Details

sample139.0ms

Algorithm

intervals

Results

62.0ms	63×	body	2560	valid
29.0ms	46×	body	640	valid
24.0ms	41×	body	1280	valid
7.0ms	74×	body	80	valid
5.0ms	17×	body	320	valid
4.0ms	15×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	30
4	30
3	28
2	23
1	15
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize23.0ms

Local error

Found 2 expressions with local error:

0.9b	(- 1 (cos x))
19.2b	(/ (- 1 (cos x)) (* x x))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-cbrt-cube` `add-exp-log`
6×	`times-frac` `associate-/l*` `difference-of-squares`
4×	`add-log-exp`
3×	`fma-neg` `distribute-lft-out--`
2×	`expm1-log1p-u` `pow1` `cbrt-undiv` `flip3--` `div-exp` `insert-posit16` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

2 → 63

Calls

2 calls:

11.0ms	(- 1 (cos x))
60.0ms	(/ (- 1 (cos x)) (* x x))

series109.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(- 1 (cos x))
76.0ms	(/ (- 1 (cos x)) (* x x))

simplify3.1s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
3	4897
2	935
1	295
0	121

prune251.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
0.2b	(* (sin x) (sin x))
0.3b	(+ 1 (cos x))
18.9b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
25×	`*-un-lft-identity`
22×	`times-frac`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
12×	`cbrt-undiv` `div-exp`
11×	`pow1` `associate-/l*`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r/` `add-log-exp`
5×	`associate-/r*` `distribute-lft-out`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`fma-def` `div-sub` `swap-sqr` `associate-r` `associate-l` `sqr-sin`
2×	`clear-num` `frac-2neg` `sin-mult` `associate-/l/`
1×	`pow2` `+-commutative` `sum-log` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `unswap-sqr`

Counts

4 → 126

Calls

4 calls:

25.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
27.0ms	(* (sin x) (sin x))
9.0ms	(+ 1 (cos x))
21.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series149.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
25.0ms	(* (sin x) (sin x))
11.0ms	(+ 1 (cos x))
69.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify1.5s

Counts

138 → 138

Iterations

Iter	Nodes
done	5000
2	1979
1	525
0	190

prune602.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sin x) (* (cbrt (+ 1 (cos x))) (cbrt (+ 1 (cos x)))))
0.8b	(cbrt (+ 1 (cos x)))
0.8b	(cbrt (+ 1 (cos x)))
0.8b	(cbrt (+ 1 (cos x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
15×	`*-un-lft-identity`
12×	`cbrt-prod`
9×	`add-sqr-sqrt` `flip3-+` `add-exp-log` `add-cube-cbrt` `flip-+`
8×	`associate-/r/`
7×	`add-cbrt-cube`
4×	`expm1-log1p-u` `frac-times` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `pow1/3` `distribute-lft-out` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `associate-l/` `associate-r/`
1×	`clear-num` `associate-/r*` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 83

Calls

4 calls:

16.0ms	(/ (sin x) (* (cbrt (+ 1 (cos x))) (cbrt (+ 1 (cos x)))))
2.0ms	(cbrt (+ 1 (cos x)))
2.0ms	(cbrt (+ 1 (cos x)))
3.0ms	(cbrt (+ 1 (cos x)))

series1.2s

Counts

4 → 12

Calls

4 calls:

438.0ms	(/ (sin x) (* (cbrt (+ 1 (cos x))) (cbrt (+ 1 (cos x)))))
245.0ms	(cbrt (+ 1 (cos x)))
245.0ms	(cbrt (+ 1 (cos x)))
247.0ms	(cbrt (+ 1 (cos x)))

simplify1.9s

Counts

95 → 95

Iterations

Iter	Nodes
done	5002
3	2742
2	870
1	274
0	123

prune609.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin x) (tan (/ x 2)))
18.9b	(/ (* (sin x) (tan (/ x 2))) (* x x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 47

Calls

2 calls:

13.0ms	(* (sin x) (tan (/ x 2)))
23.0ms	(/ (* (sin x) (tan (/ x 2))) (* x x))

series174.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(* (sin x) (tan (/ x 2)))
87.0ms	(/ (* (sin x) (tan (/ x 2))) (* x x))

simplify863.0ms

Counts

53 → 53

Iterations

Iter	Nodes
done	5018
2	1081
1	247
0	99

prune206.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes83.0ms

Accuracy

73.7% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 1.7b

bsearch141.0ms

Steps

Iters	Range		Point
8	3.770429053702113e-157	4.776604674821127e-154	1.8753012792971286e-156
9	-34.11472770615283	-3.67231414207575e-08	-0.011260686584555396

simplify3.0ms

Iterations

Iter	Nodes
done	24
1	24
0	22

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.6s	1584×	body	2560	valid
911.0ms	1210×	body	1280	valid
670.0ms	1487×	body	640	valid
639.0ms	910×	body	320	valid
247.0ms	2328×	body	80	valid
122.0ms	481×	body	160	valid