Details

sample100.0ms

Algorithm

intervals

Results

25.0ms	49×	body	1280	valid
20.0ms	35×	body	10240	exit
14.0ms	49×	body	640	valid
7.0ms	111×	body	80	valid
6.0ms	4×	body	2560	valid
5.0ms	29×	body	320	valid
3.0ms	73×	body	80	nan
1.0ms	14×	body	160	valid
1.0ms	6×	body	640	nan
1.0ms	3×	body	1280	nan
1.0ms	4×	body	320	nan
0.0ms	5×	body	160	nan

simplify220.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
1.1b	(log (+ (- 1.0 y) (* y (exp z))))
3.3b	(+ (- 1.0 y) (* y (exp z)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 82

Calls

3 calls:

37.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
15.0ms	(log (+ (- 1.0 y) (* y (exp z))))
27.0ms	(+ (- 1.0 y) (* y (exp z)))

series260.0ms

Counts

3 → 9

Calls

3 calls:

152.0ms	(/ (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)))

simplify57.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	450	843
1	1824	715
2	5002	691

prune323.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* y (expm1 z))
0.1b	(/ (log (+ 1.0 (* y (expm1 z)))) t)
4.0b	(log (+ 1.0 (* y (expm1 z))))

rewrite12.0ms

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

series263.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* y (expm1 z))
150.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
73.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify49.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (42.0ms)

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

prune277.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.7b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(* y (expm1 z))
0.1b	(* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t))
4.0b	(log (+ 1.0 (* y (expm1 z))))

rewrite15.0ms

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

series266.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* y (expm1 z))
155.0ms	(* (log (+ 1.0 (* y (expm1 z)))) (/ 1 t))
74.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify59.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (52.0ms)

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

prune301.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (* y (expm1 z))))
0.1b	(* (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) (/ 1 t))
4.1b	(log (sqrt (+ 1.0 (* y (expm1 z)))))
4.1b	(log (sqrt (+ 1.0 (* y (expm1 z)))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
28×	`*-un-lft-identity` `log-pow`
27×	`pow1`
26×	`associate-l`
21×	`add-cube-cbrt`
15×	`add-exp-log`
13×	`associate-r`
12×	`log-prod`
11×	`times-frac`
10×	`distribute-rgt-out`
9×	`sqrt-pow1` `pow1/2` `sqrt-prod` `add-cbrt-cube`
8×	`distribute-lft-out`
6×	`sqrt-div`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `log-div` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`frac-times` `distribute-lft1-in` `div-exp` `rem-log-exp` `associate-*l/` `distribute-rgt1-in` `cbrt-unprod`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `count-2` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 124

Calls

4 calls:

3.0ms	(sqrt (+ 1.0 (* y (expm1 z))))
32.0ms	(* (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) (/ 1 t))
2.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))
2.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))

series2.5s

Counts

4 → 12

Calls

4 calls:

344.0ms	(sqrt (+ 1.0 (* y (expm1 z))))
1.5s	(* (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) (/ 1 t))
332.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))
335.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))

simplify53.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1286	2048
1	5001	1762

prune511.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.4b

regimes244.0ms

Accuracy

10.3% (7.0b remaining)

Error of 10.7b against oracle of 3.7b and baseline of 11.5b

bsearch257.0ms

Steps

Iters	Range		Point
9	3.8345813158010658e+124	1.0940114201509962e+132	2.299975825642676e+127
9	3.333152020693271e-42	2.1312801684303542e-36	3.0282374466509755e-40

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	22
1	46	22

end0.0ms

sample3.1s

Algorithm

intervals

Results

746.0ms	1412×	body	1280	valid
734.0ms	1473×	body	10240	exit
469.0ms	1609×	body	640	valid
210.0ms	3542×	body	80	valid
162.0ms	902×	body	320	valid
124.0ms	96×	body	2560	valid
89.0ms	2477×	body	80	nan
52.0ms	470×	body	160	valid
50.0ms	236×	body	640	nan
32.0ms	108×	body	1280	nan
26.0ms	199×	body	320	nan
8.0ms	104×	body	160	nan