Details

Time bar (total: 8.6s)

sample226.0ms

Algorithm
intervals
Results
136.0ms101×body1280valid
51.0ms80×body640valid
14.0ms47×body320valid
5.0ms256×pre80true
4.0ms21×body160valid
0.0ms7×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0105
1115
2115

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
6.3b
(log (- 1.0 x))
6.3b
(log (+ 1.0 x))

rewrite14.0ms

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:
7.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
3.0ms
(log (- 1.0 x))
2.0ms
(log (+ 1.0 x))

series210.0ms

Counts
3 → 9
Calls
3 calls:
125.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
40.0ms
(log (- 1.0 x))
44.0ms
(log (+ 1.0 x))

simplify44.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0452686
11669638
25002623

prune215.0ms

Filtered
84 candidates to 61 candidates (72.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 58.7b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 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))))))
6.3b
(log (- 1.0 x))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
92×times-frac
83×add-sqr-sqrt
68×associate-*r*
56×unpow-prod-down
49×*-un-lft-identity
47×add-cube-cbrt
29×add-exp-log
24×unpow2 sqr-pow
17×unswap-sqr
10×pow1 div-exp prod-exp add-cbrt-cube
6×pow-to-exp pow-exp
5×log-prod log-pow
4×log-div associate-/l*
3×expm1-log1p-u associate-*l* associate-/r* log1p-expm1-u add-log-exp
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 distribute-lft-out-- difference-of-squares
Counts
3 → 165
Calls
3 calls:
28.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
7.0ms
(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
3.0ms
(log (- 1.0 x))

series245.0ms

Counts
3 → 9
Calls
3 calls:
57.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
139.0ms
(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
48.0ms
(log (- 1.0 x))

simplify91.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
09281453
138371286
250011286

prune483.0ms

Filtered
174 candidates to 116 candidates (66.7%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 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
(/ (- (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))))))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
178×times-frac
158×add-sqr-sqrt
136×associate-*r*
112×unpow-prod-down
94×*-un-lft-identity
82×add-cube-cbrt
51×add-exp-log
48×unpow2 sqr-pow
34×unswap-sqr
20×prod-exp
19×div-exp
15×add-cbrt-cube
12×pow-to-exp pow-exp
11×pow1
8×distribute-lft-out--
6×associate-*l* associate-/l*
4×log-pow cbrt-unprod difference-of-squares
3×cbrt-undiv expm1-log1p-u associate-/r* log1p-expm1-u div-inv add-log-exp
2×associate-*r/ pow-prod-down *-commutative associate-/l/
1×flip3-- frac-2neg div-sub clear-num flip--
Counts
3 → 268
Calls
3 calls:
24.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
27.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
23.0ms
(/ (- (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))))))

series227.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
47.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
127.0ms
(/ (- (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))))))

simplify84.0ms

Algorithm
egg-herbie
Counts
277 → 277
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
07532429
131742138
250012135

prune756.0ms

Filtered
277 candidates to 173 candidates (62.5%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b
(* (+ (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (log 1.0)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
0.0b
(* (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
27.5b
(/ (- (* (log 1.0) (log 1.0)) (* (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (* (+ (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (log 1.0)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
84×add-sqr-sqrt times-frac
74×associate-*r*
56×unpow-prod-down
49×*-un-lft-identity
46×add-cube-cbrt
36×add-exp-log
24×unpow2 sqr-pow
19×unswap-sqr
18×add-cbrt-cube
16×pow1
13×prod-exp
11×div-exp associate-*l*
8×flip3-+ flip-+
6×pow-to-exp associate-*l/ pow-exp
5×cbrt-unprod
4×expm1-log1p-u frac-times log1p-expm1-u associate-/l* add-log-exp
3×cbrt-undiv associate-*r/ swap-sqr pow-prod-down *-commutative
2×distribute-rgt-in distribute-lft-in associate-/r/ fma-udef div-inv associate-/l/ distribute-lft-out difference-of-squares
1×pow2 flip3-- frac-2neg pow-plus div-sub clear-num associate-/r* pow-sqr log-pow pow-prod-up flip--
Counts
4 → 205
Calls
4 calls:
24.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
11.0ms
(* (+ (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (log 1.0)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
14.0ms
(* (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
13.0ms
(/ (- (* (log 1.0) (log 1.0)) (* (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (* (+ (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (log 1.0)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))

series424.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
124.0ms
(* (+ (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (log 1.0)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
48.0ms
(* (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
197.0ms
(/ (- (* (log 1.0) (log 1.0)) (* (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (* (+ (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (log 1.0)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))

simplify60.0ms

Algorithm
egg-herbie
Counts
217 → 217
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
011033176
150012679

prune705.0ms

Filtered
217 candidates to 143 candidates (65.9%)
Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes67.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01816
11816

end0.0ms

sample4.4s

Algorithm
intervals
Results
2.8s3333×body1280valid
1.0s2508×body640valid
253.0ms1273×body320valid
98.0ms8000×pre80true
76.0ms663×body160valid
10.0ms223×body80valid