Details

Time bar (total: 3.7s)

sample16.0ms

Algorithm
intervals
Results
8.0ms279×body80valid

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0215
1375
2615
3915
41155
51215
61215

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.3b

localize7.0ms

Local error

Found 2 expressions with local error:

3.1b
(* y (+ 1.0 (* z z)))
3.7b
(/ (/ 1.0 x) (* 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
(* y (+ 1.0 (* z z)))
8.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series107.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(* y (+ 1.0 (* z z)))
58.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify51.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0409511
11963443
25001443

prune156.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
3.7b
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
18.2b
(sqrt (+ 1.0 (* z z)))
18.2b
(sqrt (+ 1.0 (* z z)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
30×add-exp-log add-cbrt-cube
28×sqrt-div
24×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
16×associate-*r/
14×flip3-+ flip-+
13×associate-/l*
11×pow1
9×cbrt-undiv div-exp prod-exp sqrt-prod cbrt-unprod
8×frac-times associate-/r/
6×associate-*r*
4×associate-*l/ add-log-exp
3×pow-prod-down div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-2neg associate-*l* clear-num associate-/r* *-commutative associate-/l/
Counts
4 → 117
Calls
4 calls:
22.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
21.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series197.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
54.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
45.0ms
(sqrt (+ 1.0 (* z z)))
41.0ms
(sqrt (+ 1.0 (* z z)))

simplify73.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06101242
128861023
250011005

prune330.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z))))) (sqrt (+ 1.0 (* z z))))
2.8b
(/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z)))))
18.2b
(sqrt (+ 1.0 (* z z)))
18.2b
(sqrt (+ 1.0 (* z z)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
299×times-frac
118×add-sqr-sqrt
116×add-cube-cbrt *-un-lft-identity
66×sqrt-prod
34×add-exp-log add-cbrt-cube
32×associate-/l*
22×sqrt-div
18×associate-/r/ div-inv
17×cbrt-undiv div-exp
16×associate-*r/
11×flip3-+ flip-+
7×associate-/r*
6×pow1
4×prod-exp cbrt-unprod add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 240
Calls
4 calls:
23.0ms
(/ (/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z))))) (sqrt (+ 1.0 (* z z))))
8.0ms
(/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z)))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series241.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(/ (/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z))))) (sqrt (+ 1.0 (* z z))))
90.0ms
(/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z)))))
48.0ms
(sqrt (+ 1.0 (* z z)))
42.0ms
(sqrt (+ 1.0 (* z z)))

simplify110.0ms

Algorithm
egg-herbie
Counts
252 → 252
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
09633413
140853172
250023077

prune649.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.3b

localize25.0ms

Local error

Found 4 expressions with local error:

1.8b
(/ (/ 1 (* (cbrt x) (cbrt x))) (* (fabs (cbrt (+ 1.0 (* z z)))) y))
18.2b
(sqrt (+ 1.0 (* z z)))
18.8b
(cbrt (+ 1.0 (* z z)))
18.8b
(cbrt (+ 1.0 (* z z)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
22×div-exp
21×add-cbrt-cube
13×times-frac prod-exp
12×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
10×cbrt-undiv
7×associate-/l*
6×cbrt-prod
5×pow1 cbrt-unprod
4×rec-exp cbrt-div 1-exp add-log-exp
3×flip3-+ sqrt-prod flip-+ div-inv
2×pow1/3 sqrt-div
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/r* associate-/l/
Counts
4 → 87
Calls
4 calls:
11.0ms
(/ (/ 1 (* (cbrt x) (cbrt x))) (* (fabs (cbrt (+ 1.0 (* z z)))) y))
3.0ms
(sqrt (+ 1.0 (* z z)))
2.0ms
(cbrt (+ 1.0 (* z z)))
2.0ms
(cbrt (+ 1.0 (* z z)))

series547.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(/ (/ 1 (* (cbrt x) (cbrt x))) (* (fabs (cbrt (+ 1.0 (* z z)))) y))
48.0ms
(sqrt (+ 1.0 (* z z)))
177.0ms
(cbrt (+ 1.0 (* z z)))
169.0ms
(cbrt (+ 1.0 (* z z)))

simplify64.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05521030
12259875
25001853

prune364.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.3b

regimes193.0ms

Accuracy

0% (1.4b remaining)

Error of 6.4b against oracle of 5.0b and baseline of 6.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02522
12522

end0.0ms

sample415.0ms

Algorithm
intervals
Results
244.0ms8611×body80valid