Details

Time bar (total: 6.3s)

sample18.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0167
1277
2337
3347
4347

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.5b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite114.0ms

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:
7.0ms
(+ (* x x) (* y y))
73.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
31.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series218.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* x x) (* y y))
44.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
147.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify131.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0310729
11303650
24811634
35001634

prune231.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.1b
(/ (+ (+ (* 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))))
35.5b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite239.0ms

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×expm1-log1p-u log1p-expm1-u 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 fma-def frac-2neg sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num sum-log *-commutative cbrt-unprod
Counts
4 → 164
Calls
4 calls:
8.0ms
(+ (* x x) (* y y))
75.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
117.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
31.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series767.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(+ (* x x) (* y y))
118.0ms
(/ (+ (+ (* 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))))
318.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify72.0ms

Algorithm
egg-herbie
Counts
176 → 176
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04832511
118692385
250012351

prune604.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 21.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
35.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.5b
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
49×sqrt-prod
38×add-sqr-sqrt
36×times-frac
34×add-cube-cbrt *-un-lft-identity
14×pow1
9×sqrt-div
8×sqrt-pow1
6×add-exp-log associate-/r* add-cbrt-cube associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square flip3-+ pow1/2 flip-+
2×hypot-def associate-/l/
1×cbrt-undiv pow2 frac-times sqrt-undiv frac-2neg pow-plus associate-*r/ div-exp pow-prod-down associate-*l/ clear-num pow-sqr pow-prod-up div-inv
Counts
4 → 122
Calls
4 calls:
49.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
33.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
32.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
47.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))

series602.0ms

Counts
4 → 12
Calls
4 calls:
208.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
92.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
93.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
208.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))

simplify105.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
02481565
17621485
237731460
350011460

prune379.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 21.0b

localize24.0ms

Local error

Found 4 expressions with local error:

20.8b
(sqrt (/ (* (cbrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (cbrt (* (cbrt 3.0) (cbrt 3.0)))))
36.5b
(cbrt (+ (+ (* x x) (* y y)) (* z z)))
36.5b
(cbrt (+ (+ (* x x) (* y y)) (* z z)))
36.5b
(cbrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
11×cbrt-prod add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
8×sqrt-prod
6×cbrt-div times-frac
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-sqrt-square flip3-+ pow1/3 flip-+
1×sqrt-pow1 pow1/2 sqrt-div div-inv
Counts
4 → 68
Calls
4 calls:
36.0ms
(sqrt (/ (* (cbrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (cbrt (* (cbrt 3.0) (cbrt 3.0)))))
18.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))
16.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))
17.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))

series856.0ms

Counts
4 → 12
Calls
4 calls:
549.0ms
(sqrt (/ (* (cbrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (cbrt (* (cbrt 3.0) (cbrt 3.0)))))
103.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))
102.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))
101.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))

simplify121.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 3 (110.0ms)

IterNodesCost
02651053
1956984
24065957
35001952

prune444.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 21.0b

regimes580.0ms

Accuracy

63% (7.4b remaining)

Error of 26.3b against oracle of 18.9b and baseline of 39.0b

bsearch48.0ms

Steps
ItersRangePoint
7
5.871846291072326e+137
4.7378067628763807e+139
9.333719392464218e+137
5
-1.3761719394239551e+125
-3.5384591291611475e+124
-3.9904763547485593e+124

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04020
15020
25320
35320

end0.0ms

sample480.0ms

Algorithm
intervals
Results
258.0ms8000×body80valid