Details

Time bar (total: 2.7s)

sample13.0ms

Algorithm
intervals
Results
5.0ms328×body80valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0143
1233
2303
3313
4313

prune1.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 6.3b

Counts
2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

5.9b
(* x (+ 1.0 (* y y)))

rewrite5.0ms

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:
5.0ms
(* x (+ 1.0 (* y y)))

series53.0ms

Counts
1 → 3
Calls
1 calls:
53.0ms
(* x (+ 1.0 (* y y)))

simplify84.0ms

Algorithm
egg-herbie
Counts
27 → 27
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0148123
1742103
23453100
35001100

prune51.0ms

Filtered
27 candidates to 22 candidates (81.5%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New22527
Fresh000
Picked011
Done000
Total22628

Merged error: 6.1b

Counts
28 → 6

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))))
5.9b
(sqrt (+ 1.0 (* y y)))
5.9b
(sqrt (+ 1.0 (* y y)))

rewrite24.0ms

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:
6.0ms
(* x (sqrt (+ 1.0 (* y y))))
10.0ms
(* (* 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)))

series198.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* x (sqrt (+ 1.0 (* y y))))
53.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
40.0ms
(sqrt (+ 1.0 (* y y)))
45.0ms
(sqrt (+ 1.0 (* y y)))

simplify43.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0318722
11367620
25002595

prune200.0ms

Filtered
105 candidates to 84 candidates (80.0%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1032105
Fresh044
Picked011
Done011
Total1038111

Merged error: 6.1b

Counts
111 → 8

localize8.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
1.9b
(* (cbrt x) (+ 1.0 (* y y)))
4.2b
(* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ 1.0 (* y y))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1 add-exp-log
13×add-sqr-sqrt
11×add-cbrt-cube
10×cbrt-prod
9×add-cube-cbrt *-un-lft-identity pow-prod-down prod-exp cbrt-unprod
7×associate-*l*
6×associate-*r/
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
2×flip3-+ pow1/3 *-commutative flip-+ unswap-sqr
Counts
4 → 84
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
8.0ms
(* (cbrt x) (+ 1.0 (* y y)))
18.0ms
(* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ 1.0 (* y y))))

series639.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(cbrt x)
197.0ms
(cbrt x)
188.0ms
(* (cbrt x) (+ 1.0 (* y y)))
73.0ms
(* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ 1.0 (* y y))))

simplify56.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0330614
11660458
25001404

prune179.0ms

Filtered
96 candidates to 71 candidates (74.0%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New96096
Fresh055
Picked011
Done022
Total968104

Merged error: 6.1b

Counts
104 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (pow y 2) (- (pow y 2) 1.0) (* 1.0 1.0))
0.2b
(pow (* y y) 3)
1.0b
(* (+ (pow 1.0 3) (pow (* y y) 3)) x)
14.3b
(/ (* (+ (pow 1.0 3) (pow (* y y) 3)) x) (fma (pow y 2) (- (pow y 2) 1.0) (* 1.0 1.0)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1 add-exp-log add-cbrt-cube
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt
6×pow-pow
5×associate-*l*
4×expm1-log1p-u associate-*l/ log1p-expm1-u add-log-exp
3×pow-unpow times-frac associate-*r* prod-exp associate-/r* cbrt-unprod
2×cbrt-undiv flip3-+ div-exp pow-prod-down pow-exp flip-+ associate-/l/ rem-cube-cbrt
1×pow2 cube-mult pow-to-exp unpow-prod-down frac-2neg pow-plus unpow3 cube-prod clear-num pow-sqr sum-cubes *-commutative pow-prod-up fma-udef div-inv distribute-lft-out associate-/l* unswap-sqr sqr-pow
Counts
4 → 87
Calls
4 calls:
1.0ms
(fma (pow y 2) (- (pow y 2) 1.0) (* 1.0 1.0))
4.0ms
(pow (* y y) 3)
14.0ms
(* (+ (pow 1.0 3) (pow (* y y) 3)) x)
11.0ms
(/ (* (+ (pow 1.0 3) (pow (* y y) 3)) x) (fma (pow y 2) (- (pow y 2) 1.0) (* 1.0 1.0)))

series234.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(fma (pow y 2) (- (pow y 2) 1.0) (* 1.0 1.0))
47.0ms
(pow (* y y) 3)
32.0ms
(* (+ (pow 1.0 3) (pow (* y y) 3)) x)
111.0ms
(/ (* (+ (pow 1.0 3) (pow (* y y) 3)) x) (fma (pow y 2) (- (pow y 2) 1.0) (* 1.0 1.0)))

simplify73.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
0334720
11747595
25003592

prune248.0ms

Filtered
99 candidates to 75 candidates (75.8%)
Pruning

8 alts after pruning (4 fresh and 4 done)

PrunedKeptTotal
New99099
Fresh044
Picked011
Done033
Total998107

Merged error: 6.1b

Counts
107 → 8

regimes125.0ms

Accuracy

0% (0.2b remaining)

Error of 5.2b against oracle of 5.0b and baseline of 5.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
083
183

end0.0ms

sample333.0ms

Algorithm
intervals
Results
180.0ms10613×body80valid