Details

sample44.0ms

Algorithm

intervals

Results

18.0ms	249×	body	80	valid
4.0ms	12×	body	1280	valid
3.0ms	19×	body	320	valid
3.0ms	13×	body	640	valid
1.0ms	8×	body	160	valid
1.0ms	2×	body	2560	valid

simplify55.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	23	6
1	46	5
2	128	5
3	362	5
4	1024	5
5	2296	5
6	5001	5

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
16.5b	(fma (- y z) (/ (- t x) (- a z)) x)

rewrite14.0ms

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:

11.0ms	(/ (- t x) (- a z))
0.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

series142.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (- t x) (- a z))
91.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

simplify59.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	268	450
1	733	425
2	2490	423
3	5001	421

prune217.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.7b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.4b	(+ x (* (- y z) (/ (- t x) (- a z))))
6.0b	(* (- y z) (/ (- t x) (- a z)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
74×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
28×	`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` `fma-def` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 128

Calls

3 calls:

11.0ms	(/ (- t x) (- a z))
3.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
32.0ms	(* (- y z) (/ (- t x) (- a z)))

series331.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ (- t x) (- a z))
148.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
130.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify57.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	488	901
1	2066	849
2	5001	847

prune374.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a z))
0.3b	(* (- t x) (/ 1 (- a z)))
5.6b	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
6.0b	(* (- y z) (* (- t x) (/ 1 (- a z))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
45×	`*-un-lft-identity`
32×	`add-exp-log` `times-frac`
26×	`add-cube-cbrt`
22×	`associate-r`
20×	`frac-times` `add-cbrt-cube`
17×	`flip3--` `flip--`
13×	`prod-exp`
12×	`pow1`
10×	`associate-r/` `associate-l` `associate-l/`
9×	`distribute-lft-out--` `difference-of-squares`
7×	`cbrt-unprod`
6×	`div-exp` `add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `pow-prod-down` `associate-/r/` `un-div-inv` `log1p-expm1-u`
3×	`cbrt-undiv` `rec-exp` `fma-def` `1-exp` `associate-/l*` `unswap-sqr`
2×	`*-commutative` `div-inv`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+` `inv-pow`

Counts

4 → 157

Calls

4 calls:

5.0ms	(/ 1 (- a z))
23.0ms	(* (- t x) (/ 1 (- a z)))
3.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
37.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))

series372.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ 1 (- a z))
49.0ms	(* (- t x) (/ 1 (- a z)))
153.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
130.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))

simplify75.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	603	1062
1	2878	940
2	5002	891

prune435.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 4.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
16.2b	(fma (- y z) (* (/ 1 (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))) x)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

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

series576.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(cbrt (- a z))
153.0ms	(cbrt (- a z))
149.0ms	(cbrt (- a z))
119.0ms	(fma (- y z) (* (/ 1 (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))) x)

simplify53.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	203	532
1	487	489
2	1741	478
3	5002	453

prune286.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 4.0b

regimes418.0ms

Accuracy

31.4% (7.5b remaining)

Error of 11.2b against oracle of 3.7b and baseline of 14.7b

bsearch192.0ms

Steps

Iters	Range		Point
7	8.143037386617837e+211	2.271139247461068e+213	4.475379326627651e+212
6	-2.3998897035896985e-228	-1.6476369987726682e-229	-6.978961612748903e-229
8	-3.2357594850027844e-11	-6.415887947727871e-14	-4.441653635190891e-13
7	-1.5931363873182533e+155	-1.016503209116054e+153	-4.884452534981531e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	35
1	43	35

end0.0ms

sample1.1s

Algorithm

intervals

Results

508.0ms	7842×	body	80	valid
113.0ms	469×	body	640	valid
80.0ms	411×	body	320	valid
77.0ms	262×	body	1280	valid
32.0ms	267×	body	160	valid
7.0ms	18×	body	2560	valid