Details

sample25.0ms

Algorithm

intervals

Results

7.0ms	214×	body	80	valid
3.0ms	26×	body	640	valid
1.0ms	8×	body	1280	valid
1.0ms	12×	body	160	valid
1.0ms	8×	body	320	valid
0.0ms	1×	body	2560	valid

simplify88.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (17.0ms)

Iter	Nodes	Cost
0	22	6
1	52	6
2	111	6
3	213	6
4	517	5
5	1051	5
6	2055	5
7	3280	5
8	5002	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: 12.8b

Counts

2 → 2

localize10.0ms

Local error

Found 1 expressions with local error:

14.4b

(fma (/ y (- a t)) (- t z) (+ x y))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma (/ y (- a t)) (- t z) (+ x y))

series83.0ms

Counts

1 → 3

Calls

1 calls:

83.0ms

(fma (/ y (- a t)) (- t z) (+ x y))

simplify69.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	40	84
1	96	73
2	354	73
3	2068	73
4	5003	73

prune55.0ms

Filtered

13 candidates to 12 candidates (92.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	8	5	13
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	8	7	15

Merged error: 8.8b

Counts

15 → 7

localize10.0ms

Local error

Found 2 expressions with local error:

4.7b	(+ (* (/ y (- a t)) (- t z)) (+ x y))
10.1b	(* (/ y (- a t)) (- t z))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt` `*-un-lft-identity`
70×	`frac-add`
66×	`frac-times`
65×	`add-cube-cbrt`
45×	`associate-/r*`
44×	`associate-l`
38×	`flip3--` `flip--`
36×	`flip3-+` `prod-diff` `flip-+`
33×	`fma-def` `associate-*l/`
32×	`times-frac`
27×	`associate-/l*`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
17×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-r`
9×	`frac-2neg` `clear-num`
7×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`associate-*r/` `distribute-lft-out`
4×	`pow1` `sub-neg` `associate-/r/` `unswap-sqr`
3×	`sum-log`
2×	`+-commutative` `expm1-log1p-u` `associate-+r+` `prod-exp` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `div-inv`
1×	`cbrt-undiv` `div-exp` `pow-prod-down`

Counts

2 → 245

Calls

2 calls:

37.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
15.0ms	(* (/ y (- a t)) (- t z))

series264.0ms

Counts

2 → 6

Calls

2 calls:

104.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
160.0ms	(* (/ y (- a t)) (- t z))

simplify81.0ms

Algorithm

egg-herbie

Counts

251 → 251

Iterations

Useful iterations: 1 (51.0ms)

Iter	Nodes	Cost
0	1926	2972
1	5001	2653

prune1.1s

Filtered

251 candidates to 177 candidates (70.5%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	233	18	251
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	236	22	258

Merged error: 8.7b

Counts

258 → 22

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
13.0b	(fma (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))) (* (/ (cbrt y) (cbrt (- a t))) (- t z)) (+ x y))

rewrite12.0ms

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

series1.2s

Counts

4 → 12

Calls

4 calls:

165.0ms	(cbrt (- a t))
158.0ms	(cbrt (- a t))
165.0ms	(cbrt (- a t))
685.0ms	(fma (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))) (* (/ (cbrt y) (cbrt (- a t))) (- t z)) (+ x y))

simplify108.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	340	687
1	897	632
2	3731	588
3	5001	563

prune423.0ms

Filtered

73 candidates to 67 candidates (91.8%)

Pruning

24 alts after pruning (22 fresh and 2 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	0	20	20
Picked	0	1	1
Done	0	1	1
Total	71	24	95

Merged error: 8.7b

Counts

95 → 24

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
0.6b	(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
12.9b	(fma (/ (* (cbrt y) (cbrt y)) (* (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (cbrt (- a t)))) (cbrt (- a t)))) (* (/ (cbrt y) (cbrt (- a t))) (- t z)) (+ x y))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

73×	`cbrt-prod`
35×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
24×	`cbrt-div`
15×	`add-cube-cbrt`
10×	`swap-sqr`
8×	`flip3--` `associate-r` `associate-l` `flip--` `distribute-lft-out--`
6×	`difference-of-squares`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow1/3`
2×	`associate-r/` `associate-l/`
1×	`*-commutative` `fma-udef`

Counts

4 → 97

Calls

4 calls:

3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
13.0ms	(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
1.0ms	(fma (/ (* (cbrt y) (cbrt y)) (* (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (cbrt (- a t)))) (cbrt (- a t)))) (* (/ (cbrt y) (cbrt (- a t))) (- t z)) (+ x y))

series1.2s

Counts

4 → 12

Calls

4 calls:

164.0ms	(cbrt (- a t))
163.0ms	(cbrt (- a t))
137.0ms	(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
691.0ms	(fma (/ (* (cbrt y) (cbrt y)) (* (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (cbrt (- a t)))) (cbrt (- a t)))) (* (/ (cbrt y) (cbrt (- a t))) (- t z)) (+ x y))

simplify64.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	498	1328
1	1445	1249
2	5002	1164

prune520.0ms

Filtered

109 candidates to 83 candidates (76.1%)

Pruning

24 alts after pruning (21 fresh and 3 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	3	18	21
Picked	0	1	1
Done	0	2	2
Total	109	24	133

Merged error: 8.7b

Counts

133 → 24

regimes680.0ms

Accuracy

31.2% (3.1b remaining)

Error of 9.4b against oracle of 6.2b and baseline of 10.8b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	48
1	43	48

end0.0ms

sample653.0ms

Algorithm

intervals

Results

234.0ms	7334×	body	80	valid
64.0ms	466×	body	640	valid
38.0ms	403×	body	320	valid
34.0ms	234×	body	1280	valid
15.0ms	256×	body	160	valid
3.0ms	17×	body	2560	valid