Details

sample30.0ms

Algorithm

intervals

Results

10.0ms	241×	body	80	valid
2.0ms	17×	body	640	valid
2.0ms	16×	body	320	valid
1.0ms	4×	body	1280	valid
1.0ms	6×	body	160	valid
0.0ms	1×	body	2560	valid

simplify4.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
8	3757
7	2046
6	989
5	406
4	195
3	103
2	50
1	22
0	11

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.5b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
12.2b	(fma (- t z) (/ y (- a t)) (+ x y))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/r*`
4×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out--` `difference-of-squares`
3×	`associate-/l*`
2×	`expm1-log1p-u` `pow1` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `fma-udef` `div-inv` `flip--`

Counts

2 → 49

Calls

2 calls:

13.0ms	(/ y (- a t))
1.0ms	(fma (- t z) (/ y (- a t)) (+ x y))

series208.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(/ y (- a t))
171.0ms	(fma (- t z) (/ y (- a t)) (+ x y))

simplify1.6s

Counts

55 → 55

Iterations

Iter	Nodes
done	5000
3	1426
2	444
1	174
0	92

prune465.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.9b

localize42.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) y)
0.4b	(/ 1 (/ (- a t) y))
12.2b	(fma (- t z) (/ 1 (/ (- a t) y)) (+ x y))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
101×	`add-sqr-sqrt` `*-un-lft-identity`
69×	`add-cube-cbrt`
22×	`associate-/r*`
16×	`add-exp-log` `distribute-lft-out--` `difference-of-squares`
10×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`div-inv`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-/l/`
1×	`flip3--` `div-sub` `associate-/r/` `fma-udef` `pow-flip` `flip--` `inv-pow`

Counts

3 → 152

Calls

3 calls:

26.0ms	(/ (- a t) y)
27.0ms	(/ 1 (/ (- a t) y))
1.0ms	(fma (- t z) (/ 1 (/ (- a t) y)) (+ x y))

series410.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ (- a t) y)
115.0ms	(/ 1 (/ (- a t) y))
247.0ms	(fma (- t z) (/ 1 (/ (- a t) y)) (+ x y))

simplify2.6s

Counts

161 → 161

Iterations

Iter	Nodes
done	5056
3	4021
2	1355
1	511
0	210

prune740.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.9b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* (/ 1 (- a t)) y)
12.2b	(fma (- t z) (* (/ 1 (- a t)) y) (+ x y))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
32×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-l`
16×	`add-exp-log`
10×	`add-cbrt-cube`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-/r*`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `flip3--` `1-exp` `cbrt-unprod` `div-inv` `flip--`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

3 → 98

Calls

3 calls:

9.0ms	(/ 1 (- a t))
25.0ms	(* (/ 1 (- a t)) y)
0.0ms	(fma (- t z) (* (/ 1 (- a t)) y) (+ x y))

series435.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(/ 1 (- a t))
101.0ms	(* (/ 1 (- a t)) y)
265.0ms	(fma (- t z) (* (/ 1 (- a t)) y) (+ x y))

simplify1.8s

Counts

107 → 107

Iterations

Iter	Nodes
done	5001
3	2199
2	735
1	311
0	137

prune617.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.9b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- a t))
3.4b	(+ (* (- t z) (/ y (- a t))) (+ x y))
10.2b	(* (- t z) (/ y (- a t)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
31×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
10×	`add-cbrt-cube` `frac-add` `add-exp-log`
8×	`flip3--` `flip--` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
6×	`frac-times` `flip3-+` `associate-*l/` `flip-+`
5×	`pow1` `associate-/r` `associate-l*`
4×	`associate-/r/`
3×	`expm1-log1p-u` `sum-log` `associate-r/` `log1p-expm1-u` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`+-commutative` `associate-+r+` `clear-num` `fma-def` `frac-2neg` `pow-prod-down` `*-commutative`

Counts

3 → 113

Calls

3 calls:

16.0ms	(/ y (- a t))
36.0ms	(+ (* (- t z) (/ y (- a t))) (+ x y))
40.0ms	(* (- t z) (/ y (- a t)))

series277.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ y (- a t))
146.0ms	(+ (* (- t z) (/ y (- a t))) (+ x y))
88.0ms	(* (- t z) (/ y (- a t)))

simplify2.2s

Counts

122 → 122

Iterations

Iter	Nodes
done	5001
2	3029
1	672
0	214

prune834.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.9b

regimes612.0ms

Accuracy

35% (5.7b remaining)

Error of 8.9b against oracle of 3.2b and baseline of 11.9b

bsearch238.0ms

Steps

Iters	Range		Point
9	4.931886290112662e+48	4.9150588980470484e+53	2.676545850642376e+52
5	1.2547098983604275e-98	3.94162455355538e-98	2.5758498151188835e-98
7	-8.622901190867368e-121	-2.5108696731841273e-122	-2.942786587816137e-122
7	-1.9000080376622326e+167	-1.1823520142211497e+165	-1.841694990887126e+165

simplify5.0ms

Iterations

Iter	Nodes
done	36
1	36
0	29

end0.0ms

sample1.7s

Algorithm

intervals

Results

591.0ms	7350×	body	80	valid
434.0ms	228×	body	160	valid
128.0ms	453×	body	640	valid
109.0ms	269×	body	1280	valid
65.0ms	401×	body	320	valid
5.0ms	16×	body	2560	valid