.0ms
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

simplify69.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
03441625
115051406
250011336

prune400.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.2b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (fma z z (fma x x (* y y))) (cbrt 3.0)))
0.2b
(/ (fma z z (fma x x (* y y))) (cbrt 3.0))
32.9b
(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (fma z z (fma x x (* y y))) (cbrt 3.0))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
51×times-frac
50×add-exp-log
36×*-un-lft-identity
33×add-cube-cbrt
24×cbrt-prod
22×associate-*r*
20×prod-exp
18×add-cbrt-cube
16×div-exp
9×unswap-sqr
8×pow1 cbrt-undiv cbrt-unprod
7×associate-*l*
6×associate-/r*
4×rec-exp 1-exp
3×expm1-log1p-u sqrt-div log1p-expm1-u div-inv associate-/l* add-log-exp
2×frac-times sqrt-pow1 associate-*r/ pow-prod-down associate-*l/
1×frac-2neg pow1/2 clear-num sqrt-prod *-commutative
Counts
3 → 129
Calls
3 calls:
39.0ms
(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (fma z z (fma x x (* y y))) (cbrt 3.0)))
3.0ms
(/ (fma z z (fma x x (* y y))) (cbrt 3.0))
24.0ms
(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (fma z z (fma x x (* y y))) (cbrt 3.0))))

series798.0ms

Counts
3 → 9
Calls
3 calls:
184.0ms
(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (fma z z (fma x x (* y y))) (cbrt 3.0)))
177.0ms
(/ (fma z z (fma x x (* y y))) (cbrt 3.0))
436.0ms
(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (fma z z (fma x x (* y y))) (cbrt 3.0))))

simplify83.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
05251621
124071424
250011326

prune441.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.7b

localize12.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.3333333333333333 (+ (pow x 2) (fma y y (pow z 2))))
33.0b
(sqrt (* 0.3333333333333333 (+ (pow x 2) (fma y y (pow z 2)))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1
6×add-sqr-sqrt *-un-lft-identity
4×add-exp-log add-cube-cbrt associate-*r/ associate-*r* add-cbrt-cube
3×associate-*l*
2×expm1-log1p-u sqrt-pow1 flip3-+ sqrt-div pow-prod-down flip-+ log1p-expm1-u add-log-exp
1×distribute-rgt-in distribute-lft-in pow1/2 prod-exp sqrt-prod *-commutative cbrt-unprod distribute-lft-out unswap-sqr
Counts
2 → 40
Calls
2 calls:
22.0ms
(* 0.3333333333333333 (+ (pow x 2) (fma y y (pow z 2))))
8.0ms
(sqrt (* 0.3333333333333333 (+ (pow x 2) (fma y y (pow z 2)))))

series264.0ms

Counts
2 → 6
Calls
2 calls:
66.0ms
(* 0.3333333333333333 (+ (pow x 2) (fma y y (pow z 2))))
198.0ms
(sqrt (* 0.3333333333333333 (+ (pow x 2) (fma y y (pow z 2)))))

simplify42.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0199318
1923285
25001280

prune145.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 6.7b

regimes412.0ms

Accuracy

35.1% (20.3b remaining)

Error of 27.1b against oracle of 6.8b and baseline of 38.1b

bsearch237.0ms

Steps
ItersRangePoint
9
1.2351546022638887e+92
1.9221479926683782e+97
4.982936361432774e+94
7
-6.362100326051983e-236
-5.664935514644947e-238
-4.8975385001868427e-237
10
-2.7268042180385974e-134
-1.660924772874808e-146
-1.6807596291604125e-146
11
-5.765687123026767e+152
-2.3106012996827125e+132
-1.674837201728853e+150

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05033
15633
25633

end0.0ms

sample768.0ms

Algorithm
intervals
Results
590.0ms8000×body80valid