Details

Time bar (total: 5.8s)

sample31.0ms

Algorithm
intervals
Results
21.0ms256×body80valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0167
1277
2337
3347
4347

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.3b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.4b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite65.0ms

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:
3.0ms
(+ (* x x) (* y y))
13.0ms
(+ (+ (* x x) (* y y)) (* z z))
29.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
15.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series302.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (* x x) (* y y))
40.0ms
(+ (+ (* x x) (* y y)) (* z z))
57.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
173.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify47.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0345852
11445759
25001739

prune335.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.6b

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (- (fma x x (fma y y (* z z)))) (- 3.0))
35.4b
(sqrt (/ (- (fma x x (fma y y (* z z)))) (- 3.0)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
201×times-frac
132×add-sqr-sqrt
129×add-cube-cbrt *-un-lft-identity
126×distribute-lft-neg-in distribute-rgt-neg-in
104×sqrt-prod
42×neg-mul-1
10×associate-/r* associate-/l*
4×add-exp-log add-cbrt-cube
3×pow1
2×expm1-log1p-u rem-sqrt-square log1p-expm1-u div-inv add-log-exp
1×cbrt-undiv neg-sub0 frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub distribute-frac-neg div-exp clear-num
Counts
2 → 254
Calls
2 calls:
7.0ms
(/ (- (fma x x (fma y y (* z z)))) (- 3.0))
14.0ms
(sqrt (/ (- (fma x x (fma y y (* z z)))) (- 3.0)))

series259.0ms

Counts
2 → 6
Calls
2 calls:
64.0ms
(/ (- (fma x x (fma y y (* z z)))) (- 3.0))
195.0ms
(sqrt (/ (- (fma x x (fma y y (* z z)))) (- 3.0)))

simplify81.0ms

Algorithm
egg-herbie
Counts
260 → 260
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
05783324
117173230
250013111

prune669.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (fma x x (fma y y (* z z)))) (/ (sqrt (fma x x (fma y y (* z z)))) 3.0))
35.4b
(sqrt (* (sqrt (fma x x (fma y y (* z z)))) (/ (sqrt (fma x x (fma y y (* z z)))) 3.0)))
35.6b
(sqrt (fma x x (fma y y (* z z))))
35.6b
(sqrt (fma x x (fma y y (* z z))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
24×sqrt-prod
22×times-frac associate-*r*
21×add-cube-cbrt *-un-lft-identity
11×pow1
9×add-exp-log add-cbrt-cube
6×associate-*l* unswap-sqr
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp
3×pow1/2
2×rem-sqrt-square associate-*r/ pow-prod-down prod-exp cbrt-unprod
1×cbrt-undiv sqrt-div div-exp *-commutative div-inv
Counts
4 → 94
Calls
4 calls:
13.0ms
(* (sqrt (fma x x (fma y y (* z z)))) (/ (sqrt (fma x x (fma y y (* z z)))) 3.0))
5.0ms
(sqrt (* (sqrt (fma x x (fma y y (* z z)))) (/ (sqrt (fma x x (fma y y (* z z)))) 3.0)))
1.0ms
(sqrt (fma x x (fma y y (* z z))))
1.0ms
(sqrt (fma x x (fma y y (* z z))))

series497.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* (sqrt (fma x x (fma y y (* z z)))) (/ (sqrt (fma x x (fma y y (* z z)))) 3.0))
189.0ms
(sqrt (* (sqrt (fma x x (fma y y (* z z)))) (/ (sqrt (fma x x (fma y y (* z z)))) 3.0)))
119.0ms
(sqrt (fma x x (fma y y (* z z))))
122.0ms
(sqrt (fma x x (fma y y (* z z))))

simplify49.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0262977
11114827
25001778

prune311.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 18.6b

localize14.0ms

Local error

Found 3 expressions with local error:

0.4b
(/ (fma x x (fma y y (* z z))) (cbrt 3.0))
0.4b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (fma x x (fma y y (* z z))) (cbrt 3.0))))
35.4b
(sqrt (/ (fma x x (fma y y (* z z))) (cbrt 3.0)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
89×add-sqr-sqrt
75×times-frac sqrt-prod
52×*-un-lft-identity
48×add-cube-cbrt
35×cbrt-prod
25×associate-*r*
16×unswap-sqr
10×associate-*l*
8×pow1
7×add-exp-log
6×associate-/r* add-cbrt-cube
5×sqrt-div
4×div-inv
3×expm1-log1p-u rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down log1p-expm1-u associate-/l* add-log-exp
1×cbrt-undiv frac-times frac-2neg sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num *-commutative cbrt-unprod
Counts
3 → 148
Calls
3 calls:
3.0ms
(/ (fma x x (fma y y (* z z))) (cbrt 3.0))
42.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (fma x x (fma y y (* z z))) (cbrt 3.0))))
4.0ms
(sqrt (/ (fma x x (fma y y (* z z))) (cbrt 3.0)))

series946.0ms

Counts
3 → 9
Calls
3 calls:
160.0ms
(/ (fma x x (fma y y (* z z))) (cbrt 3.0))
386.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (fma x x (fma y y (* z z))) (cbrt 3.0))))
400.0ms
(sqrt (/ (fma x x (fma y y (* z z))) (cbrt 3.0)))

simplify146.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 3 (127.0ms)

IterNodesCost
03362008
110031940
247631915
350021909

prune590.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 18.5b

regimes235.0ms

Accuracy

62.9% (7.3b remaining)

Error of 25.0b against oracle of 17.7b and baseline of 37.5b

bsearch89.0ms

Steps
ItersRangePoint
10
1.7826190976464906e+97
7.552700620960131e+107
1.3566371815103393e+105
5
-1.7575017886047935e+118
-4.9561533689906815e+117
-1.6174687293654252e+118

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04020
15020
25320
35320

end0.0ms

sample998.0ms

Algorithm
intervals
Results
815.0ms8000×body80valid