Details

Time bar (total: 38.7s)

sample361.0ms

Algorithm
intervals
Results
122.0ms393×body80valid
101.0ms84×body10240exit
54.0ms53×body1280valid
28.0ms45×body640valid
6.0ms15×body320valid
2.0ms8×body160valid

simplify2.9s

Counts
1 → 1
Iterations
IterNodes
done5000
41338
3370
2124
147
019

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.9b

localize68.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1.0 eps) x)
0.0b
(* (- 1.0 eps) x)
0.0b
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
1.7b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite305.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
76×exp-neg frac-times
57×neg-sub0 exp-diff
42×associate-*l/
38×associate-*r/
31×flip3-+ flip-+
29×flip3-- flip--
19×un-div-inv
18×add-sqr-sqrt
16×*-un-lft-identity
13×associate-*l*
10×pow1 add-cube-cbrt add-cbrt-cube
9×add-exp-log associate-*r*
6×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×distribute-lft-out
1×sub-neg fma-neg diff-log prod-diff distribute-lft-out-- difference-of-squares
Counts
4 → 174
Calls
4 calls:
27.0ms
(* (+ 1.0 eps) x)
32.0ms
(* (- 1.0 eps) x)
112.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
113.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series657.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (+ 1.0 eps) x)
68.0ms
(* (- 1.0 eps) x)
89.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
436.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify4.9s

Counts
186 → 186
Iterations
IterNodes
done5000
24820
11300
0400

prune1.7s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize33.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (* x x) x)
5.5b
(fma (* (* x x) x) 0.6666666666666667 (- 2.0 (* (* 1.0 x) x)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
21×pow1
7×add-exp-log add-cbrt-cube
6×pow-plus pow-prod-up
4×add-sqr-sqrt
3×add-cube-cbrt *-un-lft-identity associate-*r* pow-prod-down prod-exp cbrt-unprod
2×pow2 expm1-log1p-u pow-sqr log1p-expm1-u add-log-exp
1×associate-*l* pow3 *-commutative fma-udef unswap-sqr
Counts
2 → 40
Calls
2 calls:
38.0ms
(* (* x x) x)
1.0ms
(fma (* (* x x) x) 0.6666666666666667 (- 2.0 (* (* 1.0 x) x)))

series149.0ms

Counts
2 → 6
Calls
2 calls:
62.0ms
(* (* x x) x)
86.0ms
(fma (* (* x x) x) 0.6666666666666667 (- 2.0 (* (* 1.0 x) x)))

simplify2.8s

Counts
46 → 46
Iterations
IterNodes
done5004
31184
2299
1127
058

prune268.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize60.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x x) x)
0.1b
(* (* x x) x)
5.5b
(fma (cbrt (* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))) 0.6666666666666667 (- 2.0 (* (* 1.0 x) x)))
13.9b
(cbrt (* (* (* x x) x) (* (* (* x x) x) (* (* x x) x))))

rewrite953.0ms

Algorithm
rewrite-expression-head
Rules
42×pow1
14×add-exp-log add-cbrt-cube
12×pow-plus pow-prod-up
8×add-sqr-sqrt pow-prod-down
6×add-cube-cbrt *-un-lft-identity associate-*r* prod-exp cbrt-unprod
5×pow3
4×pow2 expm1-log1p-u pow-sqr log1p-expm1-u add-log-exp
2×associate-*l* *-commutative rem-cbrt-cube unswap-sqr
1×cbrt-prod cube-unmult pow1/3 fma-udef
Counts
4 → 83
Calls
4 calls:
39.0ms
(* (* x x) x)
33.0ms
(* (* x x) x)
1.0ms
(fma (cbrt (* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))) 0.6666666666666667 (- 2.0 (* (* 1.0 x) x)))
876.0ms
(cbrt (* (* (* x x) x) (* (* (* x x) x) (* (* x x) x))))

series295.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (* x x) x)
62.0ms
(* (* x x) x)
92.0ms
(fma (cbrt (* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))) 0.6666666666666667 (- 2.0 (* (* 1.0 x) x)))
77.0ms
(cbrt (* (* (* x x) x) (* (* (* x x) x) (* (* x x) x))))

simplify6.0s

Counts
95 → 95
Iterations
IterNodes
done5002
43538
31040
2369
1170
077

prune545.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

localize89.0ms

Local error

Found 4 expressions with local error:

5.5b
(fma (* (* x x) x) 0.6666666666666667 (- 2.0 (* (* 1.0 x) x)))
9.5b
(cbrt (fma (* (* x x) x) 0.6666666666666667 (- 2.0 (* (* 1.0 x) x))))
9.5b
(cbrt (fma (* (* x x) x) 0.6666666666666667 (- 2.0 (* (* 1.0 x) x))))
9.5b
(cbrt (fma (* (* x x) x) 0.6666666666666667 (- 2.0 (* (* 1.0 x) x))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
1.0ms
(fma (* (* x x) x) 0.6666666666666667 (- 2.0 (* (* 1.0 x) x)))
2.0ms
(cbrt (fma (* (* x x) x) 0.6666666666666667 (- 2.0 (* (* 1.0 x) x))))
2.0ms
(cbrt (fma (* (* x x) x) 0.6666666666666667 (- 2.0 (* (* 1.0 x) x))))
2.0ms
(cbrt (fma (* (* x x) x) 0.6666666666666667 (- 2.0 (* (* 1.0 x) x))))

series932.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(fma (* (* x x) x) 0.6666666666666667 (- 2.0 (* (* 1.0 x) x)))
275.0ms
(cbrt (fma (* (* x x) x) 0.6666666666666667 (- 2.0 (* (* 1.0 x) x))))
277.0ms
(cbrt (fma (* (* x x) x) 0.6666666666666667 (- 2.0 (* (* 1.0 x) x))))
296.0ms
(cbrt (fma (* (* x x) x) 0.6666666666666667 (- 2.0 (* (* 1.0 x) x))))

simplify3.1s

Counts
61 → 61
Iterations
IterNodes
done5019
32343
2578
1200
091

prune635.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes217.0ms

Accuracy

97.1% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.5b

bsearch352.0ms

Steps
ItersRangePoint
9
0.0918573770391371
263824.51516633737
120.35338214257132

simplify13.0ms

Iterations
IterNodes
done38
138
030

end0.0ms

sample11.3s

Algorithm
intervals
Results
4.5s1923×body10240exit
2.6s9952×body80valid
2.1s1775×body1280valid
1.0s1220×body640valid
285.0ms638×body320valid
97.0ms356×body160valid