Details

Time bar (total: 5.7s)

sample55.0ms

Algorithm
intervals
Results
36.0ms664×body80valid

simplify95.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05315
116115
245915
3132315
4299215
5500115

prune3.0ms

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: 0.2b

Counts
2 → 1

localize21.0ms

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))
0.4b
(* (* b b) (- 1.0 (* 3.0 a)))
0.4b
(pow (+ (* a a) (* b b)) 2.0)

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
10×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt
7×associate-*r*
6×pow-prod-down prod-exp cbrt-unprod add-log-exp
4×distribute-rgt-in distribute-lft-in associate-*r/
3×unpow-prod-down pow-unpow
2×sub-neg associate-+r+ flip3-+ associate-*l* *-commutative flip-+ unswap-sqr
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out sqr-pow
Counts
4 → 79
Calls
4 calls:
8.0ms
(+ (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))
8.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
5.0ms
(pow (+ (* a a) (* b b)) 2.0)

series327.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
49.0ms
(* (* a a) (+ 1.0 a))
55.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
107.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify68.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
0504702
12520622
25002622

prune225.0ms

Filtered
91 candidates to 61 candidates (67.0%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New86591
Fresh000
Picked101
Done000
Total87592

Merged error: 0.0b

Counts
92 → 5

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))))
9.1b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.1b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.1b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×flip3-+ pow1/3 flip-+
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 87
Calls
4 calls:
16.0ms
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))) (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)))))))
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series796.0ms

Counts
4 → 12
Calls
4 calls:
222.0ms
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))))
191.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
191.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
191.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify71.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
03463215
112032996
250012773

prune390.0ms

Filtered
99 candidates to 75 candidates (75.8%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New98199
Fresh044
Picked011
Done000
Total986104

Merged error: 0.0b

Counts
104 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
0.0b
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b
(* 2 (* (pow a 2) (pow b 2)))
2.9b
(* (pow a 2) (pow b 2))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
28×prod-exp
25×add-sqr-sqrt
16×unswap-sqr
14×unpow-prod-down
12×pow-to-exp pow-exp
11×*-un-lft-identity associate-*l* add-cbrt-cube add-log-exp
10×unpow2 sqr-pow
9×add-cube-cbrt associate-*r*
6×pow1
4×sum-log cbrt-unprod
2×+-commutative flip3-+ pow-prod-down *-commutative flip-+
1×associate-+r+ distribute-lft-out
Counts
4 → 101
Calls
4 calls:
8.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
5.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
8.0ms
(* 2 (* (pow a 2) (pow b 2)))
8.0ms
(* (pow a 2) (pow b 2))

series182.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
51.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
42.0ms
(* 2 (* (pow a 2) (pow b 2)))
33.0ms
(* (pow a 2) (pow b 2))

simplify56.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0375699
11613622
25001616

prune219.0ms

Filtered
113 candidates to 60 candidates (53.1%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1130113
Fresh044
Picked011
Done011
Total1136119

Merged error: 0.0b

Counts
119 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 3)
0.4b
(* (* b b) (- 1.0 (* 3.0 a)))
0.4b
(pow (+ (* a a) (* b b)) 2.0)
30.7b
(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 3))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
12×cbrt-prod
11×pow1 add-exp-log
10×add-cbrt-cube
9×unpow-prod-down
6×pow-unpow cube-prod
4×cube-div add-log-exp
3×associate-*r* pow-prod-down prod-exp cbrt-unprod sqr-pow
2×distribute-rgt-in cube-mult pow-to-exp sub-neg cbrt-div pow-pow distribute-lft-in flip3-+ unpow3 associate-*r/ pow-exp flip-+
1×flip3-- pow1/3 associate-*l* *-commutative flip-- rem-cbrt-cube rem-cube-cbrt unswap-sqr
Counts
4 → 90
Calls
4 calls:
8.0ms
(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 3)
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
5.0ms
(pow (+ (* a a) (* b b)) 2.0)
8.0ms
(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 3))

series1.1s

Counts
4 → 12
Calls
4 calls:
799.0ms
(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 3)
55.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
105.0ms
(pow (+ (* a a) (* b b)) 2.0)
113.0ms
(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 3))

simplify82.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
05281543
125771405
250011399

prune242.0ms

Filtered
102 candidates to 60 candidates (58.8%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New1002102
Fresh123
Picked011
Done022
Total1017108

Merged error: 0b

Counts
108 → 7

regimes162.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03148
13148

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.1s20463×body80valid