Details

Time bar (total: 6.4s)

sample18.0ms

Algorithm
intervals
Results
9.0ms283×body80valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0215
1404
2694
31044
41464
51604
61604

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.9b

localize10.0ms

Local error

Found 2 expressions with local error:

3.6b
(/ (/ 1.0 x) (fma z z 1.0))
3.8b
(/ (/ (/ 1.0 x) (fma z z 1.0)) y)

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
468×times-frac
228×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
56×associate-/l*
22×div-inv
16×add-exp-log add-cbrt-cube
9×cbrt-undiv div-exp
6×associate-/r*
2×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u associate-/l/ add-log-exp
Counts
2 → 266
Calls
2 calls:
6.0ms
(/ (/ 1.0 x) (fma z z 1.0))
13.0ms
(/ (/ (/ 1.0 x) (fma z z 1.0)) y)

series130.0ms

Counts
2 → 6
Calls
2 calls:
60.0ms
(/ (/ 1.0 x) (fma z z 1.0))
70.0ms
(/ (/ (/ 1.0 x) (fma z z 1.0)) y)

simplify109.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
011482808
146382733
250032733

prune809.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (sqrt (fma z z 1.0))) (/ (/ (/ 1.0 x) (sqrt (fma z z 1.0))) y))
2.8b
(/ (/ (/ 1.0 x) (sqrt (fma z z 1.0))) y)
16.2b
(sqrt (fma z z 1.0))
16.2b
(sqrt (fma z z 1.0))

rewrite212.0ms

Algorithm
rewrite-expression-head
Rules
1513×times-frac
797×add-sqr-sqrt
680×*-un-lft-identity
668×add-cube-cbrt
310×sqrt-prod
250×associate-*r*
82×associate-/l*
73×add-exp-log
52×div-inv
45×add-cbrt-cube
38×div-exp
30×unswap-sqr
22×cbrt-undiv associate-*l*
16×prod-exp
8×pow1 cbrt-unprod
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×associate-/r*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 720
Calls
4 calls:
123.0ms
(* (/ 1 (sqrt (fma z z 1.0))) (/ (/ (/ 1.0 x) (sqrt (fma z z 1.0))) y))
21.0ms
(/ (/ (/ 1.0 x) (sqrt (fma z z 1.0))) y)
1.0ms
(sqrt (fma z z 1.0))
2.0ms
(sqrt (fma z z 1.0))

series264.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* (/ 1 (sqrt (fma z z 1.0))) (/ (/ (/ 1.0 x) (sqrt (fma z z 1.0))) y))
83.0ms
(/ (/ (/ 1.0 x) (sqrt (fma z z 1.0))) y)
53.0ms
(sqrt (fma z z 1.0))
61.0ms
(sqrt (fma z z 1.0))

simplify138.0ms

Algorithm
egg-herbie
Counts
732 → 732
Iterations

Useful iterations: 1 (50.0ms)

IterNodesCost
029619383
150029021

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (sqrt (fma z z 1.0))) (/ (/ 1.0 x) (* y (sqrt (fma z z 1.0)))))
1.9b
(/ (/ 1.0 x) (* y (sqrt (fma z z 1.0))))
16.2b
(sqrt (fma z z 1.0))
16.2b
(sqrt (fma z z 1.0))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
93×add-exp-log
75×times-frac
57×add-cbrt-cube
55×add-sqr-sqrt
43×*-un-lft-identity
41×add-cube-cbrt
40×div-exp
30×prod-exp
23×cbrt-undiv
22×associate-*l*
17×associate-*r* sqrt-prod
16×cbrt-unprod
13×associate-/l*
8×pow1
6×div-inv
5×rec-exp 1-exp unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num associate-/r* *-commutative associate-/l/
Counts
4 → 166
Calls
4 calls:
20.0ms
(* (/ 1 (sqrt (fma z z 1.0))) (/ (/ 1.0 x) (* y (sqrt (fma z z 1.0)))))
8.0ms
(/ (/ 1.0 x) (* y (sqrt (fma z z 1.0))))
1.0ms
(sqrt (fma z z 1.0))
2.0ms
(sqrt (fma z z 1.0))

series275.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(* (/ 1 (sqrt (fma z z 1.0))) (/ (/ 1.0 x) (* y (sqrt (fma z z 1.0)))))
92.0ms
(/ (/ 1.0 x) (* y (sqrt (fma z z 1.0))))
57.0ms
(sqrt (fma z z 1.0))
57.0ms
(sqrt (fma z z 1.0))

simplify93.0ms

Algorithm
egg-herbie
Counts
178 → 178
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
08131587
140591327
250021175

prune441.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (sqrt (fma z z 1.0))) (* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (sqrt (fma z z 1.0)))))
2.9b
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (sqrt (fma z z 1.0))))
16.2b
(sqrt (fma z z 1.0))
16.2b
(sqrt (fma z z 1.0))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
320×times-frac
243×add-sqr-sqrt
166×sqrt-prod
155×add-cube-cbrt *-un-lft-identity
148×add-exp-log
137×associate-*r*
90×add-cbrt-cube
59×div-exp
58×prod-exp
44×associate-*l*
34×cbrt-undiv
32×cbrt-unprod
21×unswap-sqr
13×pow1
9×div-inv
7×rec-exp 1-exp
6×frac-times associate-*r/
4×expm1-log1p-u pow-prod-down associate-*l/ log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 *-commutative
Counts
4 → 319
Calls
4 calls:
29.0ms
(* (/ 1 (sqrt (fma z z 1.0))) (* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (sqrt (fma z z 1.0)))))
68.0ms
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (sqrt (fma z z 1.0))))
1.0ms
(sqrt (fma z z 1.0))
2.0ms
(sqrt (fma z z 1.0))

series487.0ms

Counts
4 → 12
Calls
4 calls:
225.0ms
(* (/ 1 (sqrt (fma z z 1.0))) (* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (sqrt (fma z z 1.0)))))
154.0ms
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (sqrt (fma z z 1.0))))
49.0ms
(sqrt (fma z z 1.0))
58.0ms
(sqrt (fma z z 1.0))

simplify62.0ms

Algorithm
egg-herbie
Counts
331 → 331
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
015943786
150013122

prune691.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.8b

regimes125.0ms

Accuracy

0% (1.4b remaining)

Error of 6.3b against oracle of 4.9b and baseline of 6.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0169
1169

end0.0ms

sample444.0ms

Algorithm
intervals
Results
267.0ms8639×body80valid