Details

Time bar (total: 8.2s)

sample117.0ms

Algorithm
intervals
Results
95.0ms697×body80valid

simplify61.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
05515
117914
256113
3182413
4500213

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

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)
0.8b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite64.0ms

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:
30.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
14.0ms
(* (* a a) (+ 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
13.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series357.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
54.0ms
(* (* a a) (+ 1.0 a))
125.0ms
(pow (+ (* a a) (* b b)) 2.0)
54.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify91.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
0564828
12826724
25001715

prune382.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (pow (hypot a b) 2.0) (pow (hypot a 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 (hypot a b) 2.0) (pow (hypot a b) 2.0))
0.8b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
26×add-exp-log
18×unpow-prod-down *-un-lft-identity
16×add-cube-cbrt add-cbrt-cube
15×prod-exp
14×pow1 associate-*r*
11×unswap-sqr
10×sqr-pow
9×associate-*l*
7×distribute-rgt-in distribute-lft-in swap-sqr pow-prod-down cbrt-unprod
6×pow-to-exp prod-diff pow-exp add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×*-commutative
2×sub-neg associate-+r+ flip3-+ flip-+
1×+-commutative pow2 flip3-- fma-def sum-log pow-sqr pow-prod-up flip-- distribute-lft-out
Counts
4 → 129
Calls
4 calls:
5.0ms
(+ (* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
14.0ms
(* (* a a) (+ 1.0 a))
12.0ms
(* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0))
13.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series677.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(+ (* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
288.0ms
(* (* a a) (+ 1.0 a))
192.0ms
(* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0))
54.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify107.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
06331068
13219938
25001917

prune446.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
0.0b
(+ (* (pow 1 2.0) (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))
0.8b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
18×associate-*r/
16×pow1 add-exp-log add-cbrt-cube
14×add-sqr-sqrt
12×*-un-lft-identity
10×add-cube-cbrt associate-*r*
8×distribute-rgt-in distribute-lft-in
7×pow-prod-down prod-exp cbrt-unprod
6×prod-diff add-log-exp
5×flip3-+ associate-*l* flip-+
4×expm1-log1p-u frac-add log1p-expm1-u
3×flip3-- *-commutative flip-- unswap-sqr
2×sub-neg associate-+r+
1×+-commutative fma-def sum-log distribute-lft-out
Counts
4 → 103
Calls
4 calls:
40.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
5.0ms
(+ (* (pow 1 2.0) (pow (hypot a b) (* 2 2.0))) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
14.0ms
(* (* a a) (+ 1.0 a))
13.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series356.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
157.0ms
(+ (* (pow 1 2.0) (pow (hypot a b) (* 2 2.0))) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
60.0ms
(* (* a a) (+ 1.0 a))
61.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify159.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (138.0ms)

IterNodesCost
07621088
14354964
25001951

prune472.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (* b b) (- 1.0 (* 3.0 a)))
8.0b
(cbrt (+ (* (pow 1 2.0) (pow (hypot a b) (* 2 2.0))) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
8.0b
(cbrt (+ (* (pow 1 2.0) (pow (hypot a b) (* 2 2.0))) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
8.0b
(cbrt (+ (* (pow 1 2.0) (pow (hypot a b) (* 2 2.0))) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite30.0ms

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:
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
3.0ms
(cbrt (+ (* (pow 1 2.0) (pow (hypot a b) (* 2 2.0))) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
7.0ms
(cbrt (+ (* (pow 1 2.0) (pow (hypot a b) (* 2 2.0))) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
4.0ms
(cbrt (+ (* (pow 1 2.0) (pow (hypot a b) (* 2 2.0))) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series879.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
279.0ms
(cbrt (+ (* (pow 1 2.0) (pow (hypot a b) (* 2 2.0))) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
262.0ms
(cbrt (+ (* (pow 1 2.0) (pow (hypot a b) (* 2 2.0))) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
275.0ms
(cbrt (+ (* (pow 1 2.0) (pow (hypot a b) (* 2 2.0))) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify85.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
04191657
118661508
250011481

prune507.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes71.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03516
13516

end0.0ms

sample3.1s

Algorithm
intervals
Results
2.7s20589×body80valid