Details

Time bar (total: 5.6s)

sample62.0ms

Algorithm
intervals
Results
38.0ms643×body80valid

simplify77.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
0268
1518
2887
31537
43577
515727
650027

prune8.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (* b b))
0.0b
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.0b
(+ (* a a) (* b b))
0.3b
(pow (+ (* a a) (* b b)) 2.0)

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-exp-log add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity add-cbrt-cube
8×fma-def add-log-exp
6×unpow-prod-down
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow associate-*l* pow-prod-down prod-exp cbrt-unprod
2×+-commutative flip3-+ sum-log flip-+ sqr-pow
1×pow-to-exp pow-pow associate-*r* pow-exp *-commutative unswap-sqr
Counts
4 → 74
Calls
4 calls:
6.0ms
(* 4.0 (* b b))
25.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
2.0ms
(+ (* a a) (* b b))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)

series212.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* 4.0 (* b b))
58.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
30.0ms
(+ (* a a) (* b b))
96.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify38.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0339438
11458396
25002385

prune205.0ms

Filtered
86 candidates to 66 candidates (76.7%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma a a (* b b))
0.0b
(* 4.0 (* b b))
0.0b
(+ (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2))) (* 4.0 (* b b)))
0.3b
(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
21×add-exp-log
18×unpow-prod-down
13×add-cube-cbrt *-un-lft-identity
12×prod-exp
11×add-cbrt-cube
10×associate-*l* unswap-sqr sqr-pow
9×pow1
8×associate-*r*
7×swap-sqr
6×pow-to-exp pow-exp add-log-exp
4×expm1-log1p-u pow-prod-down cbrt-unprod log1p-expm1-u
2×*-commutative
1×+-commutative pow2 fma-def flip3-+ sum-log pow-sqr pow-prod-up flip-+ fma-udef
Counts
4 → 99
Calls
4 calls:
0.0ms
(fma a a (* b b))
9.0ms
(* 4.0 (* b b))
4.0ms
(+ (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2))) (* 4.0 (* b b)))
8.0ms
(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))

series265.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(fma a a (* b b))
23.0ms
(* 4.0 (* b b))
60.0ms
(+ (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2))) (* 4.0 (* b b)))
145.0ms
(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))

simplify49.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0344931
11473816
25002770

prune247.0ms

Filtered
111 candidates to 71 candidates (64.0%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (pow (fma a a (* b b)) (/ (/ 2.0 2) 2)) 3)
0.2b
(* (pow (fma a a (* b b)) (/ (/ 2.0 2) 2)) (pow (pow (fma a a (* b b)) (/ (/ 2.0 2) 2)) 3))
8.5b
(pow (fma a a (* b b)) (/ (/ 2.0 2) 2))
8.5b
(pow (fma a a (* b b)) (/ (/ 2.0 2) 2))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
132×times-frac
119×add-sqr-sqrt
89×pow-unpow
88×add-cube-cbrt *-un-lft-identity
58×unpow-prod-down
27×add-exp-log
26×sqr-pow
24×unswap-sqr
23×cube-prod pow-exp
20×associate-*r*
15×pow-to-exp prod-exp
8×div-inv
7×associate-*l* add-cbrt-cube
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-pow
2×cube-mult unpow3
1×*-commutative cbrt-unprod rem-cube-cbrt
Counts
4 → 230
Calls
4 calls:
3.0ms
(pow (pow (fma a a (* b b)) (/ (/ 2.0 2) 2)) 3)
34.0ms
(* (pow (fma a a (* b b)) (/ (/ 2.0 2) 2)) (pow (pow (fma a a (* b b)) (/ (/ 2.0 2) 2)) 3))
5.0ms
(pow (fma a a (* b b)) (/ (/ 2.0 2) 2))
5.0ms
(pow (fma a a (* b b)) (/ (/ 2.0 2) 2))

series510.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(pow (pow (fma a a (* b b)) (/ (/ 2.0 2) 2)) 3)
158.0ms
(* (pow (fma a a (* b b)) (/ (/ 2.0 2) 2)) (pow (pow (fma a a (* b b)) (/ (/ 2.0 2) 2)) 3))
113.0ms
(pow (fma a a (* b b)) (/ (/ 2.0 2) 2))
117.0ms
(pow (fma a a (* b b)) (/ (/ 2.0 2) 2))

simplify109.0ms

Algorithm
egg-herbie
Counts
242 → 242
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
06902585
133842229
250022107

prune903.0ms

Filtered
242 candidates to 168 candidates (69.4%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (pow (fma a a (* b b)) (/ (/ 2.0 4) 2)) (pow (fma a a (* b b)) (/ (/ 2.0 4) 2)))
8.5b
(pow (fma a a (* b b)) (/ (/ 2.0 2) 2))
8.7b
(pow (fma a a (* b b)) (/ (/ 2.0 4) 2))
8.7b
(pow (fma a a (* b b)) (/ (/ 2.0 4) 2))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
198×times-frac
132×add-sqr-sqrt
129×pow-unpow
120×add-cube-cbrt *-un-lft-identity
27×unpow-prod-down
19×add-exp-log
13×sqr-pow
12×div-inv
9×pow-to-exp pow-exp prod-exp unswap-sqr
7×pow1 swap-sqr associate-*r* associate-*l*
6×add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-pow
1×pow2 pow-prod-down pow-sqr *-commutative pow-prod-up cbrt-unprod
Counts
4 → 231
Calls
4 calls:
8.0ms
(* (pow (fma a a (* b b)) (/ (/ 2.0 4) 2)) (pow (fma a a (* b b)) (/ (/ 2.0 4) 2)))
5.0ms
(pow (fma a a (* b b)) (/ (/ 2.0 2) 2))
5.0ms
(pow (fma a a (* b b)) (/ (/ 2.0 4) 2))
5.0ms
(pow (fma a a (* b b)) (/ (/ 2.0 4) 2))

series477.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(* (pow (fma a a (* b b)) (/ (/ 2.0 4) 2)) (pow (fma a a (* b b)) (/ (/ 2.0 4) 2)))
106.0ms
(pow (fma a a (* b b)) (/ (/ 2.0 2) 2))
106.0ms
(pow (fma a a (* b b)) (/ (/ 2.0 4) 2))
109.0ms
(pow (fma a a (* b b)) (/ (/ 2.0 4) 2))

simplify79.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
07842008
132611862
250011850

prune1.0s

Filtered
243 candidates to 196 candidates (80.7%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes58.0ms

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
02522
12522

end0.0ms

sample1.1s

Algorithm
intervals
Results
719.0ms20640×body80valid