Details

sample580.0ms

Algorithm

intervals

Results

199.0ms	92×	body	2560	valid
155.0ms	76×	body	10240	exit
145.0ms	104×	body	1280	valid
25.0ms	32×	body	640	valid
15.0ms	332×	pre	80	true
11.0ms	16×	body	320	valid
2.0ms	11×	body	80	valid
0.0ms	1×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

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

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(expm1 (* (+ a b) eps))
7.1b	(* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps)))
17.2b	(/ eps (expm1 (* eps b)))
17.9b	(/ (* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps))) (expm1 (* eps a)))

rewrite56.0ms

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` `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 → 100

Calls

4 calls:

1.0ms	(expm1 (* (+ a b) eps))
25.0ms	(* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps)))
7.0ms	(/ eps (expm1 (* eps b)))
21.0ms	(/ (* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps))) (expm1 (* eps a)))

series538.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(expm1 (* (+ a b) eps))
157.0ms	(* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps)))
62.0ms	(/ eps (expm1 (* eps b)))
257.0ms	(/ (* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps))) (expm1 (* eps a)))

simplify9.9s

Counts

112 → 112

Iterations

Iter	Nodes
3	7466
2	1510
1	412
0	169

prune1.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite11.0ms

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-+` `log1p-expm1-u`

Counts

1 → 34

Calls

1 calls:

11.0ms

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

series12.0ms

Counts

1 → 3

Calls

1 calls:

12.0ms

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

simplify1.3s

Counts

37 → 37

Iterations

Iter	Nodes
4	2904
3	1131
2	414
1	106
0	42

prune297.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 1/12 (* (* eps eps) b) (/ 1 b))
6.8b	(* (fma -1/2 eps (fma 1/12 (* (* eps eps) b) (/ 1 b))) (expm1 (* (+ a b) eps)))
6.9b	(* (* eps eps) b)
17.2b	(/ (* (fma -1/2 eps (fma 1/12 (* (* eps eps) b) (/ 1 b))) (expm1 (* (+ a b) eps))) (expm1 (* eps a)))

rewrite63.0ms

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` `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 → 74

Calls

4 calls:

0.0ms	(fma 1/12 (* (* eps eps) b) (/ 1 b))
17.0ms	(* (fma -1/2 eps (fma 1/12 (* (* eps eps) b) (/ 1 b))) (expm1 (* (+ a b) eps)))
27.0ms	(* (* eps eps) b)
16.0ms	(/ (* (fma -1/2 eps (fma 1/12 (* (* eps eps) b) (/ 1 b))) (expm1 (* (+ a b) eps))) (expm1 (* eps a)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(fma 1/12 (* (* eps eps) b) (/ 1 b))
124.0ms	(* (fma -1/2 eps (fma 1/12 (* (* eps eps) b) (/ 1 b))) (expm1 (* (+ a b) eps)))
25.0ms	(* (* eps eps) b)
284.0ms	(/ (* (fma -1/2 eps (fma 1/12 (* (* eps eps) b) (/ 1 b))) (expm1 (* (+ a b) eps))) (expm1 (* eps a)))

simplify3.5s

Counts

86 → 86

Iterations

Iter	Nodes
3	5301
2	1177
1	360
0	153

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(expm1 (* eps (+ b a)))
7.0b	(* eps (/ (expm1 (* eps (+ b a))) (expm1 (* eps b))))
10.6b	(/ (expm1 (* eps (+ b a))) (expm1 (* eps b)))
17.9b	(/ (* eps (/ (expm1 (* eps (+ b a))) (expm1 (* eps b)))) (expm1 (* eps a)))

rewrite36.0ms

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-r`
6×	`pow1` `cbrt-undiv` `associate-/r*` `div-exp`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `associate-/l*` `add-log-exp`
3×	`associate-l` `div-inv`
2×	`clear-num` `frac-2neg` `associate-*r/` `expm1-udef` `unswap-sqr`
1×	`expm1-log1p` `div-sub` `pow-prod-down` `*-commutative` `associate-/l/`

Counts

4 → 101

Calls

4 calls:

1.0ms	(expm1 (* eps (+ b a)))
19.0ms	(* eps (/ (expm1 (* eps (+ b a))) (expm1 (* eps b))))
4.0ms	(/ (expm1 (* eps (+ b a))) (expm1 (* eps b)))
10.0ms	(/ (* eps (/ (expm1 (* eps (+ b a))) (expm1 (* eps b)))) (expm1 (* eps a)))

series613.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(expm1 (* eps (+ b a)))
186.0ms	(* eps (/ (expm1 (* eps (+ b a))) (expm1 (* eps b))))
123.0ms	(/ (expm1 (* eps (+ b a))) (expm1 (* eps b)))
262.0ms	(/ (* eps (/ (expm1 (* eps (+ b a))) (expm1 (* eps b)))) (expm1 (* eps a)))

simplify2.9s

Counts

113 → 113

Iterations

Iter	Nodes
3	5719
2	1240
1	377
0	161

prune1.4s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes155.0ms

Accuracy

0% (3.2b remaining)

Error of 3.3b against oracle of 0.0b and baseline of 3.3b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
2	7
1	7
0	6

end0.0ms

sample20.3s

Algorithm

intervals

Results

7.4s	2625×	body	2560	valid
5.5s	3374×	body	1280	valid
4.7s	2062×	body	10240	exit
975.0ms	1074×	body	640	valid
702.0ms	375×	body	320	valid
503.0ms	10067×	pre	80	true
106.0ms	436×	body	80	valid
43.0ms	121×	body	160	valid