Details

sample26.0ms

Algorithm

intervals

Results

8.0ms	257×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	7×	body	1280	valid
1.0ms	10×	body	320	valid
1.0ms	12×	body	160	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

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.4b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
14.3b	(fma (- y z) (/ (- t x) (- a z)) x)

rewrite15.0ms

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:

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

series142.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (- t x) (- a z))
93.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

simplify63.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (52.0ms)

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

prune204.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
4.0b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.9b	(* (- y z) (/ (- t x) (- a z)))

rewrite59.0ms

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:

12.0ms	(/ (- t x) (- a z))
3.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
38.0ms	(* (- y z) (/ (- t x) (- a z)))

series338.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ (- t x) (- a z))
155.0ms	(+ 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 (45.0ms)

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

prune349.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
14.3b	(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)

series577.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(cbrt (- a z))
155.0ms	(cbrt (- a z))
148.0ms	(cbrt (- a z))
122.0ms	(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 (46.0ms)

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

prune305.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
14.2b	(fma (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (/ (- a z) (cbrt (- t x)))) 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 (- t x))
2.0ms	(cbrt (- t x))
2.0ms	(cbrt (- t x))
0.0ms	(fma (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (/ (- a z) (cbrt (- t x)))) x)

series548.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt (- t x))
149.0ms	(cbrt (- t x))
154.0ms	(cbrt (- t x))
92.0ms	(fma (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (/ (- a z) (cbrt (- t x)))) x)

simplify46.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	199	519
1	448	479
2	1381	458
3	5002	435

prune272.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.6b

regimes417.0ms

Accuracy

40.7% (6.7b remaining)

Error of 10.2b against oracle of 3.6b and baseline of 14.8b

bsearch3.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	22
1	26	22

end0.0ms

sample679.0ms

Algorithm

intervals

Results

256.0ms	7764×	body	80	valid
64.0ms	501×	body	640	valid
37.0ms	420×	body	320	valid
35.0ms	236×	body	1280	valid
16.0ms	265×	body	160	valid
3.0ms	14×	body	2560	valid