Details

sample59.0ms

Algorithm

intervals

Results

15.0ms	237×	body	80	valid
4.0ms	19×	body	640	valid
4.0ms	13×	body	1280	valid
3.0ms	17×	body	320	valid
1.0ms	9×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	11	13
1	23	13
2	46	12
3	128	12
4	368	12
5	1103	12
6	4364	12
done	5000	12

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.5b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
16.7b	(fma (/ (- t x) (- a z)) (- y z) x)

rewrite43.0ms

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-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

39.0ms	(/ (- t x) (- a z))
0.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series179.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(/ (- t x) (- a z))
106.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify2.2s

Counts

70 → 70

Iterations

Useful iterations: 3 (826.0ms)

Iter	Nodes	Cost
0	118	918
1	274	890
2	848	838
3	4610	834
done	5000	834

prune310.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.9b

localize17.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (- t x) (/ 1 (- a z)))
16.7b	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`-un-lft-identity` `associate-r*`
17×	`times-frac`
12×	`add-cube-cbrt`
11×	`add-exp-log`
7×	`add-cbrt-cube`
5×	`associate-l`
4×	`pow1` `prod-exp` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `flip--` `unswap-sqr`
2×	`expm1-log1p-u` `frac-times` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `rec-exp` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `fma-udef` `div-inv`

Counts

2 → 62

Calls

2 calls:

50.0ms	(* (- t x) (/ 1 (- a z)))
0.0ms	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

series213.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(* (- t x) (/ 1 (- a z)))
122.0ms	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

simplify6.6s

Counts

68 → 68

Iterations

Useful iterations: done (6.6s)

Iter	Nodes	Cost
0	137	880
1	342	795
2	2639	634
done	5001	628

prune181.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 7.8b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.1b	(* (- t x) (/ (- y z) (- a z)))
3.1b	(+ (* (- t x) (/ (- y z) (- a z))) x)

rewrite175.0ms

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-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `fma-def` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 126

Calls

3 calls:

51.0ms	(/ (- y z) (- a z))
76.0ms	(* (- t x) (/ (- y z) (- a z)))
35.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)

series520.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(/ (- y z) (- a z))
200.0ms	(* (- t x) (/ (- y z) (- a z)))
239.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)

simplify1.9s

Counts

135 → 135

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	189	1881
1	518	1777
2	2651	1675
done	5002	1667

prune601.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.9b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- t x))
0.4b	(/ 1 (/ (- a z) (- t x)))
16.6b	(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
195×	`add-sqr-sqrt` `*-un-lft-identity`
91×	`add-cube-cbrt`
52×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`flip3--` `flip--` `div-inv`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `div-sub` `fma-udef` `inv-pow`

Counts

3 → 214

Calls

3 calls:

50.0ms	(/ (- a z) (- t x))
64.0ms	(/ 1 (/ (- a z) (- t x)))
1.0ms	(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

series640.0ms

Counts

3 → 9

Calls

3 calls:

95.0ms	(/ (- a z) (- t x))
322.0ms	(/ 1 (/ (- a z) (- t x)))
221.0ms	(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

simplify1.8s

Counts

223 → 223

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	274	3778
1	715	3266
2	3417	3112
done	5000	3037

prune546.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.9b

regimes393.0ms

Accuracy

13% (9.5b remaining)

Error of 13.3b against oracle of 3.7b and baseline of 14.7b

bsearch77.0ms

Steps

Iters	Range		Point
7	1.968769896203537e+119	4.060182744678713e+120	4.016279813338476e+120
3	-2.844533468216415e+143	-2.3250550447943957e+143	-2.6821964608970343e+143

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	23	46
1	29	35
done	29	35

end0.0ms

sample2.0s

Algorithm

intervals

Results

629.0ms	7776×	body	80	valid
383.0ms	282×	body	160	valid
140.0ms	493×	body	640	valid
116.0ms	260×	body	1280	valid
109.0ms	415×	body	320	valid
5.0ms	15×	body	2560	valid