Details

sample127.0ms

Algorithm

intervals

Results

50.0ms	800×	body	80	nan
12.0ms	170×	body	80	valid
10.0ms	13×	body	1280	valid
8.0ms	23×	body	640	valid
8.0ms	34×	body	320	valid
2.0ms	17×	body	160	valid

simplify72.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	9
1	57	8
2	136	8
3	312	8
4	709	8
5	1629	8
6	3564	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: 7.6b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.1b	(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
6.3b	(log (- 1.0 y))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`log-prod`
8×	`add-cube-cbrt`
7×	`pow1`
6×	`add-exp-log`
5×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `add-cbrt-cube`
4×	`associate-r` `distribute-lft-out--` `difference-of-squares`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `flip3--` `associate-*l/` `log-pow` `flip--`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

3 → 63

Calls

3 calls:

10.0ms	(* (- z 1.0) (log (- 1.0 y)))
1.0ms	(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
4.0ms	(log (- 1.0 y))

series301.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* (- z 1.0) (log (- 1.0 y)))
211.0ms	(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
49.0ms	(log (- 1.0 y))

simplify37.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	364	521
1	1204	461
2	5001	449

prune224.0ms

Filtered

72 candidates to 55 candidates (76.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	5	73

Merged error: 0.2b

Counts

73 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
0.0b	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.0b	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.1b	(fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-sqr-sqrt`
80×	`times-frac`
78×	`*-un-lft-identity`
74×	`associate-r`
73×	`add-cube-cbrt`
56×	`unpow-prod-down`
51×	`prod-diff`
46×	`associate--l+`
34×	`distribute-rgt-in` `distribute-lft-in`
29×	`add-exp-log`
24×	`unpow2` `sqr-pow`
21×	`pow1`
18×	`unswap-sqr`
13×	`log-pow`
12×	`log-prod`
11×	`prod-exp` `add-cbrt-cube`
9×	`div-exp`
8×	`associate-l`
7×	`flip3--` `flip--`
6×	`pow-to-exp` `pow-exp` `add-log-exp`
5×	`sub-neg`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`associate-*r/` `cbrt-unprod` `distribute-lft-out--`
2×	`pow-prod-down` `associate-l/` `-commutative` `difference-of-squares`
1×	`cbrt-undiv` `fma-neg` `diff-log` `fma-udef` `div-inv`

Counts

4 → 241

Calls

4 calls:

16.0ms	(- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
23.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
13.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
1.0ms	(fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

series500.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
54.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
64.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
228.0ms	(fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

simplify133.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1053	3734
1	4672	2536
2	5001	2536

prune839.0ms

Filtered

253 candidates to 157 candidates (62.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	249	4	253
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	251	7	258

Merged error: 0.2b

Counts

258 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (- z 1.0)) (cbrt (- z 1.0)))
0.3b	(cbrt (- z 1.0))
0.3b	(cbrt (- z 1.0))
0.3b	(cbrt (- z 1.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

43×	`cbrt-prod`
37×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
10×	`swap-sqr`
9×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`difference-of-squares`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 109

Calls

4 calls:

10.0ms	(* (cbrt (- z 1.0)) (cbrt (- z 1.0)))
3.0ms	(cbrt (- z 1.0))
3.0ms	(cbrt (- z 1.0))
3.0ms	(cbrt (- z 1.0))

series443.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (cbrt (- z 1.0)) (cbrt (- z 1.0)))
102.0ms	(cbrt (- z 1.0))
109.0ms	(cbrt (- z 1.0))
112.0ms	(cbrt (- z 1.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	384	861
1	1303	823
2	5002	757

prune597.0ms

Filtered

121 candidates to 89 candidates (73.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	121	7	128

Merged error: 0.2b

Counts

128 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- z 1.0))
0.3b	(cbrt (- z 1.0))
0.3b	(cbrt (- z 1.0))
2.9b	(expm1 (log1p (* (cbrt (- z 1.0)) (cbrt (- z 1.0)))))

rewrite15.0ms

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×	`expm1-log1p` `expm1-udef`

Counts

4 → 62

Calls

4 calls:

3.0ms	(cbrt (- z 1.0))
7.0ms	(cbrt (- z 1.0))
3.0ms	(cbrt (- z 1.0))
1.0ms	(expm1 (log1p (* (cbrt (- z 1.0)) (cbrt (- z 1.0)))))

series612.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt (- z 1.0))
97.0ms	(cbrt (- z 1.0))
104.0ms	(cbrt (- z 1.0))
313.0ms	(expm1 (log1p (* (cbrt (- z 1.0)) (cbrt (- z 1.0)))))

simplify115.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	374	547
1	1243	494
2	4473	462
3	5001	461

prune523.0ms

Filtered

74 candidates to 67 candidates (90.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	74	7	81

Merged error: 0.2b

Counts

81 → 7

regimes260.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	14
1	25	14

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.5s	24235×	body	80	nan
400.0ms	5788×	body	80	valid
285.0ms	768×	body	640	valid
210.0ms	307×	body	1280	valid
165.0ms	719×	body	320	valid
67.0ms	458×	body	160	valid