Details

sample104.0ms

Algorithm

intervals

Results

28.0ms	52×	body	1280	valid
22.0ms	45×	body	10240	exit
14.0ms	50×	body	640	valid
7.0ms	117×	body	80	valid
6.0ms	4×	body	2560	valid
5.0ms	25×	body	320	valid
3.0ms	77×	body	80	nan
1.0ms	7×	body	640	nan
1.0ms	10×	body	160	valid
1.0ms	4×	body	320	nan
0.0ms	2×	body	1280	nan
0.0ms	3×	body	160	nan

simplify214.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.0b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
0.9b	(log (+ (- 1.0 y) (* y (exp z))))
2.7b	(+ (- 1.0 y) (* y (exp z)))

rewrite32.0ms

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)
9.0ms	(log (+ (- 1.0 y) (* y (exp z))))
7.0ms	(+ (- 1.0 y) (* y (exp z)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* y (exp z))
150.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
73.0ms	(log (+ (- 1.0 y) (* y (exp z))))
34.0ms	(+ (- 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

prune341.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 4.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* y (expm1 z))
0.0b	(/ (log (+ 1.0 (* y (expm1 z)))) t)
2.6b	(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))))

series272.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* y (expm1 z))
161.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
73.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify48.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (41.0ms)

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

prune237.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* y (expm1 z))
0.1b	(* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t))
2.6b	(log (+ 1.0 (* y (expm1 z))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
16×	`associate-r`
15×	`add-exp-log` `*-un-lft-identity`
14×	`add-cube-cbrt`
11×	`times-frac`
10×	`add-cbrt-cube`
9×	`pow1`
7×	`associate-l`
5×	`prod-exp`
4×	`unswap-sqr`
3×	`expm1-log1p-u` `log-prod` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `div-exp` `pow-prod-down` `log-pow` `*-commutative`
1×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `associate-*r/` `rem-log-exp` `un-div-inv` `flip-+` `div-inv`

Counts

3 → 75

Calls

3 calls:

3.0ms	(* y (expm1 z))
8.0ms	(* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t))
3.0ms	(log (+ 1.0 (* y (expm1 z))))

series266.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(* y (expm1 z))
149.0ms	(* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t))
74.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify61.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	517	632
1	2266	551
2	5002	519

prune275.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
2.6b	(log (+ 1.0 (* y (expm1 z))))
2.6b	(log (+ 1.0 (* y (expm1 z))))
2.6b	(log (+ 1.0 (* y (expm1 z))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

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

series414.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt t)
77.0ms	(log (+ 1.0 (* y (expm1 z))))
77.0ms	(log (+ 1.0 (* y (expm1 z))))
78.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify97.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	236	544
1	782	484
2	3740	464
3	5001	461

prune381.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.4b

regimes236.0ms

Accuracy

45.8% (3.8b remaining)

Error of 8.4b against oracle of 4.6b and baseline of 11.6b

bsearch81.0ms

Steps

Iters	Range		Point
9	-6.5683629049692506e-15	-6.468064663008395e-20	-1.637836830200292e-19

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	16
1	30	16

end0.0ms

sample3.1s

Algorithm

intervals

Results

776.0ms	1469×	body	1280	valid
773.0ms	1574×	body	10240	exit
449.0ms	1581×	body	640	valid
218.0ms	3513×	body	80	valid
168.0ms	901×	body	320	valid
122.0ms	95×	body	2560	valid
89.0ms	2488×	body	80	nan
51.0ms	261×	body	640	nan
51.0ms	460×	body	160	valid
29.0ms	101×	body	1280	nan
24.0ms	184×	body	320	nan
9.0ms	111×	body	160	nan