Details

sample32.0ms

Algorithm

intervals

Results

13.0ms

272×

body

valid

simplify3.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	14	17
1	24	16
2	43	15
3	75	15
4	112	15
5	148	15
6	181	15
7	257	15
8	419	15
9	728	15
10	1525	15
11	4096	15
done	5000	15

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 21.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma z (- b y) y)
0.0b	(* z (- t a))
0.3b	(fma x y (* z (- t a)))
21.0b	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`sub-neg` `associate-*r/` `fma-udef`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 95

Calls

4 calls:

0.0ms	(fma z (- b y) y)
32.0ms	(* z (- t a))
0.0ms	(fma x y (* z (- t a)))
6.0ms	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

series522.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(fma z (- b y) y)
40.0ms	(* z (- t a))
61.0ms	(fma x y (* z (- t a)))
391.0ms	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

simplify1.7s

Counts

107 → 107

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	171	1678
1	309	1491
2	699	1283
3	2817	1241
done	5000	1187

prune344.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (- b y) z) y)
0.0b	(* z (- t a))
0.3b	(fma x y (* z (- t a)))
21.0b	(/ (fma x y (* z (- t a))) (+ (* (- b y) z) y))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`sub-neg` `flip3-+` `associate-*r/` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `flip3--` `fma-def` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 101

Calls

4 calls:

16.0ms	(+ (* (- b y) z) y)
25.0ms	(* z (- t a))
0.0ms	(fma x y (* z (- t a)))
27.0ms	(/ (fma x y (* z (- t a))) (+ (* (- b y) z) y))

series527.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (* (- b y) z) y)
41.0ms	(* z (- t a))
57.0ms	(fma x y (* z (- t a)))
393.0ms	(/ (fma x y (* z (- t a))) (+ (* (- b y) z) y))

simplify1.8s

Counts

113 → 113

Iterations

Useful iterations: 3 (740.0ms)

Iter	Nodes	Cost
0	186	1837
1	377	1588
2	933	1380
3	3734	1334
done	5000	1334

prune343.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 21.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.3b	(fma x y (* z (- t a)))
0.7b	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
20.5b	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
72×	`add-sqr-sqrt`
70×	`*-un-lft-identity`
68×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`prod-diff`
16×	`associate-/r*`
13×	`add-cbrt-cube`
11×	`distribute-rgt-in` `distribute-lft-in`
8×	`div-exp`
7×	`pow1`
6×	`div-inv` `associate-/l*`
5×	`associate-r`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`sub-neg` `rec-exp` `frac-2neg` `1-exp` `associate-*r/` `clear-num`
1×	`flip3--` `pow-flip` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 163

Calls

4 calls:

26.0ms	(* z (- t a))
0.0ms	(fma x y (* z (- t a)))
11.0ms	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
6.0ms	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

series771.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* z (- t a))
61.0ms	(fma x y (* z (- t a)))
540.0ms	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
130.0ms	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

simplify2.3s

Counts

175 → 175

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	264	3896
1	509	3507
2	1078	3118
3	4057	3058
done	5000	3058

prune489.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 11.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.3b	(fma x y (* z (- t a)))
0.7b	(/ 1 (fma z (- b y) y))
20.8b	(* (fma x y (* z (- t a))) (/ 1 (fma z (- b y) y)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
34×	`add-cube-cbrt`
20×	`times-frac`
19×	`add-exp-log`
18×	`associate-r` `prod-diff`
13×	`add-cbrt-cube`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow1`
6×	`associate-l`
5×	`prod-exp`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-r/` `associate-/r` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `rec-exp` `1-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`flip3--` `pow-flip` `frac-2neg` `clear-num` `un-div-inv` `flip--` `fma-udef` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 127

Calls

4 calls:

29.0ms	(* z (- t a))
0.0ms	(fma x y (* z (- t a)))
6.0ms	(/ 1 (fma z (- b y) y))
17.0ms	(* (fma x y (* z (- t a))) (/ 1 (fma z (- b y) y)))

series552.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* z (- t a))
56.0ms	(fma x y (* z (- t a)))
65.0ms	(/ 1 (fma z (- b y) y))
387.0ms	(* (fma x y (* z (- t a))) (/ 1 (fma z (- b y) y)))

simplify2.0s

Counts

139 → 139

Iterations

Useful iterations: 3 (886.0ms)

Iter	Nodes	Cost
0	200	2133
1	387	1818
2	915	1550
3	3816	1508
done	5000	1508

prune332.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 11.5b

regimes534.0ms

Accuracy

27.3% (8.8b remaining)

Error of 19.7b against oracle of 10.8b and baseline of 23.0b

bsearch105.0ms

Steps

Iters	Range		Point
10	3.414647358186085e+54	3.0458708391958014e+68	2.899597943526477e+68
8	-1.1193189535123491e+195	-3.5345243462981693e+192	-1.7510981625801499e+193

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	23	39
1	29	31
done	29	31

end0.0ms

sample804.0ms

Algorithm

intervals

Results

354.0ms

8420×

body

valid