Details

sample58.0ms

Algorithm

intervals

Results

25.0ms	242×	body	80	valid
6.0ms	18×	body	640	valid
5.0ms	12×	body	1280	valid
4.0ms	15×	body	320	valid
1.0ms	7×	body	160	valid

simplify3.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5005
6	2502
5	895
4	343
3	126
2	46
1	23
0	11

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.9b

localize31.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
15.2b	(fma (- y z) (/ (- t x) (- a z)) x)

rewrite18.0ms

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/` `insert-posit16` `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 → 66

Calls

2 calls:

17.0ms	(/ (- t x) (- a z))
0.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

series197.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(/ (- t x) (- a z))
133.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

simplify1.6s

Counts

72 → 72

Iterations

Iter	Nodes
done	5010
3	2144
2	663
1	276
0	120

prune400.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.9b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.7b	(* (- y z) (/ (- t x) (- a z)))
4.2b	(+ (* (- y z) (/ (- t x) (- a z))) x)

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `associate-l` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`frac-times` `cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr` `associate-/l/`
1×	`+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `associate-r/` `-commutative` `flip-+`

Counts

3 → 129

Calls

3 calls:

30.0ms	(/ (- t x) (- a z))
64.0ms	(* (- y z) (/ (- t x) (- a z)))
22.0ms	(+ (* (- y z) (/ (- t x) (- a z))) x)

series538.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(/ (- t x) (- a z))
213.0ms	(* (- y z) (/ (- t x) (- a z)))
264.0ms	(+ (* (- y z) (/ (- t x) (- a z))) x)

simplify1.5s

Counts

138 → 138

Iterations

Iter	Nodes
done	5001
2	1810
1	520
0	192

prune593.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.5b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip-+`

Counts

4 → 69

Calls

4 calls:

6.0ms	(cbrt (- a z))
6.0ms	(cbrt (- a z))
6.0ms	(cbrt (- a z))
151.0ms	(+ (* (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z)))) x)

series773.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt (- a z))
174.0ms	(cbrt (- a z))
188.0ms	(cbrt (- a z))
228.0ms	(+ (* (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z)))) x)

simplify2.3s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
3	3005
2	760
1	276
0	114

prune678.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.5b

localize58.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
12.4b	(fma (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z))) x)

rewrite15.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 65

Calls

4 calls:

5.0ms	(cbrt (- a z))
5.0ms	(cbrt (- a z))
5.0ms	(cbrt (- a z))
0.0ms	(fma (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z))) x)

series1.0s

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt (- a z))
181.0ms	(cbrt (- a z))
195.0ms	(cbrt (- a z))
450.0ms	(fma (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z))) x)

simplify2.8s

Counts

77 → 77

Iterations

Iter	Nodes
done	5000
4	4183
3	1097
2	425
1	199
0	97

prune521.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.2b

regimes748.0ms

Accuracy

29.8% (6.4b remaining)

Error of 9.7b against oracle of 3.3b and baseline of 12.4b

bsearch166.0ms

Steps

Iters	Range		Point
8	8.883612526165312e-94	2.7867056099957307e-91	1.3917837591469568e-93
10	-6.087560554388729e-120	-5.880771378225135e-135	-3.4167661692054223e-133

simplify6.0ms

Iterations

Iter	Nodes
done	28
1	28
0	25

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.1s	7795×	body	80	valid
153.0ms	473×	body	640	valid
148.0ms	288×	body	1280	valid
145.0ms	435×	body	320	valid
65.0ms	257×	body	160	valid
10.0ms	20×	body	2560	valid