Details

sample55.0ms

Algorithm

intervals

Results

19.0ms	263×	body	80	valid
2.0ms	9×	body	640	valid
2.0ms	11×	body	320	valid
2.0ms	6×	body	1280	valid
0.0ms	2×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.8b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t z) (- a t))
1.5b	(fma y (/ (- t z) (- a t)) (+ y x))

rewrite27.0ms

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:

25.0ms	(/ (- t z) (- a t))
0.0ms	(fma y (/ (- t z) (- a t)) (+ y x))

series256.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(/ (- t z) (- a t))
179.0ms	(fma y (/ (- t z) (- a t)) (+ y x))

simplify2.8s

Counts

70 → 70

Iterations

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

prune514.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t z) (- a t))
0.8b	(+ (* y (/ (- t z) (- a t))) (+ y x))
2.1b	(* y (/ (- t z) (- a t)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
71×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
22×	`distribute-lft-out--` `difference-of-squares`
10×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
5×	`pow1` `associate-/r` `associate-/l`
4×	`associate-/r/`
3×	`expm1-log1p-u` `sum-log` `flip3--` `associate-l` `associate-*r/` `log1p-expm1-u` `flip--`
2×	`cbrt-undiv` `flip3-+` `div-exp` `frac-add` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr` `associate-/l/`
1×	`+-commutative` `associate-+r+` `clear-num` `fma-def` `frac-2neg` `div-sub` `pow-prod-down` `*-commutative`

Counts

3 → 124

Calls

3 calls:

19.0ms	(/ (- t z) (- a t))
36.0ms	(+ (* y (/ (- t z) (- a t))) (+ y x))
41.0ms	(* y (/ (- t z) (- a t)))

series343.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(/ (- t z) (- a t))
195.0ms	(+ (* y (/ (- t z) (- a t))) (+ y x))
85.0ms	(* y (/ (- t z) (- a t)))

simplify2.3s

Counts

133 → 133

Iterations

Iter	Nodes
done	5001
2	2457
1	562
0	191

prune883.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.0b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t z) (- a t))
3.3b	(fma y (/ (- t z) (- a t)) y)

rewrite38.0ms

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:

33.0ms	(/ (- t z) (- a t))
0.0ms	(fma y (/ (- t z) (- a t)) y)

series202.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(/ (- t z) (- a t))
118.0ms	(fma y (/ (- t z) (- a t)) y)

simplify2.2s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
3	4382
2	820
1	258
0	110

prune575.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- t z))
0.5b	(cbrt (- t z))
0.5b	(cbrt (- t z))
14.5b	(fma y (/ (* (cbrt (- t z)) (cbrt (- t z))) (/ (- a t) (cbrt (- t z)))) y)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

7.0ms	(cbrt (- t z))
6.0ms	(cbrt (- t z))
6.0ms	(cbrt (- t z))
1.0ms	(fma y (/ (* (cbrt (- t z)) (cbrt (- t z))) (/ (- a t) (cbrt (- t z)))) y)

series796.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(cbrt (- t z))
232.0ms	(cbrt (- t z))
246.0ms	(cbrt (- t z))
113.0ms	(fma y (/ (* (cbrt (- t z)) (cbrt (- t z))) (/ (- a t) (cbrt (- t z)))) y)

simplify1.3s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
3	1548
2	467
1	187
0	90

prune664.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.0b

regimes725.0ms

Accuracy

10.9% (4.1b remaining)

Error of 7.5b against oracle of 3.4b and baseline of 8.0b

bsearch98.0ms

Steps

Iters	Range		Point
9	9.180063932475843e-204	1.0400915298588633e-197	1.1310361777097146e-203
6	-4.151288806614406e-87	-6.816939173909149e-88	-6.922040009532223e-88

simplify3.0ms

Iterations

Iter	Nodes
done	25
1	25
0	19

end0.0ms

sample1.4s

Algorithm

intervals

Results

634.0ms	7354×	body	80	valid
145.0ms	450×	body	640	valid
107.0ms	434×	body	320	valid
97.0ms	257×	body	1280	valid
31.0ms	249×	body	160	valid
5.0ms	17×	body	2560	valid