Details

Time bar (total: 4.2s)

sample14.0ms

Algorithm
intervals
Results
6.0ms353×body80valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0143
1233
2303
3313
4313

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.3b

localize4.0ms

Local error

Found 1 expressions with local error:

4.0b
(* x (+ 1.0 (* y y)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt
3×pow1 add-exp-log add-cube-cbrt *-un-lft-identity associate-*r* associate-*l* add-cbrt-cube
2×associate-*r/
1×distribute-rgt-in expm1-log1p-u distribute-lft-in flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ log1p-expm1-u add-log-exp unswap-sqr
Counts
1 → 24
Calls
1 calls:
7.0ms
(* x (+ 1.0 (* y y)))

series58.0ms

Counts
1 → 3
Calls
1 calls:
58.0ms
(* x (+ 1.0 (* y y)))

simplify85.0ms

Algorithm
egg-herbie
Counts
27 → 27
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0148123
1742103
23453100
35001100

prune58.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.2b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(* x (sqrt (+ 1.0 (* y y))))
0.1b
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
4.0b
(sqrt (+ 1.0 (* y y)))
4.0b
(sqrt (+ 1.0 (* y y)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×sqrt-div
13×pow1 sqrt-prod
12×associate-*r*
11×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
10×associate-*r/
9×flip3-+ flip-+
4×expm1-log1p-u frac-times associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ *-commutative hypot-def unswap-sqr
Counts
4 → 93
Calls
4 calls:
9.0ms
(* x (sqrt (+ 1.0 (* y y))))
20.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
3.0ms
(sqrt (+ 1.0 (* y y)))
3.0ms
(sqrt (+ 1.0 (* y y)))

series218.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* x (sqrt (+ 1.0 (* y y))))
54.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
50.0ms
(sqrt (+ 1.0 (* y y)))
50.0ms
(sqrt (+ 1.0 (* y y)))

simplify46.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0318722
11367620
25002595

prune263.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 4.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (fabs (cbrt (+ 1.0 (* y y)))) x)
0.1b
(* (* (* (fabs (cbrt (+ 1.0 (* y y)))) x) (hypot (sqrt 1.0) y)) (sqrt (cbrt (+ 1.0 (* y y)))))
4.2b
(cbrt (+ 1.0 (* y y)))
4.2b
(cbrt (+ 1.0 (* y y)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log add-cbrt-cube
13×add-sqr-sqrt
12×associate-*r*
11×add-cube-cbrt *-un-lft-identity
9×cbrt-prod
7×pow-prod-down prod-exp cbrt-unprod
6×cbrt-div sqrt-prod
4×expm1-log1p-u associate-*l* log1p-expm1-u add-log-exp
3×flip3-+ flip-+
2×pow1/3 sqrt-div associate-*r/ *-commutative
1×unswap-sqr
Counts
4 → 81
Calls
4 calls:
3.0ms
(* (fabs (cbrt (+ 1.0 (* y y)))) x)
31.0ms
(* (* (* (fabs (cbrt (+ 1.0 (* y y)))) x) (hypot (sqrt 1.0) y)) (sqrt (cbrt (+ 1.0 (* y y)))))
2.0ms
(cbrt (+ 1.0 (* y y)))
2.0ms
(cbrt (+ 1.0 (* y y)))

series946.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (fabs (cbrt (+ 1.0 (* y y)))) x)
568.0ms
(* (* (* (fabs (cbrt (+ 1.0 (* y y)))) x) (hypot (sqrt 1.0) y)) (sqrt (cbrt (+ 1.0 (* y y)))))
180.0ms
(cbrt (+ 1.0 (* y y)))
177.0ms
(cbrt (+ 1.0 (* y y)))

simplify88.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
06331119
12996973
25001956

prune374.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 4.2b

localize18.0ms

Local error

Found 4 expressions with local error:

3.4b
(- (* (* y y) (* y y)) (* 1.0 (* y y)))
4.0b
(sqrt (+ 1.0 (* y y)))
4.4b
(sqrt (+ (* 1.0 1.0) (- (* (* y y) (* y y)) (* 1.0 (* y y)))))
5.9b
(/ (* x (hypot (pow y 3) (pow 1.0 3/2))) (sqrt (+ (* 1.0 1.0) (- (* (* y y) (* y y)) (* 1.0 (* y y))))))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×sqrt-prod
10×add-cube-cbrt *-un-lft-identity
9×add-exp-log add-cbrt-cube
6×pow1 times-frac sqrt-div associate-/r* add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×flip3-+ flip-+
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-/r/ hypot-def
1×sub-neg flip3-- distribute-rgt-out-- frac-2neg fma-neg diff-log prod-diff prod-exp clear-num flip-- cbrt-unprod div-inv associate-/l*
Counts
4 → 84
Calls
4 calls:
14.0ms
(- (* (* y y) (* y y)) (* 1.0 (* y y)))
3.0ms
(sqrt (+ 1.0 (* y y)))
83.0ms
(sqrt (+ (* 1.0 1.0) (- (* (* y y) (* y y)) (* 1.0 (* y y)))))
77.0ms
(/ (* x (hypot (pow y 3) (pow 1.0 3/2))) (sqrt (+ (* 1.0 1.0) (- (* (* y y) (* y y)) (* 1.0 (* y y))))))

series827.0ms

Counts
4 → 12
Calls
4 calls:
287.0ms
(- (* (* y y) (* y y)) (* 1.0 (* y y)))
43.0ms
(sqrt (+ 1.0 (* y y)))
85.0ms
(sqrt (+ (* 1.0 1.0) (- (* (* y y) (* y y)) (* 1.0 (* y y)))))
412.0ms
(/ (* x (hypot (pow y 3) (pow 1.0 3/2))) (sqrt (+ (* 1.0 1.0) (- (* (* y y) (* y y)) (* 1.0 (* y y))))))

simplify70.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
04631114
11950999
25002987

prune381.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 4.2b

regimes99.0ms

Accuracy

0% (0.2b remaining)

Error of 5.0b against oracle of 4.8b and baseline of 5.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
083
183

end0.0ms

sample348.0ms

Algorithm
intervals
Results
192.0ms10827×body80valid