Details

sample102.0ms

Algorithm

intervals

Results

28.0ms	49×	body	1280	valid
20.0ms	41×	body	10240	exit
15.0ms	55×	body	640	valid
6.0ms	101×	body	80	valid
6.0ms	31×	body	320	valid
4.0ms	2×	body	2560	valid
2.0ms	72×	body	80	nan
2.0ms	18×	body	160	valid
1.0ms	8×	body	640	nan
1.0ms	4×	body	1280	nan
1.0ms	4×	body	320	nan
0.0ms	3×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.4b

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)
2.1b	(log (+ (- 1.0 y) (* y (exp z))))
2.4b	(+ (- 1.0 y) (* y (exp z)))

rewrite58.0ms

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:

7.0ms	(* y (exp z))
23.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
9.0ms	(log (+ (- 1.0 y) (* y (exp z))))
16.0ms	(+ (- 1.0 y) (* y (exp z)))

series280.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* y (exp z))
151.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
73.0ms	(log (+ (- 1.0 y) (* y (exp z))))
35.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify56.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (47.0ms)

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

prune362.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (/ (log (+ 1.0 (* y (expm1 z)))) t))
0.0b	(* y (expm1 z))
0.1b	(/ (log (+ 1.0 (* y (expm1 z)))) t)
3.0b	(log (+ 1.0 (* y (expm1 z))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
57×	`add-cube-cbrt`
49×	`times-frac`
48×	`prod-diff`
20×	`pow1`
14×	`log-pow`
9×	`add-exp-log`
8×	`add-cbrt-cube`
6×	`log-div` `add-log-exp`
4×	`expm1-log1p-u` `div-sub` `log1p-expm1-u` `div-inv` `associate-/l*`
3×	`log-prod` `flip3-+` `fma-neg` `associate-r` `associate-l` `associate-/r*` `flip-+`
2×	`associate--r-` `difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 141

Calls

4 calls:

10.0ms	(- x (/ (log (+ 1.0 (* y (expm1 z)))) t))
3.0ms	(* y (expm1 z))
6.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
2.0ms	(log (+ 1.0 (* y (expm1 z))))

series350.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- x (/ (log (+ 1.0 (* y (expm1 z)))) t))
37.0ms	(* y (expm1 z))
157.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
77.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify94.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	746	2869
1	2769	1983
2	5001	1785

prune410.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (+ 1.0 (* y (expm1 z))))
0.1b	(cbrt (+ 1.0 (* y (expm1 z))))
3.1b	(log (cbrt (+ 1.0 (* y (expm1 z)))))
3.1b	(log (cbrt (+ 1.0 (* y (expm1 z)))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

2.0ms	(cbrt (+ 1.0 (* y (expm1 z))))
2.0ms	(cbrt (+ 1.0 (* y (expm1 z))))
6.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))
2.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))

series627.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(cbrt (+ 1.0 (* y (expm1 z))))
167.0ms	(cbrt (+ 1.0 (* y (expm1 z))))
150.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))
148.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	318	880
1	1062	820
2	5001	794

prune458.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/3 (log (+ 1.0 (* y (expm1 z)))))
0.1b	(cbrt (+ 1.0 (* y (expm1 z))))
3.0b	(log (+ 1.0 (* y (expm1 z))))
3.1b	(log (cbrt (+ 1.0 (* y (expm1 z)))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

15×	`log-prod`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1`
8×	`add-exp-log`
6×	`cbrt-prod` `add-cbrt-cube`
4×	`expm1-log1p-u` `log-div` `cbrt-div` `associate-r` `log-pow` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `associate-l` `flip-+`
2×	`pow1/3` `rem-log-exp`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

6.0ms	(* 1/3 (log (+ 1.0 (* y (expm1 z)))))
2.0ms	(cbrt (+ 1.0 (* y (expm1 z))))
2.0ms	(log (+ 1.0 (* y (expm1 z))))
3.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))

series486.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* 1/3 (log (+ 1.0 (* y (expm1 z)))))
160.0ms	(cbrt (+ 1.0 (* y (expm1 z))))
79.0ms	(log (+ 1.0 (* y (expm1 z))))
152.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	454	873
1	1637	788
2	5001	755

prune433.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.5b

regimes368.0ms

Accuracy

44% (3.9b remaining)

Error of 7.9b against oracle of 4.0b and baseline of 11.0b

bsearch42.0ms

Steps

Iters	Range		Point
4	-1.835471523199371e-27	-1.0306700494205176e-27	-1.052384401893189e-27

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	30
1	39	30

end0.0ms

sample3.1s

Algorithm

intervals

Results

779.0ms	1567×	body	10240	exit
760.0ms	1438×	body	1280	valid
468.0ms	1643×	body	640	valid
209.0ms	3542×	body	80	valid
156.0ms	880×	body	320	valid
94.0ms	69×	body	2560	valid
93.0ms	2490×	body	80	nan
61.0ms	301×	body	640	nan
53.0ms	458×	body	160	valid
31.0ms	107×	body	1280	nan
25.0ms	188×	body	320	nan
9.0ms	115×	body	160	nan