Details

Time bar (total: 15.9s)

sample37.0ms

Algorithm
intervals
Results
6.0ms35×body1280valid
6.0ms169×body80valid
4.0ms32×body640valid
3.0ms116×body80nan
1.0ms11×body640nan
1.0ms12×body320valid
1.0ms7×body1280nan
0.0ms8×body160valid
0.0ms6×body320nan
0.0ms3×body160nan

simplify19.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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: 21.7b

localize9.0ms

Local error

Found 2 expressions with local error:

2.6b
(- 1.0 (/ (- x y) (- 1.0 y)))
5.2b
(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
138×add-sqr-sqrt
132×*-un-lft-identity
93×prod-diff
77×times-frac
68×add-cube-cbrt
34×difference-of-squares
32×distribute-lft-out--
6×log-prod associate-/r/
5×flip3-- flip--
4×add-log-exp
3×pow1 add-exp-log fma-neg div-inv
2×expm1-log1p-u log-div add-cbrt-cube log1p-expm1-u
1×sub-neg diff-log div-sub rem-log-exp log-pow associate--r-
Counts
2 → 133
Calls
2 calls:
46.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
48.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))

series143.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
90.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify80.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
07433586
123232540
250012306

prune215.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

5.6b
(/ (- x y) (- (pow 1.0 3) (pow y 3)))
5.6b
(/ (- x y) (- (pow 1.0 3) (pow y 3)))
16.1b
(* (fma 1.0 1.0 (fma y y (* 1.0 y))) (+ (- (/ (- x y) (- (pow 1.0 3) (pow y 3)))) (/ (- x y) (- (pow 1.0 3) (pow y 3)))))
21.7b
(/ (* (fma 1.0 1.0 (fma y y (* 1.0 y))) (- x y)) (- (pow 1.0 3) (pow y 3)))

rewrite7.0s

Algorithm
rewrite-expression-head
Rules
3572×*-un-lft-identity
3030×add-sqr-sqrt
2199×times-frac
1552×difference-of-squares
1432×unpow-prod-down cube-prod
1394×distribute-lft-out--
1005×associate-*r*
568×distribute-lft-neg-in distribute-rgt-out
448×sqr-pow
420×distribute-lft-out
419×distribute-rgt-neg-in
372×add-cube-cbrt
75×associate-/r*
42×difference-cubes
15×add-exp-log add-cbrt-cube
14×neg-mul-1 distribute-lft1-in associate-/r/
11×associate-/l*
10×flip3-- flip--
7×div-inv
6×pow1 associate-/l/
5×associate-*r/
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×frac-2neg associate-*l* clear-num
2×div-sub prod-exp cbrt-unprod
1×distribute-rgt-in distribute-lft-in flip3-+ pow-prod-down frac-add *-commutative flip-+ distribute-neg-frac unswap-sqr
Counts
4 → 1446
Calls
4 calls:
53.0ms
(/ (- x y) (- (pow 1.0 3) (pow y 3)))
57.0ms
(/ (- x y) (- (pow 1.0 3) (pow y 3)))
6.5s
(* (fma 1.0 1.0 (fma y y (* 1.0 y))) (+ (- (/ (- x y) (- (pow 1.0 3) (pow y 3)))) (/ (- x y) (- (pow 1.0 3) (pow y 3)))))
60.0ms
(/ (* (fma 1.0 1.0 (fma y y (* 1.0 y))) (- x y)) (- (pow 1.0 3) (pow y 3)))

series262.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(/ (- x y) (- (pow 1.0 3) (pow y 3)))
69.0ms
(/ (- x y) (- (pow 1.0 3) (pow y 3)))
44.0ms
(* (fma 1.0 1.0 (fma y y (* 1.0 y))) (+ (- (/ (- x y) (- (pow 1.0 3) (pow y 3)))) (/ (- x y) (- (pow 1.0 3) (pow y 3)))))
78.0ms
(/ (* (fma 1.0 1.0 (fma y y (* 1.0 y))) (- x y)) (- (pow 1.0 3) (pow y 3)))

simplify186.0ms

Algorithm
egg-herbie
Counts
1458 → 1458
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0122414810
1500114450

prune2.5s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))) (log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y)))))))
2.6b
(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
10.3b
(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))
11.7b
(log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y))))))

rewrite696.0ms

Algorithm
rewrite-expression-head
Rules
1120×add-sqr-sqrt
1014×*-un-lft-identity
832×prod-diff
633×unpow-prod-down cube-prod
624×times-frac
500×add-cube-cbrt
313×difference-of-squares
259×distribute-lft-out--
111×sqr-pow
81×cube-mult unpow3
72×log-prod
48×associate-/r/
33×associate--l+
28×flip3-- flip--
24×div-inv
19×pow1
16×fma-neg
15×log-pow
8×log-div
6×add-exp-log add-log-exp
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×difference-cubes associate--r+
2×associate--l- sub-neg flip3-+ diff-log rem-log-exp flip-+ associate--r-
Counts
4 → 1013
Calls
4 calls:
189.0ms
(- (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))) (log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y)))))))
154.0ms
(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
163.0ms
(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))
77.0ms
(log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
386.0ms
(- (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))) (log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y)))))))
194.0ms
(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
338.0ms
(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))
177.0ms
(log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y))))))

simplify296.0ms

Algorithm
egg-herbie
Counts
1025 → 1025
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
0182335298
1500126869

prune787.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ x (pow y 2)) (/ 1 y))
2.3b
(fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y))
2.9b
(log (fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y)))
9.4b
(/ x (pow y 2))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
636×times-frac
469×add-sqr-sqrt
440×*-un-lft-identity
428×add-cube-cbrt
364×prod-diff
141×unpow-prod-down
49×unpow2 sqr-pow
44×div-inv
28×fma-neg
15×difference-of-squares
10×add-exp-log
8×associate-/r*
6×add-cbrt-cube add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×log-prod div-exp associate-/l* distribute-lft-out--
1×cbrt-undiv pow-to-exp sub-neg flip3-- frac-2neg diff-log rem-log-exp pow-exp clear-num log-pow frac-sub flip-- fma-udef
Counts
4 → 500
Calls
4 calls:
75.0ms
(- (/ x (pow y 2)) (/ 1 y))
0.0ms
(fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y))
1.0ms
(log (fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y)))
8.0ms
(/ x (pow y 2))

series161.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (/ x (pow y 2)) (/ 1 y))
32.0ms
(fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y))
72.0ms
(log (fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y)))
24.0ms
(/ x (pow y 2))

simplify131.0ms

Algorithm
egg-herbie
Counts
512 → 512
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
0127610947
134836095
250016013

prune549.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes107.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 23.1b

bsearch171.0ms

Steps
ItersRangePoint
11
6031.575547282502
4.1240248748595035e+37
56360864.050822414
10
-15126611761059.418
-1.8689162216483415
-34737222.848607436

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05342
15342

end0.0ms

sample1.1s

Algorithm
intervals
Results
207.0ms5681×body80valid
147.0ms791×body1280valid
114.0ms817×body640valid
101.0ms3817×body80nan
57.0ms400×body1280nan
45.0ms463×body320valid
45.0ms398×body640nan
17.0ms215×body320nan
15.0ms248×body160valid
7.0ms131×body160nan