Details

sample29.0ms

Algorithm

intervals

Results

8.0ms	259×	body	80	valid
2.0ms	21×	body	640	valid
1.0ms	9×	body	1280	valid
1.0ms	14×	body	320	valid
1.0ms	10×	body	160	valid

simplify4.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	11	13
1	23	13
2	46	12
3	128	12
4	360	12
5	877	12
6	2016	12
7	3586	12
done	5000	12

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
15.1b	(fma (/ (- t x) (- a z)) (- y z) x)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 64

Calls

2 calls:

22.0ms	(/ (- t x) (- a z))
0.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series152.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(/ (- t x) (- a z))
95.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify939.0ms

Counts

70 → 70

Iterations

Useful iterations: done (937.0ms)

Iter	Nodes	Cost
0	118	918
1	269	890
2	658	838
3	1743	834
done	5000	830

prune197.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 9.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.3b	(* (- t x) (/ 1 (- a z)))
15.0b	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 105

Calls

3 calls:

12.0ms	(/ 1 (- a z))
45.0ms	(* (- t x) (/ 1 (- a z)))
0.0ms	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

series191.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ 1 (- a z))
58.0ms	(* (- t x) (/ 1 (- a z)))
97.0ms	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

simplify1.6s

Counts

114 → 114

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	155	1285
1	344	1052
2	954	948
3	3231	944
done	5000	942

prune247.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 9.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
4.1b	(+ (* (- y z) (/ (- t x) (- a z))) x)
4.4b	(* (- y z) (/ (- t x) (- a z)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 126

Calls

3 calls:

23.0ms	(/ (- t x) (- a z))
25.0ms	(+ (* (- y z) (/ (- t x) (- a z))) x)
60.0ms	(* (- y z) (/ (- t x) (- a z)))

series379.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(/ (- t x) (- a z))
170.0ms	(+ (* (- y z) (/ (- t x) (- a z))) x)
146.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify870.0ms

Counts

135 → 135

Iterations

Useful iterations: done (865.0ms)

Iter	Nodes	Cost
0	189	1881
1	485	1765
2	1765	1669
done	5001	1667

prune356.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 6.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
1.0b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
9.4b	(+ (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))) x)

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
27×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`frac-times`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `fma-def` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 143

Calls

4 calls:

5.0ms	(cbrt (- a z))
4.0ms	(cbrt (- a z))
130.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
67.0ms	(+ (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))) x)

series829.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(cbrt (- a z))
153.0ms	(cbrt (- a z))
317.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
198.0ms	(+ (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))) x)

simplify1.3s

Counts

155 → 155

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	261	3480
1	736	3292
2	2816	2749
done	5002	2561

prune647.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 6.2b

regimes394.0ms

Accuracy

5% (8.4b remaining)

Error of 12.0b against oracle of 3.6b and baseline of 12.4b

bsearch102.0ms

Steps

Iters	Range		Point
8	-5.421319756117139e-285	-3.8119735541679966e-288	-3.8790020276651695e-288
11	-2.413717548537463e-66	-3.452617791225645e-93	-9.021302549266581e-90

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	24	66
1	28	44
done	28	44

end0.0ms

sample769.0ms

Algorithm

intervals

Results

236.0ms	7806×	body	80	valid
60.0ms	497×	body	640	valid
37.0ms	268×	body	1280	valid
33.0ms	376×	body	320	valid
16.0ms	275×	body	160	valid
3.0ms	16×	body	2560	valid