Details

sample174.0ms

Algorithm

intervals

Results

87.0ms	1580×	body	80	nan
16.0ms	257×	body	80	valid

simplify72.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	9
1	61	8
2	161	8
3	393	8
4	984	8
5	2256	8
6	4095	8
7	5001	8

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.2b

Counts

2 → 1

localize14.0ms

Local error

Found 2 expressions with local error:

0.2b	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
0.5b	(+ (log (+ x y)) (log z))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
7×	`pow1` `log-prod`
5×	`add-sqr-sqrt` `add-cube-cbrt` `log-pow` `distribute-lft-out`
4×	`associate-+l+` `fma-def`
3×	`associate-+r+`
2×	`add-exp-log` `expm1-log1p-u` `associate-+l-` `log-div` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`
1×	`+-commutative` `sum-log` `fma-udef`

Counts

2 → 40

Calls

2 calls:

1.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
7.0ms	(+ (log (+ x y)) (log z))

series163.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
71.0ms	(+ (log (+ x y)) (log z))

simplify53.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	262	323
1	662	288
2	2590	282
3	5001	278

prune194.0ms

Filtered

46 candidates to 38 candidates (82.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	39	7	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	7	47

Merged error: 0.1b

Counts

47 → 7

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (log (cbrt z)))
0.4b	(fma 2 (log (cbrt z)) (log (+ x y)))
0.5b	(cbrt z)
0.5b	(cbrt z)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt`
6×	`associate-+r+` `log-prod`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def`
2×	`pow1/3` `fma-udef` `distribute-lft-out`
1×	`+-commutative` `associate-+l+` `flip3-+` `sum-log` `log-pow` `flip-+`

Counts

4 → 61

Calls

4 calls:

8.0ms	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (log (cbrt z)))
1.0ms	(fma 2 (log (cbrt z)) (log (+ x y)))
2.0ms	(cbrt z)
2.0ms	(cbrt z)

series706.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (log (cbrt z)))
146.0ms	(fma 2 (log (cbrt z)) (log (+ x y)))
190.0ms	(cbrt z)
191.0ms	(cbrt z)

simplify69.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	203	445
1	573	409
2	2204	368
3	5002	358

prune466.0ms

Filtered

73 candidates to 67 candidates (91.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	74	6	80

Merged error: 0.1b

Counts

80 → 6

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt z)
0.5b	(* (cbrt z) (cbrt z))
0.6b	(cbrt (* (cbrt z) (cbrt z)))
0.6b	(cbrt (cbrt z))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

29×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 82

Calls

4 calls:

1.0ms	(cbrt z)
6.0ms	(* (cbrt z) (cbrt z))
4.0ms	(cbrt (* (cbrt z) (cbrt z)))
2.0ms	(cbrt (cbrt z))

series1.1s

Counts

4 → 12

Calls

4 calls:

185.0ms	(cbrt z)
375.0ms	(* (cbrt z) (cbrt z))
265.0ms	(cbrt (* (cbrt z) (cbrt z)))
241.0ms	(cbrt (cbrt z))

simplify97.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	177	375
1	627	345
2	3405	314
3	5002	311

prune514.0ms

Filtered

94 candidates to 74 candidates (78.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	94	6	100

Merged error: 0.1b

Counts

100 → 6

localize36.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma 2/3 (log z) (log (+ x y)))
0.6b	(* (log z) (log z))
0.6b	(fma (fma 2/3 (log z) (log (+ x y))) (fma 2/3 (log z) (log (+ x y))) (* (- 1/9) (* (log z) (log z))))
5.1b	(pow z 1/3)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1`
14×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`add-cube-cbrt`
7×	`add-exp-log`
6×	`log-prod` `swap-sqr` `log-pow` `add-cbrt-cube`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `unpow-prod-down` `pow-unpow` `distribute-lft-in`
2×	`fma-udef`
1×	`pow2` `pow-to-exp` `pow-pow` `pow-plus` `unpow1/3` `pow-prod-down` `pow-exp` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr` `sqr-pow`

Counts

4 → 78

Calls

4 calls:

1.0ms	(fma 2/3 (log z) (log (+ x y)))
5.0ms	(* (log z) (log z))
1.0ms	(fma (fma 2/3 (log z) (log (+ x y))) (fma 2/3 (log z) (log (+ x y))) (* (- 1/9) (* (log z) (log z))))
2.0ms	(pow z 1/3)

series752.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(fma 2/3 (log z) (log (+ x y)))
148.0ms	(* (log z) (log z))
334.0ms	(fma (fma 2/3 (log z) (log (+ x y))) (fma 2/3 (log z) (log (+ x y))) (* (- 1/9) (* (log z) (log z))))
178.0ms	(pow z 1/3)

simplify43.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	339	537
1	1273	462
2	5002	434

prune454.0ms

Filtered

90 candidates to 61 candidates (67.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	90	6	96

Merged error: 0.1b

Counts

96 → 6

regimes519.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	18
1	26	18

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.7s	55964×	body	80	nan
463.0ms	8037×	body	80	valid