Details

Time bar (total: 5.9s)

sample31.0ms

Algorithm
intervals
Results
13.0ms256×body80valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0167
1277
2337
3347
4347

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
38.1b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite174.0ms

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:
8.0ms
(+ (* x x) (* y y))
33.0ms
(+ (+ (* x x) (* y y)) (* z z))
79.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
52.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series265.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(+ (* x x) (* y y))
33.0ms
(+ (+ (* x x) (* y y)) (* z z))
47.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
161.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify42.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0345852
11445759
25001739

prune296.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.2b

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))
38.0b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
38.0b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
38.1b
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

rewrite246.0ms

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:
134.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
31.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
43.0ms
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

series396.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
89.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
113.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
149.0ms
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

simplify50.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03441625
115051406
250011336

prune309.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 21.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
38.0b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
38.0b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
38.1b
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))

rewrite161.0ms

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)))
31.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
44.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))

series606.0ms

Counts
4 → 12
Calls
4 calls:
207.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
101.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
93.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
205.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))

simplify98.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
02481565
17621485
237731460
350011460

prune364.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 21.1b

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))
0.5b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
38.1b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite263.0ms

Algorithm
rewrite-expression-head
Rules
91×add-sqr-sqrt
75×times-frac sqrt-prod
54×*-un-lft-identity
50×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×expm1-log1p-u log1p-expm1-u div-inv
3×rem-sqrt-square fma-def 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 → 168
Calls
4 calls:
31.0ms
(+ (+ (* x x) (* y y)) (* z z))
73.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
118.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
34.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series820.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(+ (+ (* x x) (* y y)) (* z z))
121.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
327.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
330.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify64.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04462563
116322430
250012395

prune614.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 21.1b

regimes480.0ms

Accuracy

61.7% (7.4b remaining)

Error of 25.6b against oracle of 18.2b and baseline of 37.6b

bsearch95.0ms

Steps
ItersRangePoint
11
1.1681615625015325e+106
4.8176863792130405e+125
4.548512359051216e+125
10
-2.4246649145524328e+112
-4.737880563320688e+100
-1.6534868728770253e+103

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04128
15128
25428
35428

end0.0ms

sample482.0ms

Algorithm
intervals
Results
260.0ms8000×body80valid