Details

sample611.0ms

Algorithm

intervals

Results

189.0ms	82×	body	2560	valid
162.0ms	59×	body	10240	exit
135.0ms	108×	body	1280	valid
55.0ms	315×	pre	80	true
29.0ms	32×	body	640	valid
7.0ms	12×	body	320	valid
3.0ms	7×	body	160	valid
3.0ms	15×	body	80	valid

simplify1.7s

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (* (+ a b) eps))
6.2b	(* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps)))
16.0b	(/ (* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps))) (expm1 (* eps a)))
16.3b	(/ eps (expm1 (* eps b)))

rewrite33.0ms

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:

0.0ms	(expm1 (* (+ a b) eps))
10.0ms	(* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps)))
16.0ms	(/ (* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps))) (expm1 (* eps a)))
4.0ms	(/ eps (expm1 (* eps b)))

series488.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(expm1 (* (+ a b) eps))
147.0ms	(* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps)))
229.0ms	(/ (* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps))) (expm1 (* eps a)))
49.0ms	(/ eps (expm1 (* eps b)))

simplify9.9s

Counts

116 → 116

Iterations

Iter	Nodes
3	7683
2	1565
1	416
0	173

prune1.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 1 expressions with local error:

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

rewrite23.0ms

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:

22.0ms

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

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

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

simplify1.2s

Counts

38 → 38

Iterations

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

prune313.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt b) (cbrt b))
0.6b	(cbrt b)
0.6b	(cbrt b)
0.6b	(cbrt b)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 85

Calls

4 calls:

15.0ms	(* (cbrt b) (cbrt b))
1.0ms	(cbrt b)
1.0ms	(cbrt b)
1.0ms	(cbrt b)

series1.2s

Counts

4 → 12

Calls

4 calls:

366.0ms	(* (cbrt b) (cbrt b))
280.0ms	(cbrt b)
281.0ms	(cbrt b)
272.0ms	(cbrt b)

simplify1.1s

Counts

97 → 97

Iterations

Iter	Nodes
4	3150
3	858
2	330
1	135
0	67

prune1.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize75.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* eps eps) 1/12)
2.5b	(fma (* (* eps eps) 1/12) b (/ 1 b))
6.0b	(* (fma -1/2 eps (fma (* (* eps eps) 1/12) b (/ 1 b))) (expm1 (* (+ a b) eps)))
15.5b	(/ (* (fma -1/2 eps (fma (* (* eps eps) 1/12) b (/ 1 b))) (expm1 (* (+ a b) eps))) (expm1 (* eps a)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

18.0ms	(* (* eps eps) 1/12)
0.0ms	(fma (* (* eps eps) 1/12) b (/ 1 b))
6.0ms	(* (fma -1/2 eps (fma (* (* eps eps) 1/12) b (/ 1 b))) (expm1 (* (+ a b) eps)))
10.0ms	(/ (* (fma -1/2 eps (fma (* (* eps eps) 1/12) b (/ 1 b))) (expm1 (* (+ a b) eps))) (expm1 (* eps a)))

series504.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (* eps eps) 1/12)
46.0ms	(fma (* (* eps eps) 1/12) b (/ 1 b))
121.0ms	(* (fma -1/2 eps (fma (* (* eps eps) 1/12) b (/ 1 b))) (expm1 (* (+ a b) eps)))
289.0ms	(/ (* (fma -1/2 eps (fma (* (* eps eps) 1/12) b (/ 1 b))) (expm1 (* (+ a b) eps))) (expm1 (* eps a)))

simplify3.6s

Counts

90 → 90

Iterations

Iter	Nodes
3	5389
2	1147
1	361
0	158

prune1.5s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.2b

regimes168.0ms

Accuracy

9.4% (2.9b remaining)

Error of 2.9b against oracle of 0.0b and baseline of 3.2b

bsearch369.0ms

Steps

Iters	Range		Point
8	6.982765408101908e-56	2.0362883603176916e-52	3.532032554393501e-54

simplify7.0ms

Iterations

Iter	Nodes
2	26
1	26
0	20

end0.0ms

sample19.5s

Algorithm

intervals

Results

6.0s	2561×	body	2560	valid
5.8s	3457×	body	1280	valid
4.9s	2032×	body	10240	exit
1.5s	1115×	body	640	valid
623.0ms	10033×	pre	80	true
205.0ms	319×	body	320	valid
76.0ms	428×	body	80	valid
72.0ms	121×	body	160	valid