Details

Time bar (total: 14.9s)

sample43.0ms

Algorithm
intervals
Results
14.0ms46×body1280valid
7.0ms42×body640valid
7.0ms132×body80valid
4.0ms29×body320valid
1.0ms7×body160valid

simplify131.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (+ x 1.0) (- x 1.0))
2.3b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
81×*-un-lft-identity
40×times-frac
35×add-sqr-sqrt
18×distribute-lft-out--
14×distribute-lft-out
13×add-cube-cbrt
9×difference-of-squares
5×associate-/r*
4×add-exp-log add-cbrt-cube associate-/l* add-log-exp
2×pow1 flip3-- associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-exp clear-num frac-sub flip-+ div-inv
Counts
2 → 71
Calls
2 calls:
53.0ms
(/ (+ x 1.0) (- x 1.0))
147.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series233.0ms

Counts
2 → 6
Calls
2 calls:
56.0ms
(/ (+ x 1.0) (- x 1.0))
176.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.7s

Counts
77 → 77

prune237.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ x 1.0) (- x 1.0))
0.0b
(* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (/ (+ x 1.0) (- x 1.0))))
0.0b
(* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0))))
2.3b
(- (/ x (+ x 1.0)) (* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (/ (+ x 1.0) (- x 1.0)))))

rewrite555.0ms

Algorithm
rewrite-expression-head
Rules
284×*-un-lft-identity
188×cbrt-prod
171×times-frac
164×add-sqr-sqrt
78×add-cube-cbrt
58×associate-*r*
51×swap-sqr
49×distribute-lft-out
41×distribute-lft-out--
30×pow1 associate-*l*
29×difference-of-squares
28×cbrt-div
15×pow1/3
13×add-exp-log
12×associate-/r/ unswap-sqr
11×frac-times associate-*l/ pow-prod-up
7×flip3-- pow-plus associate-*r/ pow-prod-down frac-sub add-cbrt-cube flip--
6×div-inv add-log-exp
5×associate-/r* pow-sqr
4×prod-exp cbrt-unprod associate-/l*
3×pow2
2×*-commutative associate-/l/
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-exp pow3 clear-num flip-+
Counts
4 → 269
Calls
4 calls:
52.0ms
(/ (+ x 1.0) (- x 1.0))
223.0ms
(* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (/ (+ x 1.0) (- x 1.0))))
131.0ms
(* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0))))
129.0ms
(- (/ x (+ x 1.0)) (* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (/ (+ x 1.0) (- x 1.0)))))

series584.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(/ (+ x 1.0) (- x 1.0))
70.0ms
(* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (/ (+ x 1.0) (- x 1.0))))
248.0ms
(* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0))))
224.0ms
(- (/ x (+ x 1.0)) (* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (/ (+ x 1.0) (- x 1.0)))))

simplify1.4s

Counts
281 → 281

prune845.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (- x 1.0))
0.3b
(cbrt (- x 1.0))
0.3b
(cbrt (- x 1.0))
7.4b
(- (/ x (+ x 1.0)) (* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (* (/ 1 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (/ (+ x 1.0) (cbrt (- x 1.0)))))))

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
34×cbrt-div
17×frac-times
15×cbrt-prod frac-sub
13×add-sqr-sqrt *-un-lft-identity
11×associate-*r/ associate-*l/
7×add-cube-cbrt
6×add-log-exp
4×pow1 add-exp-log flip3-- add-cbrt-cube flip--
3×pow1/3 distribute-lft-out-- difference-of-squares
1×sub-neg diff-log
Counts
4 → 72
Calls
4 calls:
8.0ms
(cbrt (- x 1.0))
8.0ms
(cbrt (- x 1.0))
9.0ms
(cbrt (- x 1.0))
150.0ms
(- (/ x (+ x 1.0)) (* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (* (/ 1 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (/ (+ x 1.0) (cbrt (- x 1.0)))))))

series615.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(cbrt (- x 1.0))
133.0ms
(cbrt (- x 1.0))
134.0ms
(cbrt (- x 1.0))
217.0ms
(- (/ x (+ x 1.0)) (* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (* (/ 1 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (/ (+ x 1.0) (cbrt (- x 1.0)))))))

simplify1.1s

Counts
84 → 84

prune531.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 3.0 (+ (/ 1 x) (/ 1 (pow x 3))))
0.5b
(/ 1 (pow x 3))
0.6b
(/ (- 1.0) (pow x 2))
6.6b
(- (/ (- 1.0) (pow x 2)) (* 3.0 (+ (/ 1 x) (/ 1 (pow x 3)))))

rewrite380.0ms

Algorithm
rewrite-expression-head
Rules
131×times-frac
101×*-un-lft-identity
86×add-sqr-sqrt
84×add-cube-cbrt
45×unpow-prod-down
27×distribute-lft-neg-in distribute-rgt-neg-in
20×add-exp-log associate-/r*
16×associate-*r*
15×sqr-pow
13×associate-/l*
12×cube-prod
11×unpow2
10×unpow3 add-cbrt-cube
9×neg-mul-1 div-exp
7×div-inv distribute-lft-out
6×pow1 associate-*r/ add-log-exp
5×distribute-rgt-out
4×cube-mult pow-to-exp pow-exp
3×rec-exp 1-exp associate-*l* frac-sub
2×cbrt-undiv neg-sub0 distribute-rgt-in frac-2neg distribute-lft-in flip3-+ div-sub frac-add clear-num flip-+ associate--r+
1×associate--l- sub-neg flip3-- pow-flip diff-log distribute-frac-neg pow-prod-down distribute-rgt1-in prod-exp *-commutative flip-- cbrt-unprod inv-pow unswap-sqr
Counts
4 → 241
Calls
4 calls:
237.0ms
(* 3.0 (+ (/ 1 x) (/ 1 (pow x 3))))
12.0ms
(/ 1 (pow x 3))
15.0ms
(/ (- 1.0) (pow x 2))
102.0ms
(- (/ (- 1.0) (pow x 2)) (* 3.0 (+ (/ 1 x) (/ 1 (pow x 3)))))

series268.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(* 3.0 (+ (/ 1 x) (/ 1 (pow x 3))))
50.0ms
(/ 1 (pow x 3))
51.0ms
(/ (- 1.0) (pow x 2))
47.0ms
(- (/ (- 1.0) (pow x 2)) (* 3.0 (+ (/ 1 x) (/ 1 (pow x 3)))))

simplify2.3s

Counts
253 → 253

prune664.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes46.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.7b

bsearch174.0ms

Steps
ItersRangePoint
10
1.3099675947624547e-09
64828.07766974042
8087.1158975098915
11
-1.2057104386339981e+20
-1.9338314318659307
-7452.829832440167

simplify1.1s

end0.0ms

sample1.6s

Algorithm
intervals
Results
617.0ms4047×body80valid
400.0ms1702×body1280valid
291.0ms1266×body640valid
78.0ms662×body320valid
26.0ms323×body160valid