Details

Time bar (total: 26.3s)

sample211.0ms

Algorithm
intervals
Results
76.0ms314×body80valid
45.0ms73×body10240exit
41.0ms60×body1280valid
15.0ms45×body640valid
5.0ms20×body320valid
2.0ms12×body160valid

simplify2.0s

Counts
1 → 1
Iterations
IterNodes
done5000
41391
3370
2124
147
019

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(* x (+ eps 1.0))
0.0b
(* x (- eps 1.0))
0.0b
(/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ eps 1.0))))
4.4b
(fma (exp (* x (- eps 1.0))) (+ (/ 1.0 eps) 1.0) (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ eps 1.0)))))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
69×add-sqr-sqrt
49×*-un-lft-identity
36×times-frac
33×add-cube-cbrt
19×distribute-rgt-in distribute-lft-in
18×prod-diff
14×exp-sum
13×difference-of-squares
10×add-cbrt-cube
9×associate-*r* add-exp-log
8×pow1
7×distribute-lft-out--
6×associate-*l* associate-/l*
5×associate-/r*
4×expm1-log1p-u associate-*r/ log1p-expm1-u add-log-exp
2×sub-neg flip3-- pow-prod-down prod-exp *-commutative cbrt-unprod flip-- unswap-sqr associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-+ div-sub div-exp flip-+ fma-udef div-inv distribute-lft-out
Counts
4 → 139
Calls
4 calls:
29.0ms
(* x (+ eps 1.0))
18.0ms
(* x (- eps 1.0))
58.0ms
(/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ eps 1.0))))
0.0ms
(fma (exp (* x (- eps 1.0))) (+ (/ 1.0 eps) 1.0) (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ eps 1.0)))))

series284.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* x (+ eps 1.0))
48.0ms
(* x (- eps 1.0))
49.0ms
(/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ eps 1.0))))
146.0ms
(fma (exp (* x (- eps 1.0))) (+ (/ 1.0 eps) 1.0) (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ eps 1.0)))))

simplify1.9s

Counts
151 → 151
Iterations
IterNodes
done5004
21916
1701
0286

prune958.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.9b

localize35.0ms

Local error

Found 3 expressions with local error:

0.1b
(* x (* x x))
3.0b
(/ (* x (* x x)) eps)
3.0b
(fma 2.7755575615628914e-17 (/ (* x (* x x)) eps) (* 1.0 (* x x)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
17×pow1 add-cbrt-cube add-exp-log
7×add-sqr-sqrt
6×*-un-lft-identity prod-exp add-cube-cbrt cbrt-unprod
5×pow-prod-up
3×expm1-log1p-u cbrt-undiv associate-/r* times-frac div-exp associate-*l* pow-prod-down log1p-expm1-u add-log-exp
1×pow2 clear-num frac-2neg pow-plus cube-unmult associate-*r* pow-sqr *-commutative fma-udef div-inv associate-/l* unswap-sqr
Counts
3 → 61
Calls
3 calls:
26.0ms
(* x (* x x))
35.0ms
(/ (* x (* x x)) eps)
1.0ms
(fma 2.7755575615628914e-17 (/ (* x (* x x)) eps) (* 1.0 (* x x)))

series169.0ms

Counts
3 → 9
Calls
3 calls:
62.0ms
(* x (* x x))
41.0ms
(/ (* x (* x x)) eps)
66.0ms
(fma 2.7755575615628914e-17 (/ (* x (* x x)) eps) (* 1.0 (* x x)))

