Details

Time bar (total: 23.9s)

sample129.0ms

Algorithm
intervals
Results
68.0ms77×body1280valid
21.0ms45×body640valid
16.0ms27×body2560valid
8.0ms27×body320valid
6.0ms69×body80valid
2.0ms11×body160valid

simplify5.0ms

Counts
1 → 1
Iterations
IterNodes
311
211
110
07

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.6b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot 1 x)
0.5b
(+ x (hypot 1 x))
4.0b
(log (+ x (hypot 1 x)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
5×add-sqr-sqrt add-cube-cbrt add-log-exp
4×pow1 log-prod add-exp-log
3×expm1-log1p-u fma-def add-cbrt-cube insert-posit16 log1p-expm1-u
2×log-div flip3-+ flip-+ distribute-lft-out
1×+-commutative hypot-udef sum-log rem-log-exp log-pow
Counts
3 → 47
Calls
3 calls:
0.0ms
(hypot 1 x)
11.0ms
(+ x (hypot 1 x))
8.0ms
(log (+ x (hypot 1 x)))

series357.0ms

Counts
3 → 9
Calls
3 calls:
69.0ms
(hypot 1 x)
98.0ms
(+ x (hypot 1 x))
190.0ms
(log (+ x (hypot 1 x)))

simplify2.2s

Counts
56 → 56
Iterations
IterNodes
44269
31489
2592
1243
0108

prune578.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (* x x) x)
0.3b
(fma -1/6 (* (* x x) x) x)
20.3b
(fma 3/40 (pow x 5) (fma -1/6 (* (* x x) x) x))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
22×pow1
8×add-cbrt-cube add-exp-log
6×pow-plus pow-prod-up
5×add-sqr-sqrt
4×*-un-lft-identity add-cube-cbrt
3×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×pow2 pow-sqr fma-udef
1×associate-*l* pow3 *-commutative unswap-sqr
Counts
3 → 53
Calls
3 calls:
15.0ms
(* (* x x) x)
0.0ms
(fma -1/6 (* (* x x) x) x)
0.0ms
(fma 3/40 (pow x 5) (fma -1/6 (* (* x x) x) x))

series597.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(* (* x x) x)
470.0ms
(fma -1/6 (* (* x x) x) x)
67.0ms
(fma 3/40 (pow x 5) (fma -1/6 (* (* x x) x) x))

simplify3.2s

Counts
62 → 62
Iterations
IterNodes
45571
31215
2332
1132
070

prune473.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ -1/8 (* (* x x) x))
0.3b
(/ -1/16 (pow x 5))
11.4b
(log (- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x))))
19.4b
(- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))

rewrite445.0ms

Algorithm
rewrite-expression-head
Rules
178×*-un-lft-identity
138×add-sqr-sqrt
135×times-frac
118×add-cube-cbrt
100×prod-diff
59×unpow-prod-down
27×distribute-lft-out
25×fma-neg
21×sqr-pow
19×add-exp-log
15×add-cbrt-cube
9×log-prod add-log-exp
8×associate-/r* difference-of-squares
7×div-inv
6×div-exp frac-sub associate-/l*
5×pow1 log-div
4×expm1-log1p-u cbrt-undiv insert-posit16 log1p-expm1-u distribute-lft-out--
3×prod-exp cbrt-unprod
2×clear-num frac-2neg flip3-+ flip3-- diff-log frac-add flip-+ flip--
1×pow-to-exp sum-log sub-neg rem-log-exp pow-exp log-pow associate--r+
Counts
4 → 251
Calls
4 calls:
14.0ms
(/ -1/8 (* (* x x) x))
5.0ms
(/ -1/16 (pow x 5))
200.0ms
(log (- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x))))
221.0ms
(- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))

series339.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ -1/8 (* (* x x) x))
70.0ms
(/ -1/16 (pow x 5))
150.0ms
(log (- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x))))
71.0ms
(- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))

simplify1.2s

Counts
263 → 263
Iterations
IterNodes
22554
1840
0361

prune2.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

8.5b
(log (sqrt (- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))))
8.5b
(log (sqrt (- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))))
19.4b
(- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))
19.4b
(- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))

rewrite617.0ms

Algorithm
rewrite-expression-head
Rules
318×*-un-lft-identity
238×add-sqr-sqrt
222×times-frac
200×prod-diff
198×add-cube-cbrt
94×unpow-prod-down
54×distribute-lft-out
50×fma-neg
34×sqr-pow
24×log-prod
18×sqrt-prod
16×difference-of-squares
14×add-log-exp
12×frac-sub
10×log-div sqrt-div div-inv
8×pow1 distribute-lft-out--
6×add-exp-log log-pow
4×expm1-log1p-u flip3-+ flip3-- add-cbrt-cube diff-log frac-add flip-+ insert-posit16 log1p-expm1-u flip--
2×sum-log sub-neg sqrt-pow1 pow1/2 rem-log-exp associate--r+
Counts
4 → 364
Calls
4 calls:
112.0ms
(log (sqrt (- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))))
130.0ms
(log (sqrt (- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))))
178.0ms
(- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))
189.0ms
(- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))

series431.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(log (sqrt (- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))))
125.0ms
(log (sqrt (- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))))
91.0ms
(- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))
92.0ms
(- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))

simplify1.1s

Counts
376 → 376
Iterations
IterNodes
22013
1698
0315

prune4.8s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes42.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.6b

bsearch162.0ms

Steps
ItersRangePoint
10
1.4996160052323843e-06
45385424.466692075
0.007920435518071383
10
-8.26555774309129e+15
-0.755072844465923
-1.056937052753612

simplify9.0ms

Iterations
IterNodes
233
133
030

end0.0ms

sample4.7s

Algorithm
intervals
Results
2.5s2330×body1280valid
891.0ms1568×body640valid
574.0ms787×body2560valid
299.0ms822×body320valid
174.0ms2106×body80valid
77.0ms387×body160valid