Details

Time bar (total: 2.4s)

sample16.0ms

Algorithm
intervals
Results
7.0ms277×body80valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0215
1375
2615
3915
41155
51215
61215

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.1b

localize7.0ms

Local error

Found 2 expressions with local error:

3.5b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
4.5b
(* y (+ 1.0 (* z z)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
20×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
16×add-exp-log add-cbrt-cube
13×associate-/l*
6×cbrt-undiv div-exp
4×pow1 associate-*r/
3×associate-*r* associate-*l* prod-exp cbrt-unprod div-inv
2×flip3-+ associate-/r/ flip-+ add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num associate-/r* *-commutative associate-/l/ unswap-sqr
Counts
2 → 70
Calls
2 calls:
7.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
7.0ms
(* y (+ 1.0 (* z z)))

series113.0ms

Counts
2 → 6
Calls
2 calls:
57.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
55.0ms
(* y (+ 1.0 (* z z)))

simplify51.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0409511
11963443
25001443

prune170.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.2b

localize7.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ 1.0 (* (* y (+ 1.0 (* z z))) x))
3.3b
(* (* y (+ 1.0 (* z z))) x)
4.5b
(* y (+ 1.0 (* z z)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log add-cbrt-cube
10×pow1 add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
7×prod-exp cbrt-unprod
6×associate-*r/ associate-*r*
4×associate-*l* pow-prod-down associate-*l/
3×cbrt-undiv flip3-+ times-frac div-exp flip-+ associate-/l* add-log-exp
2×associate-/r/ *-commutative
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r* div-inv unswap-sqr
Counts
3 → 67
Calls
3 calls:
14.0ms
(/ 1.0 (* (* y (+ 1.0 (* z z))) x))
11.0ms
(* (* y (+ 1.0 (* z z))) x)
7.0ms
(* y (+ 1.0 (* z z)))

series169.0ms

Counts
3 → 9
Calls
3 calls:
64.0ms
(/ 1.0 (* (* y (+ 1.0 (* z z))) x))
51.0ms
(* (* y (+ 1.0 (* z z))) x)
54.0ms
(* y (+ 1.0 (* z z)))

simplify59.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0367480
12077394
25002394

prune154.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ 1.0 (* y (* (+ 1.0 (* z z)) x)))
3.1b
(* (+ 1.0 (* z z)) x)
3.8b
(* y (* (+ 1.0 (* z z)) x))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log add-cbrt-cube
10×pow1 add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
7×prod-exp cbrt-unprod
6×associate-*l* associate-*l/
4×associate-*r/ associate-*r* pow-prod-down
3×cbrt-undiv flip3-+ times-frac div-exp flip-+ associate-/l* add-log-exp
2×associate-/r/ *-commutative
1×frac-2neg clear-num associate-/r* div-inv unswap-sqr
Counts
3 → 65
Calls
3 calls:
10.0ms
(/ 1.0 (* y (* (+ 1.0 (* z z)) x)))
7.0ms
(* (+ 1.0 (* z z)) x)
10.0ms
(* y (* (+ 1.0 (* z z)) x))

series153.0ms

Counts
3 → 9
Calls
3 calls:
66.0ms
(/ 1.0 (* y (* (+ 1.0 (* z z)) x)))
38.0ms
(* (+ 1.0 (* z z)) x)
49.0ms
(* y (* (+ 1.0 (* z z)) x))

simplify46.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0330475
11578386
25001386

prune140.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (* y (* (sqrt (+ 1.0 (* z z))) (* (sqrt (+ 1.0 (* z z))) x))))
3.8b
(* y (* (sqrt (+ 1.0 (* z z))) (* (sqrt (+ 1.0 (* z z))) x)))
16.6b
(sqrt (+ 1.0 (* z z)))
16.6b
(sqrt (+ 1.0 (* z z)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
28×sqrt-div
27×add-exp-log add-cbrt-cube
20×associate-*r/
16×associate-*l/
15×pow1
14×flip3-+ flip-+
12×prod-exp cbrt-unprod
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
8×frac-times associate-/r/
6×pow-prod-down sqrt-prod
4×cbrt-undiv div-exp add-log-exp
3×times-frac associate-*l* associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-2neg associate-*r* clear-num associate-/r* *-commutative div-inv
Counts
4 → 92
Calls
4 calls:
44.0ms
(/ 1.0 (* y (* (sqrt (+ 1.0 (* z z))) (* (sqrt (+ 1.0 (* z z))) x))))
45.0ms
(* y (* (sqrt (+ 1.0 (* z z))) (* (sqrt (+ 1.0 (* z z))) x)))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series194.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(/ 1.0 (* y (* (sqrt (+ 1.0 (* z z))) (* (sqrt (+ 1.0 (* z z))) x))))
44.0ms
(* y (* (sqrt (+ 1.0 (* z z))) (* (sqrt (+ 1.0 (* z z))) x)))
45.0ms
(sqrt (+ 1.0 (* z z)))
42.0ms
(sqrt (+ 1.0 (* z z)))

simplify51.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0478980
12003757
25001740

prune245.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.2b

regimes229.0ms

Accuracy

55.4% (0.9b remaining)

Error of 5.9b against oracle of 5.1b and baseline of 7.0b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02817
12817

end0.0ms

sample425.0ms

Algorithm
intervals
Results
244.0ms8632×body80valid