Details

sample107.0ms

Algorithm

intervals

Results

27.0ms	44×	body	1280	valid
24.0ms	49×	body	10240	exit
18.0ms	62×	body	640	valid
7.0ms	115×	body	80	valid
5.0ms	28×	body	320	valid
3.0ms	81×	body	80	nan
3.0ms	2×	body	2560	valid
1.0ms	5×	body	320	nan
1.0ms	5×	body	160	valid
1.0ms	2×	body	1280	nan
1.0ms	3×	body	640	nan
0.0ms	2×	body	160	nan

simplify216.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	7
1	35	7
2	53	7
3	81	7
4	121	7
5	250	7
6	314	7
7	532	7
8	908	7
9	1397	7
10	1553	7
11	1892	7
12	4682	7
13	5001	7

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 25.0b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.0b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
1.5b	(+ (- 1.0 y) (* y (exp z)))
2.1b	(log (+ (- 1.0 y) (* y (exp z))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

5.0ms	(* y (exp z))
8.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
8.0ms	(+ (- 1.0 y) (* y (exp z)))
6.0ms	(log (+ (- 1.0 y) (* y (exp z))))

series278.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* y (exp z))
150.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
34.0ms	(+ (- 1.0 y) (* y (exp z)))
74.0ms	(log (+ (- 1.0 y) (* y (exp z))))

simplify62.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	499	918
1	2002	785
2	5001	761

prune344.0ms

Filtered

114 candidates to 91 candidates (79.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	109	5	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	5	115

Merged error: 4.7b

Counts

115 → 5

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* y (expm1 z))
0.1b	(/ (log (+ 1.0 (* y (expm1 z)))) t)
3.7b	(log (+ 1.0 (* y (expm1 z))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`pow1`
8×	`add-exp-log`
7×	`add-cbrt-cube`
5×	`log-pow`
4×	`log-div` `associate-/l*`
3×	`expm1-log1p-u` `log-prod` `associate-r` `associate-l` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`flip3-+` `div-sub` `flip-+`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

3 → 71

Calls

3 calls:

3.0ms	(* y (expm1 z))
5.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
3.0ms	(log (+ 1.0 (* y (expm1 z))))

series256.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* y (expm1 z))
149.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
71.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify51.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	429	631
1	1711	580
2	5002	571

prune208.0ms

Filtered

80 candidates to 62 candidates (77.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	78	7	85

Merged error: 4.7b

Counts

85 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (log (+ 1.0 (* y (expm1 z)))))
3.7b	(log (+ 1.0 (* y (expm1 z))))
3.7b	(log (+ 1.0 (* y (expm1 z))))
3.7b	(log (+ 1.0 (* y (expm1 z))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

9×	`log-prod`
8×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`add-exp-log`
6×	`log-div`
4×	`cbrt-prod` `expm1-log1p-u` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `rem-log-exp` `flip-+`
1×	`pow1/3`

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt (log (+ 1.0 (* y (expm1 z)))))
3.0ms	(log (+ 1.0 (* y (expm1 z))))
3.0ms	(log (+ 1.0 (* y (expm1 z))))
3.0ms	(log (+ 1.0 (* y (expm1 z))))

series763.0ms

Counts

4 → 12

Calls

4 calls:

546.0ms	(cbrt (log (+ 1.0 (* y (expm1 z)))))
72.0ms	(log (+ 1.0 (* y (expm1 z))))
73.0ms	(log (+ 1.0 (* y (expm1 z))))
71.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify44.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	373	749
1	1377	670
2	5001	632

prune327.0ms

Filtered

74 candidates to 69 candidates (93.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	74	7	81

Merged error: 4.7b

Counts

81 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
0.6b	(cbrt t)
3.7b	(log (+ 1.0 (* y (expm1 z))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `pow1/3`
2×	`log-div`
1×	`flip3-+` `rem-log-exp` `log-pow` `flip-+`

Counts

4 → 55

Calls

4 calls:

1.0ms	(cbrt t)
1.0ms	(cbrt t)
1.0ms	(cbrt t)
3.0ms	(log (+ 1.0 (* y (expm1 z))))

series635.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt t)
190.0ms	(cbrt t)
182.0ms	(cbrt t)
78.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify98.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	236	296
1	782	268
2	3740	256
3	5001	255

prune224.0ms

Filtered

67 candidates to 60 candidates (89.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	66	8	74

Merged error: 4.7b

Counts

74 → 8

regimes213.0ms

Accuracy

38.4% (4.4b remaining)

Error of 9.2b against oracle of 4.8b and baseline of 11.9b

bsearch62.0ms

Steps

Iters	Range		Point
6	-3.527629991112371e-41	-3.628344636168835e-42	-2.4124759802802916e-41

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	16
1	30	16

end0.0ms

sample3.2s

Algorithm

intervals

Results

819.0ms	1651×	body	10240	exit
785.0ms	1483×	body	1280	valid
481.0ms	1641×	body	640	valid
215.0ms	3433×	body	80	valid
173.0ms	936×	body	320	valid
100.0ms	2531×	body	80	nan
97.0ms	73×	body	2560	valid
53.0ms	467×	body	160	valid
48.0ms	239×	body	640	nan
34.0ms	118×	body	1280	nan
26.0ms	195×	body	320	nan
8.0ms	102×	body	160	nan