Details

sample66.0ms

Algorithm

intervals

Results

20.0ms	242×	body	80	valid
5.0ms	16×	body	640	valid
4.0ms	15×	body	320	valid
3.0ms	8×	body	1280	valid
1.0ms	9×	body	160	valid

simplify9.6s

Counts

1 → 1

Iterations

Useful iterations: 3 (24.0ms)

Iter	Nodes	Cost
0	11	13
1	20	13
2	45	13
3	116	12
4	322	12
5	766	12
6	1555	12
7	2873	12
8	4761	12
done	5000	12

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.5b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
3.6b	(fma (/ (- y z) (- a z)) (- t x) x)

rewrite465.0ms

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:

462.0ms	(/ (- y z) (- a z))
0.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

series305.0ms

Counts

2 → 6

Calls

2 calls:

101.0ms	(/ (- y z) (- a z))
204.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify1.8s

Counts

70 → 70

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	116	918
1	266	890
2	653	838
3	1707	834
done	5001	830

prune336.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.5b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- y z) (/ 1 (- a z)))
5.5b	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

rewrite131.0ms

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:

23.0ms	(/ 1 (- a z))
103.0ms	(* (- y z) (/ 1 (- a z)))
1.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

series340.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(/ 1 (- a z))
92.0ms	(* (- y z) (/ 1 (- a z)))
177.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

simplify2.7s

Counts

114 → 114

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	152	1285
1	334	1052
2	930	948
3	3159	944
done	5002	942

prune410.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.2b

localize34.0ms

Local error

Found 4 expressions with local error:

3.1b	(cbrt (/ (- y z) (- a z)))
3.1b	(cbrt (/ (- y z) (- a z)))
3.1b	(cbrt (/ (- y z) (- a z)))
3.6b	(fma (* (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z)))) (cbrt (/ (- y z) (- a z)))) (- t x) x)

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-sqr-sqrt` `*-un-lft-identity`
93×	`cbrt-prod`
75×	`times-frac`
37×	`add-cube-cbrt`
30×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `flip3--` `pow1/3` `flip--` `div-inv`
1×	`fma-udef`

Counts

4 → 136

Calls

4 calls:

21.0ms	(cbrt (/ (- y z) (- a z)))
19.0ms	(cbrt (/ (- y z) (- a z)))
13.0ms	(cbrt (/ (- y z) (- a z)))
1.0ms	(fma (* (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z)))) (cbrt (/ (- y z) (- a z)))) (- t x) x)

series1.8s

Counts

4 → 12

Calls

4 calls:

506.0ms	(cbrt (/ (- y z) (- a z)))
613.0ms	(cbrt (/ (- y z) (- a z)))
479.0ms	(cbrt (/ (- y z) (- a z)))
193.0ms	(fma (* (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z)))) (cbrt (/ (- y z) (- a z)))) (- t x) x)

simplify3.6s

Counts

148 → 148

Iterations

Useful iterations: 4 (2.0s)

Iter	Nodes	Cost
0	178	2811
1	339	2718
2	694	2417
3	1671	2353
4	4990	2283
done	5000	2283

prune861.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ 1 (- a z)))
3.1b	(cbrt (/ (- y z) (- a z)))
3.1b	(cbrt (/ (- y z) (- a z)))
6.3b	(fma (* (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z)))) (* (cbrt (- y z)) (cbrt (/ 1 (- a z))))) (- t x) x)

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

83×	`cbrt-prod`
81×	`add-sqr-sqrt` `*-un-lft-identity`
65×	`times-frac`
35×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `flip3--` `pow1/3` `flip--` `div-inv`
1×	`fma-udef`

Counts

4 → 126

Calls

4 calls:

14.0ms	(cbrt (/ 1 (- a z)))
21.0ms	(cbrt (/ (- y z) (- a z)))
20.0ms	(cbrt (/ (- y z) (- a z)))
1.0ms	(fma (* (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z)))) (* (cbrt (- y z)) (cbrt (/ 1 (- a z))))) (- t x) x)

series1.5s

Counts

4 → 12

Calls

4 calls:

246.0ms	(cbrt (/ 1 (- a z)))
525.0ms	(cbrt (/ (- y z) (- a z)))
522.0ms	(cbrt (/ (- y z) (- a z)))
224.0ms	(fma (* (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z)))) (* (cbrt (- y z)) (cbrt (/ 1 (- a z))))) (- t x) x)

simplify1.8s

Counts

138 → 138

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	260	2534
1	479	2400
2	978	2283
3	2497	2248
done	5001	2201

prune730.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.2b

regimes713.0ms

Accuracy

31.2% (5.8b remaining)

Error of 9.3b against oracle of 3.5b and baseline of 11.9b

bsearch4.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	94
1	37	94
done	37	94

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	7744×	body	80	valid
148.0ms	481×	body	640	valid
75.0ms	441×	body	320	valid
73.0ms	261×	body	1280	valid
48.0ms	280×	body	160	valid
4.0ms	12×	body	2560	valid