Details

Time bar (total: 3.5s)

sample22.0ms

Algorithm
intervals
Results
8.0ms256×body80valid
4.0ms256×pre80true

simplify63.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0227
1487
21047
31967
43597
56867
613557
750017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) (* y y))
20.1b
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
8×associate-/l/
7×add-exp-log add-cbrt-cube
5×flip3-+ flip-+
4×add-sqr-sqrt frac-times add-cube-cbrt *-un-lft-identity add-log-exp
3×flip3-- times-frac associate-/r* flip--
2×pow1 cbrt-undiv associate-*r/ div-exp associate-*l/ associate-/r/
1×+-commutative frac-2neg prod-exp clear-num sum-log cbrt-unprod div-inv associate-/l*
Counts
2 → 42
Calls
2 calls:
3.0ms
(+ (* x x) (* y y))
12.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series92.0ms

Counts
2 → 6
Calls
2 calls:
27.0ms
(+ (* x x) (* y y))
65.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify43.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0308388
11848330
25001322

prune114.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y))))
19.5b
(sqrt (+ (* x x) (* y y)))
19.5b
(sqrt (+ (* x x) (* y y)))
20.1b
(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt sqrt-div
24×sqrt-prod
21×pow1
18×add-exp-log add-cbrt-cube
17×flip3-+ flip-+
14×add-cube-cbrt *-un-lft-identity
12×frac-times
10×sqrt-pow1 pow1/2
8×swap-sqr associate-/r/ associate-/l/
6×associate-*r/ associate-*r* associate-*l* associate-*l/
5×prod-exp pow-prod-up cbrt-unprod
4×cbrt-undiv div-exp add-log-exp unswap-sqr
3×flip3-- pow-prod-down pow-sqr flip--
2×rem-sqrt-square
1×pow2 frac-2neg times-frac pow-plus sqrt-unprod clear-num associate-/r* rem-square-sqrt *-commutative div-inv associate-/l*
Counts
4 → 124
Calls
4 calls:
19.0ms
(* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y))))
4.0ms
(sqrt (+ (* x x) (* y y)))
3.0ms
(sqrt (+ (* x x) (* y y)))
17.0ms
(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))))

series165.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y))))
38.0ms
(sqrt (+ (* x x) (* y y)))
35.0ms
(sqrt (+ (* x x) (* y y)))
65.0ms
(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))))

simplify79.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
04551205
128611021
25003971

prune268.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

19.5b
(sqrt (+ (* x x) (* y y)))
20.1b
(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))))
20.1b
(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))))
20.1b
(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
40×add-exp-log add-cbrt-cube
38×sqrt-div
28×flip3-+ flip-+
24×frac-times associate-/r/ associate-/l/
12×cbrt-undiv associate-*r/ div-exp associate-*l/ prod-exp cbrt-unprod
9×flip3-- flip--
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-log-exp
3×frac-2neg times-frac clear-num associate-/r* sqrt-prod div-inv associate-/l*
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 126
Calls
4 calls:
3.0ms
(sqrt (+ (* x x) (* y y)))
17.0ms
(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))))
19.0ms
(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))))
17.0ms
(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))))

series214.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(sqrt (+ (* x x) (* y y)))
60.0ms
(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))))
58.0ms
(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))))
62.0ms
(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))))

simplify64.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
03861720
118741414
250031315

prune470.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

19.5b
(sqrt (+ (* x x) (* y y)))
20.1b
(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))))
20.1b
(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))))
20.1b
(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (* (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))))))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
116×sqrt-div
49×add-exp-log flip3-+ add-cbrt-cube flip-+
48×frac-times
42×associate-/r/
24×associate-*r/ associate-/l/
18×associate-*l/
17×prod-exp cbrt-unprod
14×cbrt-undiv div-exp
9×flip3-- flip--
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-log-exp
3×frac-2neg times-frac clear-num associate-/r* sqrt-prod div-inv associate-/l*
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 148
Calls
4 calls:
3.0ms
(sqrt (+ (* x x) (* y y)))
17.0ms
(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))))
17.0ms
(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))))
54.0ms
(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (* (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))))))

series218.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(sqrt (+ (* x x) (* y y)))
61.0ms
(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))))
60.0ms
(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))))
63.0ms
(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (* (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))))))

simplify81.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
08232270
134261910
250011807

prune659.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.2b

regimes90.0ms

Accuracy

60% (8.1b remaining)

Error of 8.6b against oracle of 0.5b and baseline of 20.7b

bsearch66.0ms

Steps
ItersRangePoint
6
8.111081481717822e-173
5.113248843062357e-172
1.2651211010453041e-172
10
1.6811401674555953e-213
1.537004428687799e-199
1.5133568360584157e-199
7
-1.3360462147848363e-118
-4.283502333031557e-120
-1.316818702600376e-118

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0257
1257

end0.0ms

sample504.0ms

Algorithm
intervals
Results
257.0ms8000×body80valid
110.0ms8000×pre80true