Details

Time bar (total: 8.4s)

sample112.0ms

Algorithm
intervals
Results
94.0ms650×body80valid

simplify80.0ms

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

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) (+ 3.0 a)))))
0.1b
(* (* a a) (- 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.4b
(* (* b b) (+ 3.0 a))

rewrite65.0ms

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:
29.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
15.0ms
(* (* a a) (- 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
13.0ms
(* (* b b) (+ 3.0 a))

series294.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
54.0ms
(* (* a a) (- 1.0 a))
102.0ms
(pow (+ (* a a) (* b b)) 2.0)
32.0ms
(* (* b b) (+ 3.0 a))

simplify87.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
0646990
13454779
25001776

prune331.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* (* b b) (+ 3.0 a)) 4.0)
0.0b
(fma (pow a 2) (* (- 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.4b
(* (* b b) (+ 3.0 a))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
19×pow1 add-exp-log
18×add-cbrt-cube
10×*-un-lft-identity
9×add-sqr-sqrt pow-prod-down prod-exp cbrt-unprod
8×add-cube-cbrt
7×associate-*r*
4×expm1-log1p-u associate-*r/ log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow
2×flip3-+ associate-*l* associate-*l/ *-commutative flip-+
1×distribute-rgt-in pow-to-exp pow-pow distribute-lft-in pow-exp fma-udef distribute-lft-out unswap-sqr sqr-pow
Counts
4 → 80
Calls
4 calls:
30.0ms
(* (* (* b b) (+ 3.0 a)) 4.0)
0.0ms
(fma (pow a 2) (* (- 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
13.0ms
(* (* b b) (+ 3.0 a))

series256.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (* (* b b) (+ 3.0 a)) 4.0)
72.0ms
(fma (pow a 2) (* (- 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0))
101.0ms
(pow (+ (* a a) (* b b)) 2.0)
36.0ms
(* (* b b) (+ 3.0 a))

simplify63.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0398569
12053480
25002472

prune297.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* b b) (+ 3.0 a))
14.0b
(cbrt (fma (pow a 2) (* (- 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0)))
14.0b
(cbrt (fma (pow a 2) (* (- 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0)))
14.0b
(cbrt (fma (pow a 2) (* (- 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0)))

rewrite20.0ms

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
4×expm1-log1p-u associate-*r* 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 flip3-+ associate-*l* *-commutative flip-+ distribute-lft-out unswap-sqr
Counts
4 → 65
Calls
4 calls:
17.0ms
(* (* b b) (+ 3.0 a))
1.0ms
(cbrt (fma (pow a 2) (* (- 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0)))
1.0ms
(cbrt (fma (pow a 2) (* (- 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0)))
1.0ms
(cbrt (fma (pow a 2) (* (- 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0)))

series1.5s

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (* b b) (+ 3.0 a))
503.0ms
(cbrt (fma (pow a 2) (* (- 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0)))
495.0ms
(cbrt (fma (pow a 2) (* (- 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0)))
496.0ms
(cbrt (fma (pow a 2) (* (- 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0)))

simplify41.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0307873
11233795
25001789

prune349.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

14.0b
(cbrt (fma (pow a 2) (* (- 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0)))
23.8b
(cbrt (* (* b b) (+ 3.0 a)))
23.8b
(cbrt (* (* b b) (+ 3.0 a)))
23.8b
(cbrt (* (* b b) (+ 3.0 a)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
6×cbrt-prod cbrt-div associate-*r/
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-+ flip-+
Counts
4 → 52
Calls
4 calls:
0.0ms
(cbrt (fma (pow a 2) (* (- 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0)))
7.0ms
(cbrt (* (* b b) (+ 3.0 a)))
11.0ms
(cbrt (* (* b b) (+ 3.0 a)))
8.0ms
(cbrt (* (* b b) (+ 3.0 a)))

series867.0ms

Counts
4 → 12
Calls
4 calls:
502.0ms
(cbrt (fma (pow a 2) (* (- 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0)))
120.0ms
(cbrt (* (* b b) (+ 3.0 a)))
125.0ms
(cbrt (* (* b b) (+ 3.0 a)))
120.0ms
(cbrt (* (* b b) (+ 3.0 a)))

simplify97.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 3 (89.0ms)

IterNodesCost
0345811
11006753
23999658
35001617

prune372.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes70.0ms

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
02614
12614

end0.0ms

sample3.3s

Algorithm
intervals
Results
2.9s20311×body80valid