simplify2.1s

Counts
70 → 70
Iterations
IterNodes
done5000
32861
2865
1220
093

prune388.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (log (exp (* x (* x x)))) eps)
0.1b
(* x (* x x))
1.3b
(log (exp (* x (* x x))))
2.8b
(fma 2.7755575615628914e-17 (/ (log (exp (* x (* x x)))) eps) (* 1.0 (* x x)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
23×pow1
18×add-sqr-sqrt times-frac
17×*-un-lft-identity add-cube-cbrt
15×log-pow
11×add-cbrt-cube add-exp-log
9×add-log-exp
6×associate-/l*
5×exp-prod exp-to-pow pow-prod-up
4×expm1-log1p-u log1p-expm1-u
3×log-prod associate-/r* associate-*l* pow-prod-down prod-exp cbrt-unprod
1×pow2 cbrt-undiv clear-num frac-2neg pow-plus cube-unmult div-exp rem-log-exp associate-*r* pow-sqr *-commutative fma-udef div-inv unswap-sqr
Counts
4 → 93
Calls
4 calls:
25.0ms
(/ (log (exp (* x (* x x)))) eps)
20.0ms
(* x (* x x))
3.0ms
(log (exp (* x (* x x))))
0.0ms
(fma 2.7755575615628914e-17 (/ (log (exp (* x (* x x)))) eps) (* 1.0 (* x x)))

series189.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ (log (exp (* x (* x x)))) eps)
41.0ms
(* x (* x x))
38.0ms
(log (exp (* x (* x x))))
71.0ms
(fma 2.7755575615628914e-17 (/ (log (exp (* x (* x x)))) eps) (* 1.0 (* x x)))

simplify2.4s

Counts
105 → 105
Iterations
IterNodes
done5031
33346
2689
1267
0125

prune567.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.2b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b
(* x (* x x))
1.3b
(log (* (cbrt (exp (* x (* x x)))) (cbrt (exp (* x (* x x))))))
1.3b
(log (cbrt (exp (* x (* x x)))))
2.8b
(fma 2.7755575615628914e-17 (/ (+ (log (* (cbrt (exp (* x (* x x)))) (cbrt (exp (* x (* x x)))))) (log (cbrt (exp (* x (* x x)))))) eps) (* 1.0 (* x x)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
27×pow1
13×add-exp-log
11×log-pow
9×add-cbrt-cube
8×add-sqr-sqrt
7×log-prod *-un-lft-identity pow1/3 pow-prod-up add-cube-cbrt
5×pow-prod-down
4×expm1-log1p-u prod-exp log1p-expm1-u add-log-exp
3×cbrt-prod rem-log-exp associate-*l* pow-sqr cbrt-unprod
2×pow2 pow-plus
1×cube-unmult associate-*r* *-commutative fma-udef unswap-sqr
Counts
4 → 75
Calls
4 calls:
24.0ms
(* x (* x x))
18.0ms
(log (* (cbrt (exp (* x (* x x)))) (cbrt (exp (* x (* x x))))))
4.0ms
(log (cbrt (exp (* x (* x x)))))
0.0ms
(fma 2.7755575615628914e-17 (/ (+ (log (* (cbrt (exp (* x (* x x)))) (cbrt (exp (* x (* x x)))))) (log (cbrt (exp (* x (* x x)))))) eps) (* 1.0 (* x x)))

series2.8s

Counts
4 → 12
Calls
4 calls:
63.0ms
(* x (* x x))
887.0ms
(log (* (cbrt (exp (* x (* x x)))) (cbrt (exp (* x (* x x))))))
954.0ms
(log (cbrt (exp (* x (* x x)))))
885.0ms
(fma 2.7755575615628914e-17 (/ (+ (log (* (cbrt (exp (* x (* x x)))) (cbrt (exp (* x (* x x)))))) (log (cbrt (exp (* x (* x x)))))) eps) (* 1.0 (* x x)))

simplify1.6s

Counts
87 → 87
Iterations
IterNodes
done5000
31241
2440
1182
0106

prune649.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.9b

regimes88.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.0b

bsearch224.0ms

Steps
ItersRangePoint
9
6.220956769517991e-07
20.852008069825544
1.4216286406050425

simplify6.0ms

Iterations
IterNodes
done32
132
026

end0.0ms

sample9.3s

Algorithm
intervals
Results
2.7s1723×body1280valid
2.2s2000×body10240exit
2.0s10052×body80valid
1.3s1285×body640valid
246.0ms669×body320valid
130.0ms347×body160valid