Details

sample49.0ms

Algorithm

intervals

Results

24.0ms

256×

body

valid

simplify4.2s

Counts

1 → 1

Iterations

Useful iterations: 4 (154.0ms)

Iter	Nodes	Cost
0	16	21
1	33	20
2	79	20
3	201	20
4	637	19
5	2240	19
6	4952	19
done	5000	19

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
1.4b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
2.4b	(+ (* (+ x y) z) (* (+ t y) a))
26.5b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite422.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
13×	`distribute-lft-out`
11×	`add-log-exp`
10×	`associate-*l/`
8×	`add-exp-log` `add-cbrt-cube`
7×	`flip3-+` `flip-+`
6×	`pow1`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l` `frac-add` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `prod-diff` `associate-/l*`
2×	`flip3--` `diff-log` `sum-log` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `fma-def` `frac-2neg` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `associate--l+` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

35.0ms	(* (+ t y) a)
131.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
25.0ms	(+ (* (+ x y) z) (* (+ t y) a))
228.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series1.1s

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (+ t y) a)
159.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
65.0ms	(+ (* (+ x y) z) (* (+ t y) a))
800.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify2.0s

Counts

117 → 117

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	192	2540
1	575	2315
2	2693	2104
done	5000	2080

prune562.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (+ (+ x t) y))
1.4b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
2.4b	(+ (* (+ x y) z) (* (+ t y) a))
26.5b	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

rewrite526.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
32×	`times-frac`
26×	`add-cube-cbrt`
21×	`associate-r` `distribute-lft-out`
17×	`add-exp-log`
11×	`add-cbrt-cube` `add-log-exp`
10×	`associate-*l/`
7×	`pow1` `flip3-+` `flip-+`
5×	`associate-/r*`
4×	`expm1-log1p-u` `div-exp` `frac-add` `prod-exp` `associate-/r/` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `associate-l` `prod-diff` `flip--` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `diff-log` `1-exp` `sum-log` `cbrt-unprod` `div-inv`
1×	`+-commutative` `sub-neg` `pow-flip` `fma-def` `frac-2neg` `associate-r/` `pow-prod-down` `associate--l+` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 133

Calls

4 calls:

37.0ms	(/ 1 (+ (+ x t) y))
86.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
16.0ms	(+ (* (+ x y) z) (* (+ t y) a))
382.0ms	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

series1.1s

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ 1 (+ (+ x t) y))
122.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
59.0ms	(+ (* (+ x y) z) (* (+ t y) a))
825.0ms	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

simplify3.0s

Counts

145 → 145

Iterations

Useful iterations: 2 (667.0ms)

Iter	Nodes	Cost
0	207	2953
1	627	2602
2	4354	2274
done	5000	2274

prune440.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 9.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (fma a t (* y (- a b))))))
0.8b	(fma z (+ x y) (fma a t (* y (- a b))))
1.0b	(fma a t (* y (- a b)))
26.5b	(/ (+ (+ x t) y) (fma z (+ x y) (fma a t (* y (- a b)))))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

150×	`*-un-lft-identity`
132×	`times-frac`
70×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`distribute-lft-out`
22×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `fma-udef` `associate-/l/`
1×	`pow-flip` `flip3-+` `associate-/r/` `flip-+` `inv-pow`

Counts

4 → 161

Calls

4 calls:

42.0ms	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (fma a t (* y (- a b))))))
0.0ms	(fma z (+ x y) (fma a t (* y (- a b))))
0.0ms	(fma a t (* y (- a b)))
75.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (fma a t (* y (- a b)))))

series961.0ms

Counts

4 → 12

Calls

4 calls:

672.0ms	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (fma a t (* y (- a b))))))
119.0ms	(fma z (+ x y) (fma a t (* y (- a b))))
43.0ms	(fma a t (* y (- a b)))
127.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (fma a t (* y (- a b)))))

simplify1.3s

Counts

173 → 173

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	190	5188
1	467	4825
2	2630	4581
done	5001	4422

prune409.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.8b	(fma z (+ x y) (fma t a (* y (- a b))))
1.0b	(fma t a (* y (- a b)))
9.2b	(* (* (fma z (+ x y) (fma t a (* y (- a b)))) (* (cbrt (/ 1 (+ (+ x t) y))) (cbrt (/ 1 (+ (+ x t) y))))) (cbrt (/ 1 (+ (+ x t) y))))
17.2b	(* (fma z (+ x y) (fma t a (* y (- a b)))) (* (cbrt (/ 1 (+ (+ x t) y))) (cbrt (/ 1 (+ (+ x t) y)))))

rewrite687.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
25×	`associate-r`
21×	`cbrt-prod`
18×	`pow1` `add-exp-log`
16×	`add-sqr-sqrt` `cbrt-div`
15×	`add-cube-cbrt` `times-frac`
13×	`associate-*r/`
11×	`add-cbrt-cube`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod` `distribute-lft-out`
6×	`frac-times` `associate-*l/`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
2×	`associate-/r/` `*-commutative` `fma-udef`
1×	`flip3-+` `flip-+` `div-inv` `unswap-sqr`

Counts

4 → 95

Calls

4 calls:

0.0ms	(fma z (+ x y) (fma t a (* y (- a b))))
0.0ms	(fma t a (* y (- a b)))
545.0ms	(* (* (fma z (+ x y) (fma t a (* y (- a b)))) (* (cbrt (/ 1 (+ (+ x t) y))) (cbrt (/ 1 (+ (+ x t) y))))) (cbrt (/ 1 (+ (+ x t) y))))
138.0ms	(* (fma z (+ x y) (fma t a (* y (- a b)))) (* (cbrt (/ 1 (+ (+ x t) y))) (cbrt (/ 1 (+ (+ x t) y)))))

series2.6s

Counts

4 → 12

Calls

4 calls:

116.0ms	(fma z (+ x y) (fma t a (* y (- a b))))
37.0ms	(fma t a (* y (- a b)))
492.0ms	(* (* (fma z (+ x y) (fma t a (* y (- a b)))) (* (cbrt (/ 1 (+ (+ x t) y))) (cbrt (/ 1 (+ (+ x t) y))))) (cbrt (/ 1 (+ (+ x t) y))))
1.9s	(* (fma z (+ x y) (fma t a (* y (- a b)))) (* (cbrt (/ 1 (+ (+ x t) y))) (cbrt (/ 1 (+ (+ x t) y)))))

simplify1.7s

Counts

107 → 107

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	200	3642
1	515	3470
2	2586	2736
done	5000	2637

prune370.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 5.5b

regimes596.0ms

Accuracy

41.8% (13.3b remaining)

Error of 17.4b against oracle of 4.1b and baseline of 27.0b

bsearch93.0ms

Steps

Iters	Range		Point
6	2.9310864434849316e+206	4.045916786044548e+207	2.9781073488031946e+206
9	-3.0433044982512647e+105	-2.0194296793555897e+99	-3.0562342330929877e+100

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	26	41
1	41	37
done	41	37

end0.0ms

sample1.4s

Algorithm

intervals

Results

897.0ms	7994×	body	80	valid
0.0ms	2×	body	640	valid
0.0ms	4×	body	160	valid