Details

sample45.0ms

Algorithm

intervals

Results

13.0ms	229×	body	80	valid
3.0ms	15×	body	640	valid
2.0ms	15×	body	320	valid
2.0ms	7×	body	1280	valid
1.0ms	9×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	3379
5	728
4	242
3	111
2	52
1	22
0	11

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.0b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t z) (- a t))
3.1b	(fma y (/ (- t z) (- a t)) (+ y x))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-cbrt-cube` `add-exp-log`
2×	`expm1-log1p-u` `pow1` `flip3--` `associate-/r/` `log1p-expm1-u` `flip--` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

38.0ms	(/ (- t z) (- a t))
1.0ms	(fma y (/ (- t z) (- a t)) (+ y x))

series346.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(/ (- t z) (- a t))
254.0ms	(fma y (/ (- t z) (- a t)) (+ y x))

simplify2.3s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
3	4441
2	825
1	263
0	114

prune458.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.9b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* (- t z) (/ 1 (- a t)))
4.1b	(fma y (* (- t z) (/ 1 (- a t))) (+ y x))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
32×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-/r` `associate-l*`
4×	`flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

3 → 105

Calls

3 calls:

10.0ms	(/ 1 (- a t))
59.0ms	(* (- t z) (/ 1 (- a t)))
1.0ms	(fma y (* (- t z) (/ 1 (- a t))) (+ y x))

series354.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ 1 (- a t))
65.0ms	(* (- t z) (/ 1 (- a t)))
247.0ms	(fma y (* (- t z) (/ 1 (- a t))) (+ y x))

simplify4.3s

Counts

114 → 114

Iterations

Iter	Nodes
done	5001
2	2794
1	357
0	150

prune526.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.9b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ 1 (- a t)))
0.6b	(cbrt (/ 1 (- a t)))
0.6b	(cbrt (/ 1 (- a t)))
8.9b	(fma y (* (- t z) (* (* (cbrt (/ 1 (- a t))) (cbrt (/ 1 (- a t)))) (cbrt (/ 1 (- a t))))) (+ y x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

63×	`cbrt-prod`
49×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
31×	`add-cube-cbrt`
9×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `flip3--` `pow1/3` `div-inv` `flip--`
1×	`fma-udef`

Counts

4 → 106

Calls

4 calls:

9.0ms	(cbrt (/ 1 (- a t)))
6.0ms	(cbrt (/ 1 (- a t)))
5.0ms	(cbrt (/ 1 (- a t)))
0.0ms	(fma y (* (- t z) (* (* (cbrt (/ 1 (- a t))) (cbrt (/ 1 (- a t)))) (cbrt (/ 1 (- a t))))) (+ y x))

series845.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(cbrt (/ 1 (- a t)))
206.0ms	(cbrt (/ 1 (- a t)))
234.0ms	(cbrt (/ 1 (- a t)))
202.0ms	(fma y (* (- t z) (* (* (cbrt (/ 1 (- a t))) (cbrt (/ 1 (- a t)))) (cbrt (/ 1 (- a t))))) (+ y x))

simplify1.0s

Counts

118 → 118

Iterations

Iter	Nodes
done	5000
3	1944
2	585
1	250
0	141

prune829.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 2.9b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- t z))
0.5b	(cbrt (- t z))
0.5b	(* (cbrt (- t z)) (cbrt (- t z)))
8.4b	(fma y (* (* (cbrt (- t z)) (cbrt (- t z))) (/ (cbrt (- t z)) (- a t))) (+ y x))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

38×	`cbrt-prod`
34×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
16×	`cbrt-div`
14×	`add-cube-cbrt`
11×	`pow1`
10×	`swap-sqr`
8×	`flip3--` `pow1/3` `associate-r` `associate-l` `flip--` `distribute-lft-out--`
6×	`add-exp-log` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 102

Calls

4 calls:

5.0ms	(cbrt (- t z))
3.0ms	(cbrt (- t z))
38.0ms	(* (cbrt (- t z)) (cbrt (- t z)))
1.0ms	(fma y (* (* (cbrt (- t z)) (cbrt (- t z))) (/ (cbrt (- t z)) (- a t))) (+ y x))

series908.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(cbrt (- t z))
199.0ms	(cbrt (- t z))
218.0ms	(* (cbrt (- t z)) (cbrt (- t z)))
264.0ms	(fma y (* (* (cbrt (- t z)) (cbrt (- t z))) (/ (cbrt (- t z)) (- a t))) (+ y x))

simplify953.0ms

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
2	1086
1	332
0	157

prune795.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 2.9b

regimes699.0ms

Accuracy

31.9% (5.5b remaining)

Error of 8.6b against oracle of 3.1b and baseline of 11.2b

bsearch150.0ms

Steps

Iters	Range		Point
9	2.7892275357167452e-173	6.906315603593477e-164	2.6575005849123698e-166
6	-4.9039682872818813e-91	-1.0888633833313048e-91	-2.900002769274411e-91

simplify6.0ms

Iterations

Iter	Nodes
done	27
1	27
0	20

end0.0ms

sample1.9s

Algorithm

intervals

Results

558.0ms	7366×	body	80	valid
469.0ms	255×	body	1280	valid
145.0ms	398×	body	320	valid
122.0ms	431×	body	640	valid
67.0ms	236×	body	160	valid
7.0ms	17×	body	2560	valid