Details

sample48.0ms

Algorithm

intervals

Results

13.0ms	233×	body	80	valid
9.0ms	24×	body	640	valid
3.0ms	18×	body	320	valid
2.0ms	8×	body	1280	valid
1.0ms	8×	body	160	valid

simplify4.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	11	245
1	23	245
2	46	220
3	126	220
4	343	220
5	895	220
6	2502	220
done	5005	220

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.9b

localize36.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
16.9b	(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-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:

38.0ms	(/ (- t x) (- a z))
1.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series231.0ms

Counts

2 → 6

Calls

2 calls:

75.0ms	(/ (- t x) (- a z))
156.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify2.3s

Counts

70 → 70

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	118	18729
1	274	17805
2	671	17725
3	2171	17645
done	5045	17595

prune560.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.2b	(+ x (* (- y z) (/ (- t x) (- a z))))
6.5b	(* (- y z) (/ (- t x) (- a z)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
74×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
28×	`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` `fma-def` `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` `frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `associate-r/` `-commutative` `flip-+`

Counts

3 → 128

Calls

3 calls:

28.0ms	(/ (- t x) (- a z))
6.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
68.0ms	(* (- y z) (/ (- t x) (- a z)))

series559.0ms

Counts

3 → 9

Calls

3 calls:

100.0ms	(/ (- t x) (- a z))
245.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
214.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify2.0s

Counts

137 → 137

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	189	38092
1	515	35063
2	1817	34302
done	5000	34172

prune990.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
2.8b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
10.8b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
28×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`frac-times`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `associate-l/` `associate-r/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `sum-log` `flip3-+` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 145

Calls

4 calls:

6.0ms	(cbrt (- a z))
7.0ms	(cbrt (- a z))
169.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
13.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

200.0ms	(cbrt (- a z))
193.0ms	(cbrt (- a z))
482.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
260.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify4.3s

Counts

157 → 157

Iterations

Useful iterations: done (4.2s)

Iter	Nodes	Cost
0	261	67605
1	761	62195
2	2977	61559
done	5004	54359

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.1b

localize99.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
2.8b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
13.5b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
27×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `unswap-sqr`
5×	`frac-times`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l/` `associate-r/`
2×	`pow1/3` `div-inv`
1×	`pow-prod-down` `*-commutative` `fma-udef`

Counts

4 → 139

Calls

4 calls:

4.0ms	(cbrt (- a z))
4.0ms	(cbrt (- a z))
176.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
1.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

226.0ms	(cbrt (- a z))
270.0ms	(cbrt (- a z))
438.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
227.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify3.8s

Counts

151 → 151

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	251	65995
1	705	60981
2	2698	60780
done	5002	52595

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.1b

regimes931.0ms

Accuracy

13.7% (7.7b remaining)

Error of 11.3b against oracle of 3.6b and baseline of 12.5b

bsearch170.0ms

Steps

Iters	Range		Point
7	1.2557600262013267e-92	3.521499667301013e-91	2.2136574792826275e-92
10	-1.8574909432381172e-115	-1.493044719713805e-132	-4.4616959443899906e-130

simplify18.0ms

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	30	1217
1	35	1217
done	35	1217

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.0s	7746×	body	80	valid
132.0ms	269×	body	1280	valid
104.0ms	409×	body	320	valid
101.0ms	474×	body	640	valid
26.0ms	251×	body	160	valid
2.0ms	8×	body	2560	valid