Details

Time bar (total: 5.4s)

sample50.0ms

Algorithm
intervals
Results
32.0ms628×body80valid

simplify79.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
05314
117313
253212
3168112
4427812
5500112

prune9.0ms

Pruning

2 alts after pruning (2 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))

rewrite34.0ms

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:
8.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
9.0ms
(* (* a a) (- 1.0 a))
5.0ms
(pow (+ (* a a) (* b b)) 2.0)
8.0ms
(* (* b b) (+ 3.0 a))

series309.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(+ (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))
110.0ms
(pow (+ (* a a) (* b b)) 2.0)
34.0ms
(* (* b b) (+ 3.0 a))

simplify91.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
0646990
13454779
25001776

prune337.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.7b
(* (* b b) (+ 3.0 a))
12.2b
(sqrt (pow (+ (* a a) (* b b)) 2.0))
12.2b
(sqrt (pow (+ (* a a) (* b b)) 2.0))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×sqrt-prod
13×*-un-lft-identity
11×add-cube-cbrt unpow-prod-down
10×pow1 add-exp-log
9×add-cbrt-cube
6×rem-sqrt-square
5×sqr-pow
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
3×pow-unpow pow-prod-down prod-exp cbrt-unprod
2×sqrt-pow1 pow1/2 associate-*r/
1×distribute-rgt-in pow-to-exp pow-pow distribute-lft-in flip3-+ associate-*l* pow-exp *-commutative flip-+ distribute-lft-out unswap-sqr
Counts
4 → 87
Calls
4 calls:
5.0ms
(pow (+ (* a a) (* b b)) 2.0)
8.0ms
(* (* b b) (+ 3.0 a))
5.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))
5.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))

series446.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(pow (+ (* a a) (* b b)) 2.0)
34.0ms
(* (* b b) (+ 3.0 a))
153.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))
150.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))

simplify42.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0299564
11364514
25002509

prune406.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.7b
(* (* b b) (+ 3.0 a))
10.7b
(sqrt (+ (* a a) (* b b)))
12.2b
(sqrt (pow (+ (* a a) (* b b)) 2.0))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity
11×pow1
10×add-exp-log add-cube-cbrt sqrt-prod
9×add-cbrt-cube
7×unpow-prod-down
4×expm1-log1p-u rem-sqrt-square associate-*r* log1p-expm1-u add-log-exp
3×pow-unpow pow-prod-down prod-exp cbrt-unprod sqr-pow
2×sqrt-pow1 flip3-+ pow1/2 sqrt-div associate-*r/ flip-+
1×distribute-rgt-in pow-to-exp pow-pow distribute-lft-in associate-*l* pow-exp *-commutative hypot-def distribute-lft-out unswap-sqr
Counts
4 → 84
Calls
4 calls:
5.0ms
(pow (+ (* a a) (* b b)) 2.0)
8.0ms
(* (* b b) (+ 3.0 a))
4.0ms
(sqrt (+ (* a a) (* b b)))
5.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))

series333.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(pow (+ (* a a) (* b b)) 2.0)
34.0ms
(* (* b b) (+ 3.0 a))
42.0ms
(sqrt (+ (* a a) (* b b)))
148.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))

simplify45.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0368509
11695468
25002459

prune442.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* b b) (+ 3.0 a))
11.3b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
11.3b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
11.3b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×pow1 add-exp-log cbrt-prod add-sqr-sqrt add-cbrt-cube
8×add-cube-cbrt
6×cbrt-div
4×expm1-log1p-u flip3-+ associate-*r* flip-+ log1p-expm1-u add-log-exp
3×pow1/3 pow-prod-down prod-exp cbrt-unprod
2×associate-*r/
1×distribute-rgt-in distribute-lft-in associate-*l* *-commutative distribute-lft-out unswap-sqr
Counts
4 → 71
Calls
4 calls:
8.0ms
(* (* b b) (+ 3.0 a))
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
10.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series614.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (* b b) (+ 3.0 a))
193.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
192.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
195.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify51.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
03511377
115581248
250011230

prune387.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes151.0ms

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
02821
12821

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.1s20319×body80valid