Details

sample25.0ms

Algorithm

intervals

Results

7.0ms	235×	body	80	valid
1.0ms	10×	body	1280	valid
1.0ms	12×	body	640	valid
1.0ms	14×	body	320	valid
1.0ms	14×	body	160	valid

simplify8.0s

Counts

1 → 1

Iterations

Useful iterations: 4 (29.0ms)

Iter	Nodes	Cost
0	11	13
1	22	13
2	51	13
3	104	13
4	214	12
5	481	12
6	937	12
7	1715	12
8	2446	12
9	4989	12
done	5000	12

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (fma (/ (- t z) (- a t)) y y))
0.0b	(/ (- t z) (- a t))
2.2b	(fma (/ (- t z) (- a t)) y y)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 82

Calls

3 calls:

3.0ms	(+ x (fma (/ (- t z) (- a t)) y y))
12.0ms	(/ (- t z) (- a t))
0.0ms	(fma (/ (- t z) (- a t)) y y)

series226.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(+ x (fma (/ (- t z) (- a t)) y y))
41.0ms	(/ (- t z) (- a t))
94.0ms	(fma (/ (- t z) (- a t)) y y)

simplify1.2s

Counts

91 → 91

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	135	1177
1	319	1116
2	823	1063
3	2778	1061
done	5000	1059

prune260.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (fma (/ (- t z) (- a t)) y y)) (cbrt (fma (/ (- t z) (- a t)) y y)))
2.2b	(fma (/ (- t z) (- a t)) y y)
2.2b	(fma (/ (- t z) (- a t)) y y)
2.2b	(fma (/ (- t z) (- a t)) y y)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
6×	`add-exp-log` `pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`fma-udef`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 72

Calls

4 calls:

6.0ms	(* (cbrt (fma (/ (- t z) (- a t)) y y)) (cbrt (fma (/ (- t z) (- a t)) y y)))
0.0ms	(fma (/ (- t z) (- a t)) y y)
0.0ms	(fma (/ (- t z) (- a t)) y y)
0.0ms	(fma (/ (- t z) (- a t)) y y)

series677.0ms

Counts

4 → 12

Calls

4 calls:

392.0ms	(* (cbrt (fma (/ (- t z) (- a t)) y y)) (cbrt (fma (/ (- t z) (- a t)) y y)))
95.0ms	(fma (/ (- t z) (- a t)) y y)
94.0ms	(fma (/ (- t z) (- a t)) y y)
96.0ms	(fma (/ (- t z) (- a t)) y y)

simplify1.2s

Counts

84 → 84

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	88	1692
1	177	1567
2	603	1408
3	2254	1179
done	5000	1178

prune320.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (fma (* (- t z) (/ 1 (- a t))) y y))
0.0b	(/ 1 (- a t))
0.2b	(* (- t z) (/ 1 (- a t)))
5.8b	(fma (* (- t z) (/ 1 (- a t))) y y)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
32×	`times-frac`
25×	`add-cube-cbrt`
21×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`pow1`
6×	`add-log-exp`
5×	`associate-l` `associate-/r*`
4×	`expm1-log1p-u` `flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--` `log1p-expm1-u`
3×	`fma-def` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `fma-udef` `div-inv`
1×	`+-commutative` `associate-+r+` `pow-flip` `frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `flip-+` `distribute-lft-out` `inv-pow`

Counts

4 → 123

Calls

4 calls:

3.0ms	(+ x (fma (* (- t z) (/ 1 (- a t))) y y))
6.0ms	(/ 1 (- a t))
26.0ms	(* (- t z) (/ 1 (- a t)))
0.0ms	(fma (* (- t z) (/ 1 (- a t))) y y)

series395.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(+ x (fma (* (- t z) (/ 1 (- a t))) y y))
56.0ms	(/ 1 (- a t))
64.0ms	(* (- t z) (/ 1 (- a t)))
133.0ms	(fma (* (- t z) (/ 1 (- a t))) y y)

simplify2.6s

Counts

135 → 135

Iterations

Useful iterations: 3 (863.0ms)

Iter	Nodes	Cost
0	171	1588
1	401	1322
2	1384	1173
3	4639	1171
done	5000	1171

prune334.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.4b

localize14.0ms

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)))
12.6b	(fma (* (* (- t z) (* (cbrt (/ 1 (- a t))) (cbrt (/ 1 (- a t))))) (cbrt (/ 1 (- a t)))) y y)

rewrite16.0ms

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×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `flip3--` `pow1/3` `flip--` `div-inv`
1×	`fma-udef`

Counts

4 → 106

Calls

4 calls:

4.0ms	(cbrt (/ 1 (- a t)))
4.0ms	(cbrt (/ 1 (- a t)))
4.0ms	(cbrt (/ 1 (- a t)))
0.0ms	(fma (* (* (- t z) (* (cbrt (/ 1 (- a t))) (cbrt (/ 1 (- a t))))) (cbrt (/ 1 (- a t)))) y y)

series528.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt (/ 1 (- a t)))
140.0ms	(cbrt (/ 1 (- a t)))
140.0ms	(cbrt (/ 1 (- a t)))
92.0ms	(fma (* (* (- t z) (* (cbrt (/ 1 (- a t))) (cbrt (/ 1 (- a t))))) (cbrt (/ 1 (- a t)))) y y)

simplify1.1s

Counts

118 → 118

Iterations

Useful iterations: 3 (273.0ms)

Iter	Nodes	Cost
0	138	1795
1	247	1645
2	598	1387
3	1985	1327
done	5000	1327

prune306.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 3.4b

regimes418.0ms

Accuracy

16.2% (3.7b remaining)

Error of 6.8b against oracle of 3.0b and baseline of 7.5b

bsearch78.0ms

Steps

Iters	Range		Point
8	2.959584178149656e-120	3.228369110132154e-116	4.1955295958532206e-120
7	-3.000333177767969e-178	-2.196513126071919e-180	-2.4270769705098634e-178

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	21	88
1	26	52
done	26	52

end0.0ms

sample653.0ms

Algorithm

intervals

Results

242.0ms	7365×	body	80	valid
53.0ms	460×	body	640	valid
44.0ms	287×	body	1280	valid
33.0ms	383×	body	320	valid
13.0ms	223×	body	160	valid
4.0ms	21×	body	2560	valid