Details

Time bar (total: 5.1s)

sample51.0ms

Algorithm
intervals
Results
34.0ms654×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

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
0.0b
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
1.2b
(* (* b b) (+ 3.0 a))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-exp-log
9×*-un-lft-identity add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow pow-prod-down prod-exp cbrt-unprod
2×associate-*r/ fma-udef
1×distribute-rgt-in pow-to-exp pow-pow distribute-lft-in flip3-+ associate-*l* pow-exp *-commutative flip-+ distribute-lft-out unswap-sqr sqr-pow
Counts
4 → 65
Calls
4 calls:
1.0ms
(fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
1.0ms
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
5.0ms
(pow (+ (* a a) (* b b)) 2.0)
11.0ms
(* (* b b) (+ 3.0 a))

series280.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
47.0ms
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
102.0ms
(pow (+ (* a a) (* b b)) 2.0)
32.0ms
(* (* b b) (+ 3.0 a))

simplify44.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0335551
11554479
25001471

prune237.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (* b b) (+ 3.0 a))
19.0b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.0b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.0b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
13×*-un-lft-identity
12×add-sqr-sqrt
11×add-cube-cbrt
9×pow1 add-exp-log unpow-prod-down add-cbrt-cube
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
3×pow1/3 pow-prod-down prod-exp cbrt-unprod sqr-pow
2×associate-*r/
1×distribute-rgt-in distribute-lft-in flip3-+ associate-*l* *-commutative flip-+ distribute-lft-out unswap-sqr
Counts
4 → 77
Calls
4 calls:
7.0ms
(* (* b b) (+ 3.0 a))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series464.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (* b b) (+ 3.0 a))
147.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
141.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
144.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify44.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0270642
11138585
25001579

prune345.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

9.1b
(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
9.1b
(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
19.0b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.0b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
34×cbrt-prod
18×unpow-prod-down
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×sqrt-prod
4×pow1 add-exp-log expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u add-log-exp sqr-pow
Counts
4 → 74
Calls
4 calls:
5.0ms
(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
5.0ms
(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series665.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
148.0ms
(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
180.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
172.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify144.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 3 (40.0ms)

IterNodesCost
0179814
1384760
21210750
34950740
45001740

prune467.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (/ 1 a) -4.0) 1.0))
0.0b
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
0.3b
(pow (/ 1 a) -4.0)
1.2b
(* (* b b) (+ 3.0 a))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
14×add-exp-log add-sqr-sqrt
13×add-cube-cbrt unpow-prod-down
11×pow1
9×times-frac add-cbrt-cube
4×expm1-log1p-u associate-*r* pow-exp log1p-expm1-u add-log-exp
3×pow-unpow pow-pow pow-prod-down prod-exp cbrt-unprod
2×associate-*r/ div-exp fma-udef
1×distribute-rgt-in pow-to-exp rec-exp pow-flip distribute-lft-in flip3-+ 1-exp associate-*l* *-commutative flip-+ div-inv distribute-lft-out inv-pow unswap-sqr sqr-pow
Counts
4 → 80
Calls
4 calls:
1.0ms
(fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (/ 1 a) -4.0) 1.0))
1.0ms
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
5.0ms
(pow (/ 1 a) -4.0)
8.0ms
(* (* b b) (+ 3.0 a))

series335.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (/ 1 a) -4.0) 1.0))
42.0ms
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
182.0ms
(pow (/ 1 a) -4.0)
32.0ms
(* (* b b) (+ 3.0 a))

simplify50.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0439567
11882495
25002489

prune251.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes69.0ms

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
01912
11912

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.1s20313×body80valid