Details

Time bar (total: 10.6s)

sample25.0ms

Algorithm
intervals
Results
16.0ms274×body80valid

simplify17.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0215
1404
2694
31044
41464
51604
61604

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.2b

localize7.0ms

Local error

Found 2 expressions with local error:

2.9b
(/ (/ 1.0 x) (fma z z 1.0))
3.9b
(/ (/ (/ 1.0 x) (fma z z 1.0)) y)

rewrite43.0ms

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))
17.0ms
(/ (/ (/ 1.0 x) (fma z z 1.0)) y)

series136.0ms

Counts
2 → 6
Calls
2 calls:
67.0ms
(/ (/ 1.0 x) (fma z z 1.0))
69.0ms
(/ (/ (/ 1.0 x) (fma z z 1.0)) y)

simplify110.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
011482808
146382733
250032733

prune822.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (/ (sqrt 1.0) 1) (sqrt (fma z z 1.0))) (/ (/ (/ (sqrt 1.0) x) (sqrt (fma z z 1.0))) y))
2.2b
(/ (/ (/ (sqrt 1.0) x) (sqrt (fma z z 1.0))) y)
13.8b
(sqrt (fma z z 1.0))
13.8b
(sqrt (fma z z 1.0))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
3067×times-frac
1741×add-sqr-sqrt
1296×*-un-lft-identity
1264×add-cube-cbrt
1093×sqrt-prod
412×associate-*r*
136×associate-*l* associate-/l*
88×unswap-sqr
85×add-exp-log
67×add-cbrt-cube
58×div-inv
50×div-exp
36×cbrt-undiv
16×prod-exp
12×cbrt-unprod
8×pow1
4×expm1-log1p-u 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 → 1274
Calls
4 calls:
771.0ms
(* (/ (/ (sqrt 1.0) 1) (sqrt (fma z z 1.0))) (/ (/ (/ (sqrt 1.0) x) (sqrt (fma z z 1.0))) y))
44.0ms
(/ (/ (/ (sqrt 1.0) x) (sqrt (fma z z 1.0))) y)
1.0ms
(sqrt (fma z z 1.0))
1.0ms
(sqrt (fma z z 1.0))

series474.0ms

Counts
4 → 12
Calls
4 calls:
242.0ms
(* (/ (/ (sqrt 1.0) 1) (sqrt (fma z z 1.0))) (/ (/ (/ (sqrt 1.0) x) (sqrt (fma z z 1.0))) y))
108.0ms
(/ (/ (/ (sqrt 1.0) x) (sqrt (fma z z 1.0))) y)
59.0ms
(sqrt (fma z z 1.0))
65.0ms
(sqrt (fma z z 1.0))

simplify258.0ms

Algorithm
egg-herbie
Counts
1286 → 1286
Iterations

Useful iterations: 1 (72.0ms)

IterNodesCost
0435020404
1500219694

prune3.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (sqrt 1.0) (/ (sqrt 1.0) x)) (sqrt (fma z z 1.0)))
3.9b
(* (/ (/ (* (sqrt 1.0) (/ (sqrt 1.0) x)) (sqrt (fma z z 1.0))) (sqrt (fma z z 1.0))) (/ 1 y))
13.8b
(sqrt (fma z z 1.0))
13.8b
(sqrt (fma z z 1.0))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
123×times-frac
98×add-exp-log
85×add-sqr-sqrt
64×associate-*l*
63×sqrt-prod
59×*-un-lft-identity
58×add-cbrt-cube
56×add-cube-cbrt
46×div-exp
30×prod-exp
25×cbrt-undiv
16×cbrt-unprod
13×associate-*r*
9×div-inv unswap-sqr
8×pow1
6×associate-/r*
5×rec-exp 1-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/
1×frac-times frac-2neg pow-prod-down associate-*l/ clear-num un-div-inv *-commutative associate-/l/ associate-/l*
Counts
4 → 193
Calls
4 calls:
11.0ms
(/ (* (sqrt 1.0) (/ (sqrt 1.0) x)) (sqrt (fma z z 1.0)))
60.0ms
(* (/ (/ (* (sqrt 1.0) (/ (sqrt 1.0) x)) (sqrt (fma z z 1.0))) (sqrt (fma z z 1.0))) (/ 1 y))
1.0ms
(sqrt (fma z z 1.0))
1.0ms
(sqrt (fma z z 1.0))

