Details

sample84.0ms

Algorithm

intervals

Results

42.0ms	840×	body	80	nan
14.0ms	288×	body	80	valid

simplify101.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	10
1	76	10
2	211	10
3	530	10
4	1065	10
5	2198	10
6	3794	10
7	5001	10

prune2.0ms

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: 0.1b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
26×	`*-un-lft-identity` `times-frac`
24×	`add-cube-cbrt` `associate-l`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
8×	`associate-*r/` `sqrt-prod`
6×	`flip3--` `sqrt-div` `associate-r` `flip--`
4×	`expm1-log1p-u` `frac-times` `associate-/r*` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `associate-l/` `prod-exp` `cbrt-unprod` `flip-+` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `sqrt-pow1` `div-exp` `*-commutative` `div-inv` `difference-of-squares`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 122

Calls

4 calls:

10.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
20.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
13.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series515.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
74.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
181.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
143.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify96.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	860	1389
1	3774	1282
2	5001	1276

prune354.0ms

Filtered

134 candidates to 115 candidates (85.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	125	9	134
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	126	9	135

Merged error: 0.0b

Counts

135 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
8.8b	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`times-frac`
25×	`*-un-lft-identity`
24×	`associate-l`
23×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
8×	`sqrt-prod`
7×	`associate-*r/` `prod-exp` `cbrt-unprod`
6×	`sqrt-div` `associate-*l/`
5×	`flip3--` `pow-prod-down` `flip--`
4×	`expm1-log1p-u` `associate-r` `associate-/r*` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`frac-times` `sqrt-pow1` `*-commutative` `div-inv` `difference-of-squares` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 119

Calls

4 calls:

20.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
13.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
18.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

series556.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
181.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
144.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
159.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

simplify75.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	787	1284
1	3157	1135
2	5002	1129

prune310.0ms

Filtered

131 candidates to 107 candidates (81.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	128	3	131
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	132	8	140

Merged error: 0.0b

Counts

140 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b	(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand)
0.3b	(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`times-frac`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
9×	`associate-*l/`
8×	`associate-*r/` `sqrt-prod`
7×	`flip3--` `associate-l` `prod-exp` `flip--` `cbrt-unprod`
6×	`sqrt-div`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `frac-times` `associate-/r*` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`sqrt-pow1` `*-commutative` `div-inv` `difference-of-squares` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 123

Calls

4 calls:

17.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
21.0ms	(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand)
19.0ms	(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series505.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
157.0ms	(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand)
130.0ms	(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
143.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify91.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	758	1394
1	3358	1232
2	5001	1226

prune324.0ms

Filtered

135 candidates to 109 candidates (80.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	1	5	6
Picked	1	0	1
Done	1	0	1
Total	137	6	143

Merged error: 0b

Counts

143 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b	(* (/ (* (- a (/ 1.0 3.0)) 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b	(/ (* (- a (/ 1.0 3.0)) 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-sqr-sqrt`
81×	`*-un-lft-identity`
79×	`add-cube-cbrt`
78×	`prod-diff`
63×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
20×	`add-exp-log` `add-cbrt-cube`
13×	`associate-l`
11×	`pow1`
9×	`associate-r`
8×	`associate-*r/` `div-inv`
6×	`sqrt-div` `prod-exp` `cbrt-unprod`
5×	`flip3--` `flip--`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r*` `sqrt-prod` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `associate-*l/`
2×	`sub-neg` `sqrt-pow1` `*-commutative` `associate-/l/` `difference-of-squares` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `associate-/l*` `distribute-lft-out--`

Counts

4 → 183

Calls

4 calls:

12.0ms	(* 9.0 (- a (/ 1.0 3.0)))
21.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
18.0ms	(* (/ (* (- a (/ 1.0 3.0)) 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
16.0ms	(/ (* (- a (/ 1.0 3.0)) 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series402.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* 9.0 (- a (/ 1.0 3.0)))
74.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
160.0ms	(* (/ (* (- a (/ 1.0 3.0)) 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
124.0ms	(/ (* (- a (/ 1.0 3.0)) 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify114.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	1069	2958
1	4526	2257
2	5001	2233

prune289.0ms

Filtered

195 candidates to 102 candidates (52.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	194	1	195
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	195	6	201

Merged error: 0b

Counts

201 → 6

regimes74.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	13
1	17	13

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	27243×	body	80	nan
438.0ms	9176×	body	80	valid