Details

sample94.0ms

Algorithm

intervals

Results

27.0ms	49×	body	1280	valid
18.0ms	38×	body	10240	exit
13.0ms	48×	body	640	valid
8.0ms	127×	body	80	valid
3.0ms	19×	body	320	valid
2.0ms	72×	body	80	nan
2.0ms	1×	body	2560	valid
1.0ms	8×	body	640	nan
1.0ms	12×	body	160	valid
1.0ms	3×	body	1280	nan
1.0ms	6×	body	320	nan
0.0ms	2×	body	160	nan

simplify212.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.7b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.1b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
1.0b	(+ (- 1.0 y) (* y (exp z)))
1.3b	(log (+ (- 1.0 y) (* y (exp z))))

rewrite72.0ms

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))
34.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
22.0ms	(+ (- 1.0 y) (* y (exp z)))
9.0ms	(log (+ (- 1.0 y) (* y (exp z))))

series285.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* y (exp z))
148.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
33.0ms	(+ (- 1.0 y) (* y (exp z)))
83.0ms	(log (+ (- 1.0 y) (* y (exp z))))

simplify58.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (49.0ms)

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

prune367.0ms

Filtered

114 candidates to 91 candidates (79.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* y (expm1 z))
0.1b	(/ (log (+ 1.0 (* y (expm1 z)))) t)
4.3b	(log (+ 1.0 (* y (expm1 z))))

rewrite15.0ms

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))
8.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
2.0ms	(log (+ 1.0 (* y (expm1 z))))

series256.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* y (expm1 z))
150.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
68.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify48.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (40.0ms)

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

prune252.0ms

Filtered

80 candidates to 62 candidates (77.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (expm1 z))
0.5b	(cbrt (expm1 z))
0.5b	(cbrt (expm1 z))
4.3b	(log (+ 1.0 (* (* y (* (cbrt (expm1 z)) (cbrt (expm1 z)))) (cbrt (expm1 z)))))

rewrite4.0ms

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:

0.0ms	(cbrt (expm1 z))
0.0ms	(cbrt (expm1 z))
0.0ms	(cbrt (expm1 z))
2.0ms	(log (+ 1.0 (* (* y (* (cbrt (expm1 z)) (cbrt (expm1 z)))) (cbrt (expm1 z)))))

series341.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(cbrt (expm1 z))
90.0ms	(cbrt (expm1 z))
93.0ms	(cbrt (expm1 z))
69.0ms	(log (+ 1.0 (* (* y (* (cbrt (expm1 z)) (cbrt (expm1 z)))) (cbrt (expm1 z)))))

simplify37.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	261	544
1	925	483
2	5001	471

prune260.0ms

Filtered

67 candidates to 57 candidates (85.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (expm1 z))
0.5b	(cbrt (expm1 z))
4.1b	(log (cbrt (+ 1.0 (* (* y (* (cbrt (expm1 z)) (cbrt (expm1 z)))) (cbrt (expm1 z))))))
4.1b	(log (cbrt (+ 1.0 (* (* y (* (cbrt (expm1 z)) (cbrt (expm1 z)))) (cbrt (expm1 z))))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

0.0ms	(cbrt (expm1 z))
0.0ms	(cbrt (expm1 z))
2.0ms	(log (cbrt (+ 1.0 (* (* y (* (cbrt (expm1 z)) (cbrt (expm1 z)))) (cbrt (expm1 z))))))
3.0ms	(log (cbrt (+ 1.0 (* (* y (* (cbrt (expm1 z)) (cbrt (expm1 z)))) (cbrt (expm1 z))))))

series472.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(cbrt (expm1 z))
93.0ms	(cbrt (expm1 z))
140.0ms	(log (cbrt (+ 1.0 (* (* y (* (cbrt (expm1 z)) (cbrt (expm1 z)))) (cbrt (expm1 z))))))
143.0ms	(log (cbrt (+ 1.0 (* (* y (* (cbrt (expm1 z)) (cbrt (expm1 z)))) (cbrt (expm1 z))))))

simplify41.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	292	1058
1	966	964
2	5002	956

prune392.0ms

Filtered

78 candidates to 66 candidates (84.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.0b

regimes189.0ms

Accuracy

33% (4.6b remaining)

Error of 9.2b against oracle of 4.6b and baseline of 11.5b

bsearch105.0ms

Steps

Iters	Range		Point
9	-7.445920645447926e-216	-6.1945215495571335e-223	-5.359355648797567e-216

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	23
1	34	23

end0.0ms

sample3.1s

Algorithm

intervals

Results

757.0ms	1532×	body	10240	exit
748.0ms	1428×	body	1280	valid
464.0ms	1608×	body	640	valid
205.0ms	3487×	body	80	valid
175.0ms	929×	body	320	valid
105.0ms	83×	body	2560	valid
87.0ms	2458×	body	80	nan
54.0ms	494×	body	160	valid
49.0ms	254×	body	640	nan
33.0ms	115×	body	1280	nan
23.0ms	161×	body	320	nan
9.0ms	107×	body	160	nan