Details

sample44.0ms

Algorithm

intervals

Results

16.0ms	259×	body	80	valid
3.0ms	14×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	4×	body	1280	valid
1.0ms	6×	body	160	valid
0.0ms	1×	body	2560	valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	1910
5	805
4	299
3	108
2	43
1	20
0	11

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.7b

localize36.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
11.4b	(fma (/ (- t x) (- a z)) (- y z) x)

rewrite40.0ms

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:

35.0ms	(/ (- t x) (- a z))
1.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series240.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(/ (- t x) (- a z))
158.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify1.7s

Counts

70 → 70

Iterations

Iter	Nodes
done	5045
3	2171
2	671
1	274
0	118

prune505.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.3b	(* (- t x) (/ 1 (- a z)))
11.4b	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

rewrite81.0ms

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:

9.0ms	(/ 1 (- a z))
68.0ms	(* (- t x) (/ 1 (- a z)))
0.0ms	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

series318.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ 1 (- a z))
102.0ms	(* (- t x) (/ 1 (- a z)))
166.0ms	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

simplify3.4s

Counts

114 → 114

Iterations

Iter	Nodes
done	5004
3	3519
2	1191
1	369
0	155

prune820.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.9b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
2.1b	(+ (* (/ (- t x) (- a z)) (- y z)) x)
5.0b	(* (/ (- t x) (- a z)) (- y z))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-sqr-sqrt`
97×	`*-un-lft-identity`
51×	`times-frac` `add-cube-cbrt`
36×	`prod-diff`
31×	`associate-l`
23×	`distribute-lft-out--` `difference-of-squares`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `associate-r` `flip--` `associate-/l` `add-log-exp`
4×	`sub-neg` `associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`frac-times` `cbrt-undiv` `div-exp` `prod-exp` `associate-*r/` `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-l/` `-commutative` `flip-+`

Counts

3 → 170

Calls

3 calls:

26.0ms	(/ (- t x) (- a z))
25.0ms	(+ (* (/ (- t x) (- a z)) (- y z)) x)
103.0ms	(* (/ (- t x) (- a z)) (- y z))

series724.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(/ (- t x) (- a z))
239.0ms	(+ (* (/ (- t x) (- a z)) (- y z)) x)
391.0ms	(* (/ (- t x) (- a z)) (- y z))

simplify2.0s

Counts

179 → 179

Iterations

Iter	Nodes
done	5000
2	1995
1	712
0	256

prune1.1s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 4.9b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite148.0ms

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` `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 → 126

Calls

3 calls:

36.0ms	(/ (- y z) (- a z))
37.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)
67.0ms	(* (- t x) (/ (- y z) (- a z)))

series584.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(/ (- y z) (- a z))
282.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)
217.0ms	(* (- t x) (/ (- y z) (- a z)))

simplify1.7s

Counts

135 → 135

Iterations

Iter	Nodes
done	5000
2	1759
1	517
0	189

prune714.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.3b

regimes610.0ms

Accuracy

12.2% (6.7b remaining)

Error of 9.9b against oracle of 3.2b and baseline of 10.9b

bsearch134.0ms

Steps

Iters	Range		Point
6	3.675373565137037e-110	5.196415815707473e-109	1.7997039304786746e-109
9	-7.89161991821833e-149	-1.3510450405699621e-155	-1.00328380395392e-150

simplify5.0ms

Iterations

Iter	Nodes
done	27
1	27
0	24

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.0s	7884×	body	80	valid
104.0ms	245×	body	1280	valid
98.0ms	465×	body	640	valid
63.0ms	242×	body	160	valid
57.0ms	377×	body	320	valid
5.0ms	16×	body	2560	valid