Details

Time bar (total: 6.0s)

sample70.0ms

Algorithm
intervals
Results
52.0ms691×body80valid

simplify77.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
05314
117313
253212
3168112
4427812
5500112

prune6.0ms

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) (+ 3.0 a)))))
0.1b
(* (* a a) (- 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.7b
(* (* b b) (+ 3.0 a))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt *-un-lft-identity
22×add-cube-cbrt
18×prod-diff
15×pow1 add-exp-log
14×add-cbrt-cube
13×distribute-rgt-in distribute-lft-in
9×associate-*r*
7×fma-def
6×unpow-prod-down 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 distribute-lft-out-- difference-of-squares
Counts
4 → 114
Calls
4 calls:
27.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
16.0ms
(* (* a a) (- 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
14.0ms
(* (* b b) (+ 3.0 a))

series288.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
52.0ms
(* (* a a) (- 1.0 a))
99.0ms
(pow (+ (* a a) (* b b)) 2.0)
32.0ms
(* (* b b) (+ 3.0 a))

simplify86.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
0646990
13454779
25001776

prune307.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
0.1b
(* (* a a) (- 1.0 a))
0.3b
(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))
0.7b
(* (* b b) (+ 3.0 a))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
30×*-un-lft-identity
26×add-exp-log add-cube-cbrt
18×unpow-prod-down prod-diff
16×associate-*r* add-cbrt-cube
15×prod-exp
14×pow1
13×distribute-rgt-in distribute-lft-in
11×unswap-sqr
10×sqr-pow
9×associate-*l*
7×swap-sqr pow-prod-down cbrt-unprod
6×pow-to-exp 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 distribute-lft-out-- difference-of-squares
Counts
4 → 143
Calls
4 calls:
5.0ms
(+ (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
16.0ms
(* (* a a) (- 1.0 a))
9.0ms
(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))
14.0ms
(* (* b b) (+ 3.0 a))

series343.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(+ (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
53.0ms
(* (* a a) (- 1.0 a))
149.0ms
(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))
36.0ms
(* (* b b) (+ 3.0 a))

simplify102.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
07231510
138861232
250021210

prune384.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (pow (fma a a (* b b)) (/ 2.0 2))) (pow (sqrt (pow (fma a a (* b b)) (/ 2.0 2))) 3))
0.7b
(* (* b b) (+ 3.0 a))
9.4b
(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))
9.4b
(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
89×sqrt-prod
82×add-sqr-sqrt
61×unpow-prod-down
41×unswap-sqr
30×associate-*r* sqr-pow
26×cube-prod
21×*-un-lft-identity
19×add-cube-cbrt
14×add-exp-log
11×associate-*l* add-cbrt-cube
10×pow1
6×rem-sqrt-square prod-exp
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×pow-prod-down
2×sqrt-pow1 pow1/2 associate-*r/ *-commutative
1×distribute-rgt-in cube-mult pow-to-exp distribute-lft-in flip3-+ unpow3 pow-exp pow-prod-up flip-+ distribute-lft-out
Counts
4 → 159
Calls
4 calls:
28.0ms
(* (sqrt (pow (fma a a (* b b)) (/ 2.0 2))) (pow (sqrt (pow (fma a a (* b b)) (/ 2.0 2))) 3))
14.0ms
(* (* b b) (+ 3.0 a))
2.0ms
(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))
2.0ms
(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))

series500.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(* (sqrt (pow (fma a a (* b b)) (/ 2.0 2))) (pow (sqrt (pow (fma a a (* b b)) (/ 2.0 2))) 3))
37.0ms
(* (* b b) (+ 3.0 a))
153.0ms
(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))
157.0ms
(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))

simplify76.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
04712199
121331798
250021728

prune556.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (sqrt (pow (fma a a (* b b)) (/ 2.0 2))) 4) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
0.1b
(* (* a a) (- 1.0 a))
0.7b
(* (* b b) (+ 3.0 a))
9.4b
(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
28×*-un-lft-identity
24×add-cube-cbrt
18×prod-diff
17×unpow-prod-down
14×pow1 add-exp-log fma-def sqrt-prod add-cbrt-cube
13×distribute-rgt-in distribute-lft-in
9×associate-*r*
6×pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u sqr-pow
3×rem-sqrt-square
2×sub-neg associate-+r+ flip3-+ associate-*l* *-commutative flip-+ unswap-sqr
1×+-commutative flip3-- sqrt-pow1 pow1/2 sum-log flip-- distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 123
Calls
4 calls:
23.0ms
(+ (pow (sqrt (pow (fma a a (* b b)) (/ 2.0 2))) 4) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
16.0ms
(* (* a a) (- 1.0 a))
17.0ms
(* (* b b) (+ 3.0 a))
2.0ms
(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))

series352.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(+ (pow (sqrt (pow (fma a a (* b b)) (/ 2.0 2))) 4) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
55.0ms
(* (* a a) (- 1.0 a))
32.0ms
(* (* b b) (+ 3.0 a))
158.0ms
(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))

simplify86.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
06631064
13430848
25001843

prune420.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes89.0ms

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
02916
12916

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.6s21017×body80valid