Details

Time bar (total: 4.2s)

sample17.0ms

Algorithm
intervals
Results
8.0ms279×body80valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0215
1404
2694
31044
41464
51604
61604

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.4b

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×expm1-log1p-u flip3-+ associate-/r/ flip-+ log1p-expm1-u 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 → 74
Calls
2 calls:
7.0ms
(* y (+ 1.0 (* z z)))
8.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series113.0ms

Counts
2 → 6
Calls
2 calls:
52.0ms
(* y (+ 1.0 (* z z)))
60.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify52.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0416531
12028428
25001420

prune188.0ms

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)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
30×add-exp-log add-cbrt-cube
28×sqrt-div
26×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×expm1-log1p-u associate-*l/ log1p-expm1-u add-log-exp
3×pow-prod-down div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
1×frac-2neg associate-*l* clear-num associate-/r* *-commutative associate-/l/
Counts
4 → 127
Calls
4 calls:
20.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
25.0ms
(/ (/ 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)))

series206.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
62.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
42.0ms
(sqrt (+ 1.0 (* z z)))
49.0ms
(sqrt (+ 1.0 (* z z)))

simplify74.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
06241296
129331032
25002989

prune362.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.3b

localize13.0ms

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)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
299×times-frac
120×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×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num hypot-def associate-/l/
Counts
4 → 250
Calls
4 calls:
19.0ms
(/ (/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z))))) (sqrt (+ 1.0 (* z z))))
9.0ms
(/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z)))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series251.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(/ (/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z))))) (sqrt (+ 1.0 (* z z))))
93.0ms
(/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z)))))
43.0ms
(sqrt (+ 1.0 (* z z)))
52.0ms
(sqrt (+ 1.0 (* z z)))

simplify106.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
09773463
141303155
250013042

prune699.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.3b

localize22.0ms

Local error

Found 4 expressions with local error:

1.8b
(/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (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)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log
29×add-cbrt-cube
18×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
7×times-frac
6×cbrt-prod
5×pow1 associate-/l*
4×expm1-log1p-u cbrt-div log1p-expm1-u 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* hypot-def associate-/l/
Counts
4 → 92
Calls
4 calls:
11.0ms
(/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (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)))

series710.0ms

Counts
4 → 12
Calls
4 calls:
304.0ms
(/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x))) (* (fabs (cbrt (+ 1.0 (* z z)))) y))
44.0ms
(sqrt (+ 1.0 (* z z)))
185.0ms
(cbrt (+ 1.0 (* z z)))
177.0ms
(cbrt (+ 1.0 (* z z)))

simplify71.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
05971244
13004965
25002919

prune472.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.3b

regimes207.0ms

Accuracy

0% (1.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02426
12426

end0.0ms

sample414.0ms

Algorithm
intervals
Results
244.0ms8611×body80valid