Details

Time bar (total: 19.4s)

sample195.0ms

Algorithm
intervals
Results
46.0ms63×body1280valid
42.0ms63×body10240exit
30.0ms20×body320valid
30.0ms299×body80valid
17.0ms39×body640valid
3.0ms13×body160valid

simplify1.4s

Counts
1 → 1
Iterations
IterNodes
done5001
42356
3395
2124
147
019

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (- 1.0 eps) x)))
0.2b
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.2b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
3.2b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite263.0ms

Algorithm
rewrite-expression-head
Rules
81×exp-neg frac-sub
80×frac-times
61×neg-sub0 exp-diff
40×associate-*l/ associate-*r/
31×flip3-- flip--
30×flip3-+ flip-+
20×un-div-inv
18×add-sqr-sqrt
13×*-un-lft-identity
10×associate-*l*
9×add-cube-cbrt
8×pow1 add-cbrt-cube add-log-exp
6×exp-prod associate-*r* add-exp-log
4×expm1-log1p-u log1p-expm1-u
2×pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr rem-exp-log
1×distribute-lft-neg-in neg-mul-1 sub-neg distribute-rgt-neg-in times-frac fma-neg diff-log prod-diff neg-log distribute-lft-out distribute-lft-out--
Counts
4 → 178
Calls
4 calls:
15.0ms
(exp (- (* (- 1.0 eps) x)))
77.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
85.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
66.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series538.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(exp (- (* (- 1.0 eps) x)))
79.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
82.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
325.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify692.0ms

Counts
190 → 190
Iterations
IterNodes
done5000
11366
0393

prune967.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma (pow x 3) 0.6666666666666667 2.0)
6.6b
(- (fma (pow x 3) 0.6666666666666667 2.0) (* (* x x) 1.0))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt add-log-exp
3×fma-neg prod-diff
2×expm1-log1p-u pow1 add-cbrt-cube add-exp-log fma-udef log1p-expm1-u
1×sub-neg flip3-- diff-log associate--l+ flip--
Counts
2 → 31
Calls
2 calls:
0.0ms
(fma (pow x 3) 0.6666666666666667 2.0)
5.0ms
(- (fma (pow x 3) 0.6666666666666667 2.0) (* (* x x) 1.0))

series172.0ms

Counts
2 → 6
Calls
2 calls:
120.0ms
(fma (pow x 3) 0.6666666666666667 2.0)
52.0ms
(- (fma (pow x 3) 0.6666666666666667 2.0) (* (* x x) 1.0))

simplify611.0ms

Counts
37 → 37
Iterations
IterNodes
done5001
2588
1132
056

prune189.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0)))) (cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0)))))
11.1b
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))
11.1b
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))
11.1b
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 flip-+
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 95
Calls
4 calls:
52.0ms
(* (cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0)))) (cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0)))))
5.0ms
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))
5.0ms
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))
5.0ms
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))

series956.0ms

Counts
4 → 12
Calls
4 calls:
263.0ms
(* (cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0)))) (cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0)))))
234.0ms
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))
209.0ms
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))
250.0ms
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))

simplify849.0ms

Counts
107 → 107
Iterations
IterNodes
done5001
21781
1451
0180

prune908.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize57.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 2.0)
6.6b
(- (fma (pow x 3) 0.1111111111111111 1) (* 0.16666666666666666 (pow x 2)))
11.1b
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))
11.1b
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×add-log-exp
4×expm1-log1p-u pow1 cbrt-div add-cbrt-cube add-exp-log log1p-expm1-u
3×fma-neg pow1/3 prod-diff
2×flip3-+ flip-+
1×sub-neg flip3-- diff-log associate--l+ fma-udef flip--
Counts
4 → 64
Calls
4 calls:
1.0ms
(cbrt 2.0)
5.0ms
(- (fma (pow x 3) 0.1111111111111111 1) (* 0.16666666666666666 (pow x 2)))
2.0ms
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))
3.0ms
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))

series533.0ms

Counts
4 → 10
Calls
4 calls:
0.0ms
(cbrt 2.0)
72.0ms
(- (fma (pow x 3) 0.1111111111111111 1) (* 0.16666666666666666 (pow x 2)))
245.0ms
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))
216.0ms
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))

simplify911.0ms

Counts
74 → 74
Iterations
IterNodes
done5000
21500
1357
0149

prune690.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

regimes165.0ms

Accuracy

96% (0.7b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 17.2b

bsearch323.0ms

Steps
ItersRangePoint
10
1.5375988180684124e-09
886.592532349027
162.56045792773165

simplify14.0ms

Iterations
IterNodes
done57
357
252
146
033

end0.0ms

sample8.8s

Algorithm
intervals
Results
3.2s1832×body10240exit
2.1s1703×body1280valid
1.9s9991×body80valid
750.0ms1290×body640valid
214.0ms599×body320valid
70.0ms314×body160valid