Details

Time bar (total: 14.1s)

sample83.0ms

Algorithm
intervals
Results
42.0ms77×body10240exit
15.0ms278×body80valid
4.0ms6×body1280valid
3.0ms9×body640valid
1.0ms6×body320valid
0.0ms3×body160valid

simplify10.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
089
1129
2199
3239
done239

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize25.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ 1.0 (exp x))
0.7b
(log (+ 1.0 (exp x)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
4×add-sqr-sqrt add-cube-cbrt log-prod add-log-exp
3×pow1 add-exp-log fma-def
2×expm1-log1p-u log-div flip3-+ add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out
1×+-commutative rem-log-exp sum-log log-pow
Counts
2 → 34
Calls
2 calls:
11.0ms
(+ 1.0 (exp x))
10.0ms
(log (+ 1.0 (exp x)))

series94.0ms

Counts
2 → 6
Calls
2 calls:
11.0ms
(+ 1.0 (exp x))
83.0ms
(log (+ 1.0 (exp x)))

simplify2.7s

Counts
40 → 40
Iterations

Useful iterations: done (2.7s)

IterNodesCost
065314
1138297
2315275
3711273
41611270
53432269
done5000268

prune127.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (exp x) 3)
0.6b
(/ (+ (pow 1.0 3) (pow (exp x) 3)) (fma 1.0 1.0 (* (exp x) (- (exp x) 1.0))))
0.7b
(log (/ (+ (pow 1.0 3) (pow (exp x) 3)) (fma 1.0 1.0 (* (exp x) (- (exp x) 1.0)))))
4.1b
(- (exp x) 1.0)

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
114×*-un-lft-identity
54×times-frac
44×add-sqr-sqrt
42×add-cube-cbrt
35×distribute-lft-out
31×unpow-prod-down log-prod cube-prod
9×add-exp-log prod-diff associate-/l*
7×sum-cubes add-cbrt-cube
6×pow1 add-log-exp
4×expm1-log1p-u pow-pow log1p-expm1-u
3×pow-unpow exp-prod fma-neg associate-/r*
2×div-exp rem-log-exp div-inv associate-/l/
1×cbrt-undiv cube-mult pow-to-exp sub-neg log-div flip3-- frac-2neg flip3-+ diff-log unpow3 pow-exp clear-num log-pow flip-- flip-+ distribute-lft-out-- rem-cube-cbrt difference-of-squares sqr-pow
Counts
4 → 155
Calls
4 calls:
9.0ms
(pow (exp x) 3)
121.0ms
(/ (+ (pow 1.0 3) (pow (exp x) 3)) (fma 1.0 1.0 (* (exp x) (- (exp x) 1.0))))
29.0ms
(log (/ (+ (pow 1.0 3) (pow (exp x) 3)) (fma 1.0 1.0 (* (exp x) (- (exp x) 1.0)))))
29.0ms
(- (exp x) 1.0)

series360.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(pow (exp x) 3)
105.0ms
(/ (+ (pow 1.0 3) (pow (exp x) 3)) (fma 1.0 1.0 (* (exp x) (- (exp x) 1.0))))
200.0ms
(log (/ (+ (pow 1.0 3) (pow (exp x) 3)) (fma 1.0 1.0 (* (exp x) (- (exp x) 1.0)))))
31.0ms
(- (exp x) 1.0)

simplify1.1s

Counts
167 → 167
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02333908
14993598
214533380
done50003265

prune515.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (exp x) (- (exp x) 1.0))
0.6b
(/ (+ (pow 1.0 3) (pow (exp 1) (* 3 x))) (fma 1.0 1.0 (* (exp x) (- (exp x) 1.0))))
0.7b
(log (/ (+ (pow 1.0 3) (pow (exp 1) (* 3 x))) (fma 1.0 1.0 (* (exp x) (- (exp x) 1.0)))))
4.1b
(- (exp x) 1.0)

rewrite239.0ms

Algorithm
rewrite-expression-head
Rules
60×*-un-lft-identity
48×add-sqr-sqrt
42×add-cube-cbrt
27×prod-diff
24×times-frac
16×log-prod
11×distribute-rgt-in distribute-lft-in
10×add-exp-log
8×add-cbrt-cube
7×pow1 distribute-lft-out
6×add-log-exp
5×associate-*r*
4×expm1-log1p-u log1p-expm1-u associate-/l*
3×sub-neg fma-neg associate-*l* associate-/r*
2×flip3-- associate-*r/ div-exp rem-log-exp flip-- div-inv associate-/l/ distribute-lft-out-- difference-of-squares
1×cbrt-undiv log-div frac-2neg flip3-+ diff-log pow-prod-down prod-exp clear-num log-pow *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 138
Calls
4 calls:
56.0ms
(* (exp x) (- (exp x) 1.0))
117.0ms
(/ (+ (pow 1.0 3) (pow (exp 1) (* 3 x))) (fma 1.0 1.0 (* (exp x) (- (exp x) 1.0))))
41.0ms
(log (/ (+ (pow 1.0 3) (pow (exp 1) (* 3 x))) (fma 1.0 1.0 (* (exp x) (- (exp x) 1.0)))))
16.0ms
(- (exp x) 1.0)

series467.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (exp x) (- (exp x) 1.0))
121.0ms
(/ (+ (pow 1.0 3) (pow (exp 1) (* 3 x))) (fma 1.0 1.0 (* (exp x) (- (exp x) 1.0))))
288.0ms
(log (/ (+ (pow 1.0 3) (pow (exp 1) (* 3 x))) (fma 1.0 1.0 (* (exp x) (- (exp x) 1.0)))))
23.0ms
(- (exp x) 1.0)

simplify2.8s

Counts
150 → 150
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
02353534
14913119
213672793
348612643
done50002643

prune571.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
7.5b
(log (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
3×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt log-prod *-un-lft-identity
2×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
1×rem-log-exp log-pow fma-udef
Counts
2 → 24
Calls
2 calls:
0.0ms
(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
1.0ms
(log (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

series156.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
127.0ms
(log (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

simplify1.2s

Counts
30 → 30
Iterations

Useful iterations: done (1.2s)

IterNodesCost
067459
1140444
2376387
31330385
done5000318

prune99.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

regimes45.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01826
12525
done2525

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.9s2432×body10240exit
625.0ms8361×body80valid
92.0ms256×body640valid
90.0ms134×body1280valid
41.0ms186×body320valid
14.0ms103×body160valid