Details

sample93.0ms

Algorithm

intervals

Results

28.0ms	47×	body	1280	valid
16.0ms	46×	body	640	valid
9.0ms	121×	body	80	valid
6.0ms	25×	body	320	valid
4.0ms	2×	body	2560	valid
3.0ms	74×	body	80	nan
3.0ms	52×	body	80	overflowed
2.0ms	11×	body	640	nan
2.0ms	16×	body	160	valid
1.0ms	6×	body	320	nan
1.0ms	3×	body	1280	nan
1.0ms	5×	body	160	nan

simplify211.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 23.0b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.0b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
2.3b	(+ (- 1.0 y) (* y (exp z)))
3.6b	(log (+ (- 1.0 y) (* y (exp z))))

rewrite28.0ms

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)
7.0ms	(+ (- 1.0 y) (* y (exp z)))
6.0ms	(log (+ (- 1.0 y) (* y (exp z))))

series283.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* y (exp z))
152.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
35.0ms	(+ (- 1.0 y) (* y (exp z)))
76.0ms	(log (+ (- 1.0 y) (* y (exp z))))

simplify58.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (48.0ms)

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

prune349.0ms

Filtered

114 candidates to 91 candidates (79.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	108	6	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	6	115

Merged error: 5.4b

Counts

115 → 6

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* y (expm1 z))
0.0b	(/ (log (+ 1.0 (* y (expm1 z)))) t)
4.7b	(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)
2.0ms	(log (+ 1.0 (* y (expm1 z))))

series273.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* y (expm1 z))
149.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
87.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify46.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (39.0ms)

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

prune196.0ms

Filtered

80 candidates to 62 candidates (77.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	81	5	86

Merged error: 5.4b

Counts

86 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (log (+ 1.0 (* y (expm1 z)))))
4.7b	(log (+ 1.0 (* y (expm1 z))))
4.7b	(log (+ 1.0 (* y (expm1 z))))
4.7b	(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)))))
2.0ms	(log (+ 1.0 (* y (expm1 z))))
2.0ms	(log (+ 1.0 (* y (expm1 z))))
3.0ms	(log (+ 1.0 (* y (expm1 z))))

series760.0ms

Counts

4 → 12

Calls

4 calls:

546.0ms	(cbrt (log (+ 1.0 (* y (expm1 z)))))
73.0ms	(log (+ 1.0 (* y (expm1 z))))
69.0ms	(log (+ 1.0 (* y (expm1 z))))
72.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify42.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (34.0ms)

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

prune284.0ms

Filtered

74 candidates to 69 candidates (93.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	74	5	79

Merged error: 5.4b

Counts

79 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt (log (+ 1.0 (* y (expm1 z))))) t)
0.1b	(* (sqrt (log (+ 1.0 (* y (expm1 z))))) (/ (sqrt (log (+ 1.0 (* y (expm1 z))))) t))
4.7b	(log (+ 1.0 (* y (expm1 z))))
4.7b	(log (+ 1.0 (* y (expm1 z))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
46×	`times-frac`
38×	`add-cube-cbrt` `*-un-lft-identity`
37×	`sqrt-prod`
25×	`associate-r`
16×	`pow1`
13×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`log-pow`
7×	`associate-l` `associate-/l*`
6×	`log-prod` `unswap-sqr`
4×	`expm1-log1p-u` `log-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`cbrt-undiv` `flip3-+` `div-exp` `rem-log-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 131

Calls

4 calls:

4.0ms	(/ (sqrt (log (+ 1.0 (* y (expm1 z))))) t)
11.0ms	(* (sqrt (log (+ 1.0 (* y (expm1 z))))) (/ (sqrt (log (+ 1.0 (* y (expm1 z))))) t))
4.0ms	(log (+ 1.0 (* y (expm1 z))))
3.0ms	(log (+ 1.0 (* y (expm1 z))))

series1.1s

Counts

4 → 12

Calls

4 calls:

763.0ms	(/ (sqrt (log (+ 1.0 (* y (expm1 z))))) t)
213.0ms	(* (sqrt (log (+ 1.0 (* y (expm1 z))))) (/ (sqrt (log (+ 1.0 (* y (expm1 z))))) t))
70.0ms	(log (+ 1.0 (* y (expm1 z))))
76.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify76.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	636	1804
1	2627	1583
2	5001	1512

prune390.0ms

Filtered

143 candidates to 103 candidates (72.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	143	5	148

Merged error: 5.4b

Counts

148 → 5

regimes183.0ms

Accuracy

40.1% (4.4b remaining)

Error of 8.8b against oracle of 4.4b and baseline of 11.7b

bsearch78.0ms

Steps

Iters	Range		Point
8	-1.5706045608568243e-21	-7.405075169216416e-25	-7.673193290916664e-25

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	21
1	31	21

end0.0ms

sample2.8s

Algorithm

intervals

Results

843.0ms	1432×	body	1280	valid
573.0ms	1648×	body	640	valid
251.0ms	3448×	body	80	valid
207.0ms	936×	body	320	valid
124.0ms	2521×	body	80	nan
115.0ms	83×	body	2560	valid
84.0ms	1498×	body	80	overflowed
67.0ms	267×	body	640	nan
65.0ms	482×	body	160	valid
40.0ms	116×	body	1280	nan
30.0ms	181×	body	320	nan
11.0ms	105×	body	160	nan