Details

sample28.0ms

Algorithm

intervals

Results

9.0ms	240×	body	80	valid
2.0ms	13×	body	1280	valid
2.0ms	14×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	3×	body	2560	valid
0.0ms	6×	body	160	valid

simplify74.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	116	5
3	324	5
4	861	5
5	1912	5
6	4581	5
7	5001	5

prune8.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 11.4b

Counts

2 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
3.0b	(fma (/ (- y z) (- a z)) (- t x) x)

rewrite12.0ms

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:

9.0ms	(/ (- y z) (- a z))
1.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

series164.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (- y z) (- a z))
118.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify60.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	265	450
1	729	425
2	2562	423
3	5002	421

prune190.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	58	12	70
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	59	13	72

Merged error: 4.1b

Counts

72 → 13

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
1.9b	(+ (* (/ (- y z) (- a z)) (- t x)) x)
2.1b	(* (/ (- y z) (- a z)) (- t x))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 170

Calls

3 calls:

8.0ms	(/ (- y z) (- a z))
14.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)
17.0ms	(* (/ (- y z) (- a z)) (- t x))

series521.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ (- y z) (- a z))
176.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)
298.0ms	(* (/ (- y z) (- a z)) (- t x))

simplify79.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	682	1497
1	2657	1254
2	5002	1252

prune391.0ms

Filtered

179 candidates to 119 candidates (66.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	170	9	179
Fresh	8	4	12
Picked	0	1	1
Done	0	0	0
Total	178	14	192

Merged error: 4.0b

Counts

192 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

1.9b	(+ (* (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z)))) (* (cbrt (/ (- y z) (- a z))) (- t x))) x)
3.7b	(cbrt (/ (- y z) (- a z)))
3.7b	(cbrt (/ (- y z) (- a z)))
3.7b	(cbrt (/ (- y z) (- a z)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

121×	`add-sqr-sqrt` `*-un-lft-identity`
93×	`cbrt-prod`
75×	`times-frac`
61×	`add-cube-cbrt`
44×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
36×	`prod-diff`
30×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-div` `flip3--` `pow1/3` `flip--` `div-inv`
1×	`+-commutative` `fma-def` `flip3-+` `sum-log` `flip-+`

Counts

4 → 184

Calls

4 calls:

43.0ms	(+ (* (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z)))) (* (cbrt (/ (- y z) (- a z))) (- t x))) x)
7.0ms	(cbrt (/ (- y z) (- a z)))
7.0ms	(cbrt (/ (- y z) (- a z)))
7.0ms	(cbrt (/ (- y z) (- a z)))

series1.1s

Counts

4 → 12

Calls

4 calls:

170.0ms	(+ (* (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z)))) (* (cbrt (/ (- y z) (- a z))) (- t x))) x)
296.0ms	(cbrt (/ (- y z) (- a z)))
308.0ms	(cbrt (/ (- y z) (- a z)))
311.0ms	(cbrt (/ (- y z) (- a z)))

simplify62.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	559	2646
1	1553	2225
2	5002	2091

prune826.0ms

Filtered

196 candidates to 154 candidates (78.6%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	196	14	210

Merged error: 4.0b

Counts

210 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- y z))
0.6b	(cbrt (- y z))
0.6b	(cbrt (- y z))
9.3b	(fma (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x) x)

rewrite14.0ms

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:

3.0ms	(cbrt (- y z))
4.0ms	(cbrt (- y z))
5.0ms	(cbrt (- y z))
1.0ms	(fma (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x) x)

series558.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(cbrt (- y z))
149.0ms	(cbrt (- y z))
141.0ms	(cbrt (- y z))
124.0ms	(fma (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x) x)

simplify52.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	199	519
1	454	479
2	1395	458
3	5001	435

prune213.0ms

Filtered

73 candidates to 65 candidates (89.0%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	73	14	87

Merged error: 4.0b

Counts

87 → 14

regimes356.0ms

Accuracy

24.1% (6.3b remaining)

Error of 10.1b against oracle of 3.8b and baseline of 12.0b

bsearch81.0ms

Steps

Iters	Range		Point
8	4.96871780850416e-154	4.611816222947149e-150	9.01266496219421e-152
7	-3.1356306227112667e-109	-6.530422565126355e-111	-1.1419396522048079e-110

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	10
1	26	10

end0.0ms

sample780.0ms

Algorithm

intervals

Results

306.0ms	7759×	body	80	valid
74.0ms	492×	body	640	valid
57.0ms	307×	body	1280	valid
44.0ms	412×	body	320	valid
19.0ms	256×	body	160	valid
5.0ms	21×	body	2560	valid