Details

Time bar (total: 18.5s)

sample76.0ms

Algorithm
intervals
Results
31.0ms52×body1280valid
10.0ms33×body640valid
9.0ms142×body80valid
3.0ms16×body320valid
2.0ms13×body160valid

simplify2.5s

Counts
1 → 1
Iterations
IterNodes
done5012
82654
7760
6224
598
449
328
220
115
09

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b
(+ 1.0 (exp (* -2.0 x)))
3.1b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
99×*-un-lft-identity
68×add-sqr-sqrt
63×add-cube-cbrt
61×times-frac
54×prod-diff
18×fma-neg
17×distribute-lft-out
10×associate-/r/
7×add-log-exp
6×flip3-+ flip-+
5×add-cbrt-cube add-exp-log div-inv
4×associate-/r*
3×expm1-log1p-u pow1 fma-def log1p-expm1-u associate-/l*
2×difference-of-squares
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg flip3-- diff-log div-exp flip-- distribute-lft-out--
Counts
3 → 141
Calls
3 calls:
11.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
10.0ms
(+ 1.0 (exp (* -2.0 x)))
92.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series166.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
19.0ms
(+ 1.0 (exp (* -2.0 x)))
106.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify2.6s

Counts
150 → 150
Iterations
IterNodes
done5000
33707
21131
1419
0180

prune685.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (exp (* -2.0 x)))
0.0b
(+ 1.0 (exp (* -2.0 x)))
0.0b
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
3.1b
(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
88×*-un-lft-identity
64×times-frac
54×add-sqr-sqrt
42×add-cube-cbrt
24×swap-sqr
20×distribute-lft-out
18×associate-*r* associate-*l*
16×add-cbrt-cube add-exp-log
11×pow1
10×add-log-exp
8×associate-/r/
6×fma-def flip3-+ flip-+
4×expm1-log1p-u cbrt-undiv div-exp prod-exp cbrt-unprod log1p-expm1-u div-inv unswap-sqr
2×+-commutative sum-log
1×pow2 frac-times sub-neg pow-plus flip3-- fma-neg diff-log prod-diff pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip-- difference-of-squares
Counts
4 → 141
Calls
4 calls:
13.0ms
(+ 1.0 (exp (* -2.0 x)))
11.0ms
(+ 1.0 (exp (* -2.0 x)))
104.0ms
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
45.0ms
(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

series237.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ 1.0 (exp (* -2.0 x)))
18.0ms
(+ 1.0 (exp (* -2.0 x)))
62.0ms
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
128.0ms
(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

simplify2.2s

Counts
153 → 153
Iterations
IterNodes
done5001
22004
1601
0187

prune888.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (+ 1.0 (exp (* -2.0 x))))
0.4b
(cbrt (+ 1.0 (exp (* -2.0 x))))
0.4b
(cbrt (+ 1.0 (exp (* -2.0 x))))
26.9b
(fma (/ (sqrt 2.0) (* (cbrt (+ 1.0 (exp (* -2.0 x)))) (cbrt (+ 1.0 (exp (* -2.0 x)))))) (/ (sqrt 2.0) (cbrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-div
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 flip-+ distribute-lft-out
1×fma-udef
Counts
4 → 58
Calls
4 calls:
4.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
4.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
5.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
0.0ms
(fma (/ (sqrt 2.0) (* (cbrt (+ 1.0 (exp (* -2.0 x)))) (cbrt (+ 1.0 (exp (* -2.0 x)))))) (/ (sqrt 2.0) (cbrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
167.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
193.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
180.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
607.0ms
(fma (/ (sqrt 2.0) (* (cbrt (+ 1.0 (exp (* -2.0 x)))) (cbrt (+ 1.0 (exp (* -2.0 x)))))) (/ (sqrt 2.0) (cbrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

simplify2.3s

Counts
70 → 70
Iterations
IterNodes
done5000
32661
2703
1232
099

prune482.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b
(* x (* x x))
0.1b
(* (* x x) (* x x))
10.5b
(fma (* x (* x x)) 0.33333333333333337 (* 5.551115123125783e-17 (* (* x x) (* x x))))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
128×pow1
41×pow-prod-up
26×pow-prod-down
23×pow-sqr
20×add-cbrt-cube add-exp-log
19×pow-plus
14×pow2
11×prod-exp cbrt-unprod
5×add-sqr-sqrt
4×*-un-lft-identity associate-*l* add-cube-cbrt
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×associate-*r* *-commutative unswap-sqr
1×cube-unmult swap-sqr fma-udef
Counts
3 → 101
Calls
3 calls:
28.0ms
(* x (* x x))
42.0ms
(* (* x x) (* x x))
1.0ms
(fma (* x (* x x)) 0.33333333333333337 (* 5.551115123125783e-17 (* (* x x) (* x x))))

series214.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(* x (* x x))
40.0ms
(* (* x x) (* x x))
125.0ms
(fma (* x (* x x)) 0.33333333333333337 (* 5.551115123125783e-17 (* (* x x) (* x x))))

simplify1.8s

Counts
110 → 110
Iterations
IterNodes
done5001
31326
2401
1190
085

prune292.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes592.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 28.9b

bsearch2.0ms

simplify7.0ms

Iterations
IterNodes
done37
137
028

end0.0ms

sample1.9s

Algorithm
intervals
Results
873.0ms1684×body1280valid
348.0ms1247×body640valid
285.0ms4140×body80valid
155.0ms627×body320valid
29.0ms302×body160valid