Details

Time bar (total: 5.2s)

sample60.0ms

Algorithm
intervals
Results
42.0ms618×body80valid

simplify54.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
05515
117914
256113
3182413
4500213

prune7.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 0.2b

Counts
2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b
(* (* a a) (+ 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.9b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-sqr-sqrt *-un-lft-identity add-cbrt-cube
12×add-cube-cbrt
7×distribute-rgt-in fma-def distribute-lft-in associate-*r*
6×unpow-prod-down prod-diff pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×pow-unpow
2×sub-neg associate-+r+ flip3-+ associate-*l* *-commutative flip-+ unswap-sqr sqr-pow
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out
Counts
4 → 100
Calls
4 calls:
11.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
8.0ms
(* (* a a) (+ 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
8.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series301.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
51.0ms
(* (* a a) (+ 1.0 a))
99.0ms
(pow (+ (* a a) (* b b)) 2.0)
47.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify73.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
0564828
12826724
25001715

prune297.0ms

Filtered
112 candidates to 80 candidates (71.4%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1057112
Fresh000
Picked011
Done000
Total1058113

Merged error: 0.0b

Counts
113 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.9b
(* (* b b) (- 1.0 (* 3.0 a)))
9.4b
(sqrt (+ (* a a) (* b b)))
9.4b
(sqrt (+ (* a a) (* b b)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
11×pow1
9×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×prod-diff sqrt-prod
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*r/ flip-+ hypot-def
1×flip3-- associate-*l* *-commutative flip-- fma-udef unswap-sqr
Counts
4 → 79
Calls
4 calls:
1.0ms
(fma (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
4.0ms
(sqrt (+ (* a a) (* b b)))
8.0ms
(sqrt (+ (* a a) (* b b)))

series257.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(fma (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
52.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
33.0ms
(sqrt (+ (* a a) (* b b)))
34.0ms
(sqrt (+ (* a a) (* b b)))

simplify48.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0379738
11669640
25001616

prune286.0ms

Filtered
91 candidates to 70 candidates (76.9%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New90191
Fresh336
Picked101
Done011
Total94599

Merged error: 0.0b

Counts
99 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1.0 (* 3.0 a))
0.0b
(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b
(* (* a a) (+ 1.0 a))
0.9b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1 add-exp-log add-sqr-sqrt *-un-lft-identity add-cbrt-cube
12×add-cube-cbrt
9×prod-diff
8×add-log-exp
7×distribute-rgt-in fma-def distribute-lft-in associate-*r*
6×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×sub-neg unpow-prod-down fma-neg
2×associate-+r+ flip3-- flip3-+ associate-*l* *-commutative flip-- flip-+ unswap-sqr
1×+-commutative diff-log sum-log distribute-lft-out sqr-pow
Counts
4 → 101
Calls
4 calls:
6.0ms
(- 1.0 (* 3.0 a))
7.0ms
(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
8.0ms
(* (* a a) (+ 1.0 a))
8.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series289.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- 1.0 (* 3.0 a))
138.0ms
(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
52.0ms
(* (* a a) (+ 1.0 a))
64.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify76.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
0524782
12623672
25002667

prune299.0ms

Filtered
113 candidates to 78 candidates (69.0%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1121113
Fresh123
Picked011
Done011
Total1135118

Merged error: 0.0b

Counts
118 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (* b b) (- 1.0 (* 3.0 a)))
10.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
10.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
10.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow1 add-exp-log cbrt-prod add-cbrt-cube
6×cbrt-div prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod flip-+
2×sub-neg associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 78
Calls
4 calls:
8.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series598.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
180.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
181.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
184.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify54.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04011582
116891442
250021408

prune342.0ms

Filtered
90 candidates to 74 candidates (82.2%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New89190
Fresh112
Picked011
Done022
Total90595

Merged error: 0b

Counts
95 → 5

regimes191.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02914
12914

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.4s20562×body80valid