Details

sample25.0ms

Algorithm

intervals

Results

13.0ms

280×

body

valid

simplify58.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	17	5
1	32	5
2	60	4
3	112	4
4	172	4
5	231	4
6	279	4
7	352	4
8	485	4
9	648	4
10	1074	4
11	1358	4
12	1399	4
13	1399	4

prune7.0ms

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: 0.1b

Counts

2 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
3.3b	(fma (/ y (- a t)) (- z t) x)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
3×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `fma-udef` `div-inv`

Counts

2 → 49

Calls

2 calls:

5.0ms	(/ y (- a t))
1.0ms	(fma (/ y (- a t)) (- z t) x)

series199.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(/ y (- a t))
172.0ms	(fma (/ y (- a t)) (- z t) x)

simplify105.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	166	265
1	444	246
2	1278	244
3	4359	243
4	5001	243

prune141.0ms

Filtered

55 candidates to 43 candidates (78.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	50	5	55
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	50	7	57

Merged error: 0.0b

Counts

57 → 7

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.1b	(* y (/ 1 (- a t)))
3.3b	(fma (* y (/ 1 (- a t))) (- z t) x)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
32×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-/r*`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `flip3--` `1-exp` `flip--` `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 → 99

Calls

3 calls:

6.0ms	(/ 1 (- a t))
11.0ms	(* y (/ 1 (- a t)))
1.0ms	(fma (* y (/ 1 (- a t))) (- z t) x)

series243.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ 1 (- a t))
27.0ms	(* y (/ 1 (- a t)))
176.0ms	(fma (* y (/ 1 (- a t))) (- z t) x)

simplify74.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	284	497
1	1119	429
2	4119	381
3	5001	381

prune185.0ms

Filtered

108 candidates to 64 candidates (59.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	108	7	115

Merged error: 0.0b

Counts

115 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma (/ y (- a t)) (- z t) x))
3.3b	(fma (/ y (- a t)) (- z t) x)
3.3b	(fma (/ y (- a t)) (- z t) x)
3.3b	(fma (/ y (- a t)) (- z t) x)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 43

Calls

4 calls:

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

series1.1s

Counts

4 → 12

Calls

4 calls:

594.0ms	(cbrt (fma (/ y (- a t)) (- z t) x))
170.0ms	(fma (/ y (- a t)) (- z t) x)
172.0ms	(fma (/ y (- a t)) (- z t) x)
174.0ms	(fma (/ y (- a t)) (- z t) x)

simplify50.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	156	357
1	421	319
2	1835	309
3	5001	305

prune170.0ms

Filtered

55 candidates to 51 candidates (92.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	55	7	62

Merged error: 0.0b

Counts

62 → 7

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (/ (* y (- z t)) (- a t)))
0.0b	(* y (- z t))
9.7b	(/ (* y (- z t)) (- a t))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 94

Calls

3 calls:

7.0ms	(+ x (/ (* y (- z t)) (- a t)))
7.0ms	(* y (- z t))
10.0ms	(/ (* y (- z t)) (- a t))

series178.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(+ x (/ (* y (- z t)) (- a t)))
34.0ms	(* y (- z t))
66.0ms	(/ (* y (- z t)) (- a t))

simplify58.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	421	660
1	1895	494
2	5002	492

prune172.0ms

Filtered

103 candidates to 63 candidates (61.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	99	4	103
Fresh	3	0	3
Picked	1	0	1
Done	2	1	3
Total	105	5	110

Merged error: 0b

Counts

110 → 5

regimes178.0ms

Accuracy

32.5% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 1.4b

bsearch67.0ms

Steps

Iters	Range		Point
9	6.056511580473963e-105	2.513454972484143e-99	6.973062393892111e-103
5	-1.272348569829707e-05	-3.7147878101902474e-06	-5.972939612261978e-06

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	15
1	30	15

end0.0ms

sample789.0ms

Algorithm

intervals

Results

526.0ms	8735×	body	80	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	160	valid