Details

sample29.0ms

Algorithm

intervals

Results

11.0ms

264×

body

valid

simplify3.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	14	17
1	24	16
2	43	15
3	66	15
4	97	15
5	131	15
6	164	15
7	240	15
8	473	15
9	1023	15
10	3735	15
done	5000	15

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize15.0ms

Local error

Found 2 expressions with local error:

0.8b	(fma x y (* z (- t a)))
25.9b	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube`
3×	`associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 39

Calls

2 calls:

0.0ms	(fma x y (* z (- t a)))
2.0ms	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

series393.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(fma x y (* z (- t a)))
337.0ms	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

simplify688.0ms

Counts

45 → 45

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	69	841
1	120	830
2	339	750
3	1187	750
done	5000	750

prune211.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 26.2b

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1 (/ (fma z (- b y) y) (fma y x (* z (- t a)))))
0.8b	(fma y x (* z (- t a)))
26.0b	(/ (fma z (- b y) y) (fma y x (* z (- t a))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log` `associate-/r*`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`pow-flip` `associate-/r/` `fma-udef` `inv-pow`

Counts

3 → 117

Calls

3 calls:

5.0ms	(/ 1 (/ (fma z (- b y) y) (fma y x (* z (- t a)))))
0.0ms	(fma y x (* z (- t a)))
2.0ms	(/ (fma z (- b y) y) (fma y x (* z (- t a))))

series733.0ms

Counts

3 → 9

Calls

3 calls:

552.0ms	(/ 1 (/ (fma z (- b y) y) (fma y x (* z (- t a)))))
60.0ms	(fma y x (* z (- t a)))
120.0ms	(/ (fma z (- b y) y) (fma y x (* z (- t a))))

simplify3.1s

Counts

126 → 126

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	171	3175
1	359	3003
2	1188	2680
3	3112	2662
done	5000	2662

prune376.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 10.5b

localize14.0ms

Local error

Found 3 expressions with local error:

0.6b	(/ 1 (fma z (- b y) y))
0.8b	(fma y x (* z (- t a)))
25.5b	(* (/ 1 (fma z (- b y) y)) (fma y x (* z (- t a))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
13×	`associate-l`
10×	`add-cbrt-cube`
6×	`pow1`
4×	`div-exp` `prod-exp`
3×	`expm1-log1p-u` `associate-r` `associate-/r` `fma-udef` `log1p-expm1-u` `associate-/l` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv`
1×	`distribute-rgt-in` `pow-flip` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `inv-pow`

Counts

3 → 82

Calls

3 calls:

2.0ms	(/ 1 (fma z (- b y) y))
0.0ms	(fma y x (* z (- t a)))
9.0ms	(* (/ 1 (fma z (- b y) y)) (fma y x (* z (- t a))))

series679.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(/ 1 (fma z (- b y) y))
66.0ms	(fma y x (* z (- t a)))
548.0ms	(* (/ 1 (fma z (- b y) y)) (fma y x (* z (- t a))))

simplify2.2s

Counts

91 → 91

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	114	1465
1	250	1356
2	833	1172
3	2712	1172
done	5000	1172

prune271.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 10.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (fma z (- b y) y) (/ 1 (fma y x (* z (- t a))))))
0.8b	(fma y x (* z (- t a)))
1.6b	(/ 1 (fma y x (* z (- t a))))
24.3b	(* (fma z (- b y) y) (/ 1 (fma y x (* z (- t a)))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log`
29×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `times-frac`
22×	`add-cube-cbrt`
20×	`div-exp` `add-cbrt-cube`
16×	`prod-exp`
13×	`associate-r`
10×	`pow1` `rec-exp` `1-exp`
6×	`cbrt-undiv` `associate-/l*`
4×	`expm1-log1p-u` `associate-/r*` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `associate-l` `div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-*r/` `pow-prod-down` `clear-num` `associate-/r/` `un-div-inv` `inv-pow`
1×	`*-commutative` `fma-udef`

Counts

4 → 123

Calls

4 calls:

12.0ms	(/ 1 (* (fma z (- b y) y) (/ 1 (fma y x (* z (- t a))))))
0.0ms	(fma y x (* z (- t a)))
2.0ms	(/ 1 (fma y x (* z (- t a))))
9.0ms	(* (fma z (- b y) y) (/ 1 (fma y x (* z (- t a)))))

series814.0ms

Counts

4 → 12

Calls

4 calls:

555.0ms	(/ 1 (* (fma z (- b y) y) (/ 1 (fma y x (* z (- t a))))))
62.0ms	(fma y x (* z (- t a)))
74.0ms	(/ 1 (fma y x (* z (- t a))))
122.0ms	(* (fma z (- b y) y) (/ 1 (fma y x (* z (- t a)))))

simplify3.3s

Counts

135 → 135

Iterations

Useful iterations: 2 (136.0ms)

Iter	Nodes	Cost
0	148	2456
1	342	2204
2	1152	1824
3	3138	1824
done	5001	1824

prune320.0ms

Pruning

12 alts after pruning (8 fresh and 4 done)

Merged error: 10.5b

regimes584.0ms

Accuracy

24.6% (9.5b remaining)

Error of 20.4b against oracle of 10.9b and baseline of 23.5b

bsearch116.0ms

Steps

Iters	Range		Point
9	1.5247250177203267e+35	7.86294764107312e+43	7.736950116967238e+43
8	-1.4335373150418553e+75	-4.5705223523792306e+70	-7.710255796225628e+72

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	21	37
1	25	31
done	25	31

end0.0ms

sample655.0ms

Algorithm

intervals

Results

360.0ms

8392×

body

valid