Details

Time bar (total: 5.9s)

sample94.0ms

Algorithm
intervals
Results
75.0ms639×body80valid

simplify95.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05315
116115
245915
3132315
4299215
5500115

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

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)
1.3b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite57.0ms

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:
24.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
13.0ms
(* (* a a) (+ 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
13.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series301.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(+ (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))
98.0ms
(pow (+ (* a a) (* b b)) 2.0)
50.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify70.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
0504702
12520622
25002622

prune233.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (* b b) (- 1.0 (* 3.0 a)))
9.4b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.4b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.4b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-exp-log cbrt-prod add-sqr-sqrt add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div
4×add-log-exp
3×flip3-+ pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod flip-+
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 64
Calls
4 calls:
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
16.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
14.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
14.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series577.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
177.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
174.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
176.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify47.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03481404
114381278
250011257

prune318.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 2 (* (pow a 2) (pow b 2)))
0.0b
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
2.5b
(* (pow a 2) (pow b 2))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
38×add-exp-log
28×prod-exp
24×add-sqr-sqrt
16×unswap-sqr
14×unpow-prod-down
12×pow-to-exp pow-exp
11×associate-*l*
10×add-cbrt-cube unpow2 sqr-pow
9×associate-*r*
8×add-cube-cbrt *-un-lft-identity
5×pow1 add-log-exp
4×cbrt-unprod
2×pow-prod-down *-commutative
1×+-commutative flip3-+ sum-log flip-+
Counts
3 → 87
Calls
3 calls:
10.0ms
(* 2 (* (pow a 2) (pow b 2)))
6.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
9.0ms
(* (pow a 2) (pow b 2))

series119.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(* 2 (* (pow a 2) (pow b 2)))
48.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
34.0ms
(* (pow a 2) (pow b 2))

simplify45.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0297518
11268445
25002432

prune209.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (/ -1 a) -4.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b
(* (* a a) (+ 1.0 a))
0.4b
(pow (/ -1 a) -4.0)
1.3b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
17×add-exp-log
16×add-sqr-sqrt *-un-lft-identity
15×pow1
14×add-cube-cbrt add-cbrt-cube
13×unpow-prod-down
9×times-frac
7×associate-*r*
6×pow-prod-down prod-exp cbrt-unprod add-log-exp
4×distribute-rgt-in distribute-lft-in associate-*r/
3×pow-unpow
2×sub-neg associate-+r+ flip3-+ associate-*l* pow-exp *-commutative flip-+ unswap-sqr
1×+-commutative pow-to-exp flip3-- pow-pow div-exp sum-log flip-- div-inv distribute-lft-out sqr-pow
Counts
4 → 90
Calls
4 calls:
21.0ms
(+ (pow (/ -1 a) -4.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
14.0ms
(* (* a a) (+ 1.0 a))
3.0ms
(pow (/ -1 a) -4.0)
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series396.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(+ (pow (/ -1 a) -4.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
51.0ms
(* (* a a) (+ 1.0 a))
202.0ms
(pow (/ -1 a) -4.0)
54.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify68.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0591705
12701619
25003619

prune250.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0b

regimes153.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02715
12715

end0.0ms

sample2.7s

Algorithm
intervals
Results
2.3s20597×body80valid