series482.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(/ (* (sqrt 1.0) (/ (sqrt 1.0) x)) (sqrt (fma z z 1.0)))
224.0ms
(* (/ (/ (* (sqrt 1.0) (/ (sqrt 1.0) x)) (sqrt (fma z z 1.0))) (sqrt (fma z z 1.0))) (/ 1 y))
60.0ms
(sqrt (fma z z 1.0))
54.0ms
(sqrt (fma z z 1.0))

simplify111.0ms

Algorithm
egg-herbie
Counts
205 → 205
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
09462235
146771666
250021664

prune564.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.1b

localize19.0ms

Local error

Found 4 expressions with local error:

13.8b
(sqrt (fma z z 1.0))
18.8b
(cbrt (* (/ (/ (sqrt 1.0) 1) (sqrt (fma z z 1.0))) (/ (/ (/ (sqrt 1.0) x) (sqrt (fma z z 1.0))) y)))
18.8b
(cbrt (* (/ (/ (sqrt 1.0) 1) (sqrt (fma z z 1.0))) (/ (/ (/ (sqrt 1.0) x) (sqrt (fma z z 1.0))) y)))
18.8b
(cbrt (* (/ (/ (sqrt 1.0) 1) (sqrt (fma z z 1.0))) (/ (/ (/ (sqrt 1.0) x) (sqrt (fma z z 1.0))) y)))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-div
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-prod frac-times pow1/3 associate-*r/ associate-*l/ sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 57
Calls
4 calls:
1.0ms
(sqrt (fma z z 1.0))
51.0ms
(cbrt (* (/ (/ (sqrt 1.0) 1) (sqrt (fma z z 1.0))) (/ (/ (/ (sqrt 1.0) x) (sqrt (fma z z 1.0))) y)))
53.0ms
(cbrt (* (/ (/ (sqrt 1.0) 1) (sqrt (fma z z 1.0))) (/ (/ (/ (sqrt 1.0) x) (sqrt (fma z z 1.0))) y)))
55.0ms
(cbrt (* (/ (/ (sqrt 1.0) 1) (sqrt (fma z z 1.0))) (/ (/ (/ (sqrt 1.0) x) (sqrt (fma z z 1.0))) y)))

series1.6s

Counts
4 → 12
Calls
4 calls:
60.0ms
(sqrt (fma z z 1.0))
506.0ms
(cbrt (* (/ (/ (sqrt 1.0) 1) (sqrt (fma z z 1.0))) (/ (/ (/ (sqrt 1.0) x) (sqrt (fma z z 1.0))) y)))
507.0ms
(cbrt (* (/ (/ (sqrt 1.0) 1) (sqrt (fma z z 1.0))) (/ (/ (/ (sqrt 1.0) x) (sqrt (fma z z 1.0))) y)))
506.0ms
(cbrt (* (/ (/ (sqrt 1.0) 1) (sqrt (fma z z 1.0))) (/ (/ (/ (sqrt 1.0) x) (sqrt (fma z z 1.0))) y)))

simplify133.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (123.0ms)

IterNodesCost
02711008
1880921
24279848
35001829

prune358.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 5.1b

regimes140.0ms

Accuracy

0% (1.2b remaining)

Error of 6.2b against oracle of 5.0b and baseline of 6.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01712
11712

end0.0ms

sample684.0ms

Algorithm
intervals
Results
505.0ms8631×body80valid