Details

sample525.0ms

Algorithm

intervals

Results

155.0ms	75×	body	2560	valid
139.0ms	118×	body	1280	valid
136.0ms	69×	body	10240	exit
27.0ms	15×	body	320	valid
23.0ms	29×	body	640	valid
15.0ms	325×	pre	80	true
3.0ms	17×	body	80	valid
1.0ms	2×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
5	3998
4	640
3	189
2	78
1	44
0	17

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (* (+ a b) eps))
7.4b	(* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps)))
15.5b	(/ (* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps))) (expm1 (* eps a)))
16.5b	(/ eps (expm1 (* eps b)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
20×	`add-cbrt-cube` `add-exp-log`
13×	`associate-l`
6×	`pow1` `cbrt-undiv` `associate-/r*` `div-exp`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `associate-/l*` `add-log-exp`
3×	`associate-r` `div-inv`
2×	`clear-num` `frac-2neg` `associate-*l/` `unswap-sqr`
1×	`expm1-log1p` `pow-prod-down` `*-commutative` `expm1-udef` `associate-/l/`

Counts

4 → 104

Calls

4 calls:

1.0ms	(expm1 (* (+ a b) eps))
19.0ms	(* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps)))
21.0ms	(/ (* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps))) (expm1 (* eps a)))
8.0ms	(/ eps (expm1 (* eps b)))

series524.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(expm1 (* (+ a b) eps))
155.0ms	(* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps)))
245.0ms	(/ (* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps))) (expm1 (* eps a)))
69.0ms	(/ eps (expm1 (* eps b)))

simplify10.2s

Counts

116 → 116

Iterations

Iter	Nodes
3	7683
2	1565
1	416
0	173

prune1.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize371.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (/ 1 b) (/ 1 a))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
15×	`times-frac`
13×	`fma-def`
10×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`distribute-lft-out`
5×	`div-inv`
3×	`add-log-exp`
1×	`expm1-log1p-u` `pow1` `+-commutative` `sum-log` `flip3-+` `add-cbrt-cube` `frac-add` `add-exp-log` `flip-+` `insert-posit16` `log1p-expm1-u`

Counts

1 → 35

Calls

1 calls:

12.0ms

(+ (/ 1 b) (/ 1 a))

series13.0ms

Counts

1 → 3

Calls

1 calls:

13.0ms

(+ (/ 1 b) (/ 1 a))

simplify1.2s

Counts

38 → 38

Iterations

Iter	Nodes
4	2780
3	1109
2	412
1	107
0	43

prune287.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ 1 b)) (cbrt (/ 1 b)))
0.5b	(cbrt (/ 1 b))
0.5b	(cbrt (/ 1 b))
0.5b	(cbrt (/ 1 b))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

119×	`cbrt-prod`
97×	`add-sqr-sqrt`
79×	`times-frac`
67×	`*-un-lft-identity`
57×	`add-cube-cbrt`
18×	`swap-sqr`
16×	`associate-r` `associate-l` `unswap-sqr`
11×	`pow1`
9×	`pow1/3` `div-inv`
7×	`cbrt-div`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 165

Calls

4 calls:

22.0ms	(* (cbrt (/ 1 b)) (cbrt (/ 1 b)))
1.0ms	(cbrt (/ 1 b))
1.0ms	(cbrt (/ 1 b))
2.0ms	(cbrt (/ 1 b))

series1.3s

Counts

4 → 12

Calls

4 calls:

386.0ms	(* (cbrt (/ 1 b)) (cbrt (/ 1 b)))
292.0ms	(cbrt (/ 1 b))
309.0ms	(cbrt (/ 1 b))
289.0ms	(cbrt (/ 1 b))

simplify2.6s

Counts

177 → 177

Iterations

Iter	Nodes
4	4079
3	1228
2	490
1	249
0	145

prune1.9s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (* (+ a b) eps))
7.4b	(* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps)))
15.4b	(/ (expm1 (* eps a)) (* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps))))
16.5b	(/ eps (expm1 (* eps b)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
20×	`add-cbrt-cube` `add-exp-log`
13×	`associate-l`
6×	`pow1` `cbrt-undiv` `div-exp` `associate-/l*`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `associate-/r*` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`associate-r` `div-inv`
2×	`clear-num` `frac-2neg` `associate-*l/` `expm1-udef` `unswap-sqr`
1×	`expm1-log1p` `div-sub` `pow-prod-down` `associate-/r/` `*-commutative`

Counts

4 → 105

Calls

4 calls:

0.0ms	(expm1 (* (+ a b) eps))
11.0ms	(* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps)))
15.0ms	(/ (expm1 (* eps a)) (* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps))))
8.0ms	(/ eps (expm1 (* eps b)))

series552.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(expm1 (* (+ a b) eps))
154.0ms	(* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps)))
268.0ms	(/ (expm1 (* eps a)) (* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps))))
49.0ms	(/ eps (expm1 (* eps b)))

simplify5.5s

Counts

117 → 117

Iterations

Iter	Nodes
3	7818
2	1552
1	419
0	173

prune1.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes131.0ms

Accuracy

15.8% (2.8b remaining)

Error of 2.8b against oracle of 0.0b and baseline of 3.4b

bsearch338.0ms

Steps

Iters	Range		Point
9	4.21421307457194e-59	3.741402905337886e-51	1.4538299418999213e-51

simplify6.0ms

Iterations

Iter	Nodes
2	27
1	27
0	21

end0.0ms

sample19.5s

Algorithm

intervals

Results

6.5s	3462×	body	1280	valid
5.7s	2525×	body	2560	valid
4.4s	2008×	body	10240	exit
1.1s	1099×	body	640	valid
925.0ms	10011×	pre	80	true
224.0ms	342×	body	320	valid
77.0ms	450×	body	80	valid
45.0ms	125×	body	160	valid