Details

sample30.0ms

Algorithm

intervals

Results

11.0ms	244×	body	80	valid
2.0ms	18×	body	640	valid
1.0ms	16×	body	320	valid
1.0ms	8×	body	1280	valid
1.0ms	10×	body	160	valid
0.0ms	1×	body	2560	valid

simplify7.3s

Counts

1 → 1

Iterations

Useful iterations: 3 (12.0ms)

Iter	Nodes	Cost
0	11	13
1	20	13
2	45	13
3	114	12
4	278	12
5	618	12
6	1260	12
7	2332	12
8	4233	12
done	5001	12

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.5b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
3.5b	(fma (/ (- y z) (- a z)) (- t x) x)

rewrite15.0ms

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:

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

series183.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(/ (- y z) (- a z))
123.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify2.5s

Counts

70 → 70

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	116	918
1	266	890
2	623	838
3	1565	834
4	4615	828
done	5000	828

prune251.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.9b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- y z) (/ 1 (- a z)))
4.5b	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

rewrite37.0ms

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-l` `associate-/r*`
4×	`flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

3 → 105

Calls

3 calls:

7.0ms	(/ 1 (- a z))
26.0ms	(* (- y z) (/ 1 (- a z)))
0.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

series245.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ 1 (- a z))
63.0ms	(* (- y z) (/ 1 (- a z)))
141.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

simplify2.8s

Counts

114 → 114

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	152	1285
1	341	1096
2	1014	948
3	3164	944
done	5000	943

prune301.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.5b	(+ (* (- t x) (/ (- y z) (- a z))) x)
2.9b	(* (- t x) (/ (- y z) (- a z)))

rewrite66.0ms

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:

12.0ms	(/ (- y z) (- a z))
11.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)
37.0ms	(* (- t x) (/ (- y z) (- a z)))

series345.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(/ (- y z) (- a z))
164.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)
122.0ms	(* (- t x) (/ (- y z) (- a z)))

simplify1.1s

Counts

135 → 135

Iterations

Useful iterations: 2 (293.0ms)

Iter	Nodes	Cost
0	189	1881
1	491	1765
2	1726	1669
done	5000	1669

prune409.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- y z))
0.6b	(cbrt (- y z))
0.6b	(cbrt (- y z))
11.1b	(fma (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x) x)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

2.0ms	(cbrt (- y z))
2.0ms	(cbrt (- y z))
2.0ms	(cbrt (- y z))
0.0ms	(fma (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x) x)

series619.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(cbrt (- y z))
174.0ms	(cbrt (- y z))
161.0ms	(cbrt (- y z))
123.0ms	(fma (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x) x)

simplify1.8s

Counts

73 → 73

Iterations

Useful iterations: 4 (763.0ms)

Iter	Nodes	Cost
0	96	925
1	201	907
2	442	749
3	1080	676
4	3746	636
done	5001	636

prune298.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 3.6b

regimes356.0ms

Accuracy

6.7% (7.7b remaining)

Error of 11.1b against oracle of 3.4b and baseline of 11.7b

bsearch102.0ms

Steps

Iters	Range		Point
8	1.3789796957155067e+42	1.8415551369076098e+46	1.4012784117723927e+42
8	-1.1766157657047581e-163	-1.090162501590038e-166	-3.6771152743398664e-164

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	21	45
1	28	32
done	28	32

end0.0ms

sample697.0ms

Algorithm

intervals

Results

256.0ms	7828×	body	80	valid
57.0ms	490×	body	640	valid
47.0ms	282×	body	1280	valid
38.0ms	401×	body	320	valid
17.0ms	242×	body	160	valid
3.0ms	18×	body	2560	valid