Details

Time bar (total: 6.0s)

sample70.0ms

Algorithm
intervals
Results
18.0ms192×body80valid
10.0ms140×body80nan
9.0ms25×body1280valid
7.0ms24×body640valid
4.0ms8×body160valid
3.0ms11×body1280nan
3.0ms11×body640nan
2.0ms12×body320nan
1.0ms7×body320valid
1.0ms5×body160nan

simplify19.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0196
1296
2416
3606
4786
5946
61096
71396
82146
92796
102796

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x y) (- 1.0 y))
2.0b
(- 1.0 (/ (- x y) (- 1.0 y)))
4.9b
(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
175×add-sqr-sqrt
169×*-un-lft-identity
102×times-frac
93×prod-diff
81×add-cube-cbrt
46×difference-of-squares
44×distribute-lft-out--
8×associate-/r/
7×flip3-- flip--
6×add-exp-log log-prod
5×associate-/r* add-cbrt-cube associate-/l* add-log-exp
4×pow1 div-inv
3×expm1-log1p-u fma-neg log1p-expm1-u
2×log-div div-sub associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp rem-log-exp clear-num log-pow associate--r-
Counts
3 → 187
Calls
3 calls:
12.0ms
(/ (- x y) (- 1.0 y))
27.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
28.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))

series176.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(/ (- x y) (- 1.0 y))
53.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
87.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify88.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
08473956
127662899
250012689

prune334.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- x y))
0.5b
(cbrt (- x y))
4.9b
(log (- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y)))))
10.2b
(- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt *-un-lft-identity
10×cbrt-prod
9×add-cube-cbrt
6×add-log-exp
5×pow1 add-exp-log
4×expm1-log1p-u cbrt-div flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×log-prod fma-neg prod-diff
2×log-div pow1/3 distribute-lft-out-- difference-of-squares
1×sub-neg diff-log rem-log-exp log-pow
Counts
4 → 70
Calls
4 calls:
2.0ms
(cbrt (- x y))
2.0ms
(cbrt (- x y))
2.0ms
(log (- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y)))))
2.0ms
(- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))

series443.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(cbrt (- x y))
148.0ms
(cbrt (- x y))
89.0ms
(log (- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y)))))
55.0ms
(- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))

simplify110.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 3 (100.0ms)

IterNodesCost
0342988
1996844
24583772
35001751

prune278.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

2.0b
(- 1.0 (/ (- x y) (- 1.0 y)))
2.0b
(- 1.0 (/ (- x y) (- 1.0 y)))
2.0b
(- 1.0 (/ (- x y) (- 1.0 y)))
4.9b
(log (* (* (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))) (cbrt (- 1.0 (/ (- x y) (- 1.0 y))))) (cbrt (- 1.0 (/ (- x y) (- 1.0 y))))))

rewrite298.0ms

Algorithm
rewrite-expression-head
Rules
394×add-sqr-sqrt
385×*-un-lft-identity
279×prod-diff
228×times-frac
199×add-cube-cbrt
96×difference-of-squares
93×distribute-lft-out--
54×cbrt-div
39×flip3-- flip--
28×frac-times
26×log-div
24×pow1
18×associate-/r/
15×log-pow
14×associate-*l/
10×add-exp-log add-log-exp
9×fma-neg pow1/3 pow-prod-up div-inv
8×associate-*r/
6×pow-plus
5×pow-prod-down
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×sub-neg diff-log div-sub rem-log-exp prod-exp pow-sqr associate--r-
2×pow2
1×log-prod pow3
Counts
4 → 396
Calls
4 calls:
26.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
25.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
26.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
189.0ms
(log (* (* (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))) (cbrt (- 1.0 (/ (- x y) (- 1.0 y))))) (cbrt (- 1.0 (/ (- x y) (- 1.0 y))))))

series255.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
51.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
57.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
92.0ms
(log (* (* (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))) (cbrt (- 1.0 (/ (- x y) (- 1.0 y))))) (cbrt (- 1.0 (/ (- x y) (- 1.0 y))))))

simplify136.0ms

Algorithm
egg-herbie
Counts
408 → 408
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
091311784
125408593
250027655

prune666.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (* (/ (- x y) (- 1.0 y)) (- (- x y))) (- 1.0 y))
2.0b
(fma 1 (* 1.0 1.0) (/ (* (/ (- x y) (- 1.0 y)) (- (- x y))) (- 1.0 y)))
4.9b
(log (/ (fma 1 (* 1.0 1.0) (/ (* (/ (- x y) (- 1.0 y)) (- (- x y))) (- 1.0 y))) (fma (/ 1.0 2) 2 (/ (- x y) (- 1.0 y)))))
8.5b
(/ (fma 1 (* 1.0 1.0) (/ (* (/ (- x y) (- 1.0 y)) (- (- x y))) (- 1.0 y))) (fma (/ 1.0 2) 2 (/ (- x y) (- 1.0 y))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt *-un-lft-identity
23×times-frac
21×add-cube-cbrt
18×add-exp-log
15×add-cbrt-cube
13×log-prod
8×associate-/r*
6×div-exp
5×pow1 cbrt-undiv associate-/l/
4×expm1-log1p-u log1p-expm1-u distribute-neg-frac associate-/l* add-log-exp
3×flip3-- flip-- div-inv
2×frac-times frac-2neg associate-*r/ rem-log-exp prod-exp clear-num associate-/r/ cbrt-unprod distribute-lft-out-- difference-of-squares
1×log-div distribute-frac-neg associate-*l/ log-pow distribute-rgt-neg-out fma-udef
Counts
4 → 102
Calls
4 calls:
22.0ms
(/ (* (/ (- x y) (- 1.0 y)) (- (- x y))) (- 1.0 y))
0.0ms
(fma 1 (* 1.0 1.0) (/ (* (/ (- x y) (- 1.0 y)) (- (- x y))) (- 1.0 y)))
2.0ms
(log (/ (fma 1 (* 1.0 1.0) (/ (* (/ (- x y) (- 1.0 y)) (- (- x y))) (- 1.0 y))) (fma (/ 1.0 2) 2 (/ (- x y) (- 1.0 y)))))
5.0ms
(/ (fma 1 (* 1.0 1.0) (/ (* (/ (- x y) (- 1.0 y)) (- (- x y))) (- 1.0 y))) (fma (/ 1.0 2) 2 (/ (- x y) (- 1.0 y))))

series406.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(/ (* (/ (- x y) (- 1.0 y)) (- (- x y))) (- 1.0 y))
86.0ms
(fma 1 (* 1.0 1.0) (/ (* (/ (- x y) (- 1.0 y)) (- (- x y))) (- 1.0 y)))
153.0ms
(log (/ (fma 1 (* 1.0 1.0) (/ (* (/ (- x y) (- 1.0 y)) (- (- x y))) (- 1.0 y))) (fma (/ 1.0 2) 2 (/ (- x y) (- 1.0 y)))))
109.0ms
(/ (fma 1 (* 1.0 1.0) (/ (* (/ (- x y) (- 1.0 y)) (- (- x y))) (- 1.0 y))) (fma (/ 1.0 2) 2 (/ (- x y) (- 1.0 y))))

simplify66.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05602043
122941829
250011818

prune385.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

regimes164.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 17.3b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03025
13025

end0.0ms

sample1.9s

Algorithm
intervals
Results
543.0ms5699×body80valid
287.0ms801×body1280valid
271.0ms3688×body80nan
216.0ms785×body640valid
107.0ms341×body1280nan
90.0ms449×body320valid
89.0ms362×body640nan
38.0ms266×body160valid
37.0ms200×body320nan
15.0ms118×body160nan