Details

Time bar (total: 9.2s)

sample164.0ms

Algorithm
intervals
Results
99.0ms110×body1280valid
38.0ms83×body640valid
9.0ms39×body320valid
5.0ms256×pre80true
2.0ms18×body160valid
0.0ms6×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1115
2115

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 62.1b

Counts
2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.4b
(log (+ 1.0 x))
5.6b
(log (- 1.0 x))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
17×add-sqr-sqrt
16×times-frac
15×pow1 add-cube-cbrt
12×log-pow
9×log-prod
7×add-exp-log
6×log-div
5×add-cbrt-cube
4×associate-/r* associate-/l*
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×flip3-- div-sub rem-log-exp flip--
1×cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
3 → 75
Calls
3 calls:
6.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
3.0ms
(log (+ 1.0 x))
4.0ms
(log (- 1.0 x))

series208.0ms

Counts
3 → 9
Calls
3 calls:
121.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
44.0ms
(log (+ 1.0 x))
43.0ms
(log (- 1.0 x))

simplify46.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0452686
11669638
25001623

prune189.0ms

Filtered
84 candidates to 61 candidates (72.6%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New78684
Fresh000
Picked101
Done000
Total79685

Merged error: 59.8b

Counts
85 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
0.0b
(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
0.0b
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
5.6b
(log (- 1.0 x))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
92×times-frac
84×add-sqr-sqrt
68×associate-*r*
56×unpow-prod-down
50×*-un-lft-identity
48×add-cube-cbrt
30×add-exp-log
24×unpow2 sqr-pow
17×unswap-sqr
11×pow1 add-cbrt-cube
10×div-exp prod-exp
6×pow-to-exp pow-exp
5×log-prod log-pow
4×expm1-log1p-u log-div log1p-expm1-u associate-/l* add-log-exp
3×associate-*l* associate-/r*
2×cbrt-undiv flip3-- div-sub flip-- cbrt-unprod div-inv
1×frac-2neg associate-*r/ rem-log-exp pow-prod-down clear-num *-commutative fma-udef distribute-lft-out-- difference-of-squares
Counts
4 → 175
Calls
4 calls:
1.0ms
(fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
6.0ms
(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
19.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
4.0ms
(log (- 1.0 x))

series275.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
136.0ms
(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
49.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
47.0ms
(log (- 1.0 x))

simplify98.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
09391568
138671383
250011383

prune454.0ms

Filtered
187 candidates to 126 candidates (67.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1861187
Fresh235
Picked101
Done000
Total1894193

Merged error: 0.0b

Counts
193 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
0.0b
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
178×times-frac
159×add-sqr-sqrt
136×associate-*r*
112×unpow-prod-down
95×*-un-lft-identity
83×add-cube-cbrt
52×add-exp-log
48×unpow2 sqr-pow
34×unswap-sqr
20×prod-exp
19×div-exp
16×add-cbrt-cube
12×pow1 pow-to-exp pow-exp
8×distribute-lft-out--
6×associate-*l* associate-/l* add-log-exp
4×expm1-log1p-u log-pow cbrt-unprod log1p-expm1-u difference-of-squares
3×cbrt-undiv associate-/r* div-inv
2×associate-*r/ pow-prod-down *-commutative associate-/l/
1×+-commutative flip3-- fma-def frac-2neg flip3-+ div-sub clear-num sum-log flip-- flip-+
Counts
4 → 282
Calls
4 calls:
4.0ms
(+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
19.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
20.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
9.0ms
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

series322.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
49.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
52.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
121.0ms
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

simplify99.0ms

Algorithm
egg-herbie
Counts
294 → 294
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
08242689
139592259
250012256

prune699.0ms

Filtered
294 candidates to 187 candidates (63.6%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2913294
Fresh033
Picked101
Done000
Total2926298

Merged error: 0.0b

Counts
298 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b
(/ 1 (/ (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
0.0b
(/ (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
322×times-frac
248×add-sqr-sqrt
196×*-un-lft-identity
148×add-cube-cbrt
136×associate-*r*
112×unpow-prod-down
63×add-exp-log
48×unpow2 sqr-pow
34×unswap-sqr
32×distribute-lft-out--
30×associate-/r*
26×div-exp
25×pow1
21×add-cbrt-cube
20×prod-exp
16×log-pow difference-of-squares
12×pow-to-exp pow-exp
11×associate-/r/
8×div-inv
6×cbrt-undiv associate-*l* associate-/l*
5×flip3-- flip--
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
2×rec-exp frac-2neg 1-exp associate-*r/ pow-prod-down clear-num *-commutative
1×pow-flip inv-pow
Counts
4 → 389
Calls
4 calls:
20.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
23.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
11.0ms
(/ 1 (/ (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
7.0ms
(/ (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

series346.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
50.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
119.0ms
(/ 1 (/ (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
126.0ms
(/ (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

simplify161.0ms

Algorithm
egg-herbie
Counts
401 → 401
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010535941
149385415
250015415

prune933.0ms

Filtered
401 candidates to 239 candidates (59.6%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New4001401
Fresh145
Picked011
Done000
Total4016407

Merged error: 0.0b

Counts
407 → 6

regimes29.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02217
12217

end0.0ms

sample4.9s

Algorithm
intervals
Results
3.0s3305×body1280valid
1.2s2587×body640valid
291.0ms1248×body320valid
135.0ms8000×pre80true
89.0ms642×body160valid
15.0ms218×body80valid