Details

sample292.0ms

Algorithm

intervals

Results

10.0ms	40×	body	1280	valid
6.0ms	41×	body	640	valid
5.0ms	142×	body	80	valid
4.0ms	21×	body	320	valid
1.0ms	12×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	9
1	21	9
2	26	9
3	34	9
4	37	9
5	37	9

prune3.0ms

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: 0.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`associate-/l*`
3×	`associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 105

Calls

4 calls:

3.0ms	(- 1.0 (* (tan x) (tan x)))
6.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))

series224.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- 1.0 (* (tan x) (tan x)))
98.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
32.0ms	(* (tan x) (tan x))
60.0ms	(* (tan x) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	314	909
1	1157	838
2	5001	824

prune251.0ms

Filtered

117 candidates to 77 candidates (65.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	107	10	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	10	118

Merged error: 0.0b

Counts

118 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (cos x) 2)
0.2b	(pow (cos x) 2)
0.2b	(pow (sin x) 2)
0.2b	(pow (sin x) 2)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `pow-unpow` `*-un-lft-identity`
8×	`pow1` `add-exp-log`
4×	`pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

2.0ms	(pow (cos x) 2)
2.0ms	(pow (cos x) 2)
3.0ms	(pow (sin x) 2)
3.0ms	(pow (sin x) 2)

series76.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (cos x) 2)
17.0ms	(pow (cos x) 2)
19.0ms	(pow (sin x) 2)
24.0ms	(pow (sin x) 2)

simplify62.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	141	284
1	469	240
2	1590	240
3	5001	236

prune224.0ms

Filtered

84 candidates to 48 candidates (57.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	84	10	94

Merged error: 0.0b

Counts

94 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.5b	(pow (* (tan x) (tan x)) 3)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

33×	`pow1`
23×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
16×	`tan-quot`
13×	`add-exp-log` `add-cbrt-cube`
9×	`swap-sqr` `associate-r` `associate-l`
6×	`pow-pow`
4×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `pow-prod-up` `cbrt-unprod` `add-log-exp`
3×	`cube-div` `pow-unpow` `*-commutative` `unswap-sqr`
2×	`pow-exp` `rem-cube-cbrt`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `sqr-pow`

Counts

4 → 113

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
6.0ms	(* (tan x) (tan x))
6.0ms	(pow (* (tan x) (tan x)) 3)

series171.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (tan x) (tan x))
37.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))
69.0ms	(pow (* (tan x) (tan x)) 3)

simplify41.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	211	452
1	971	401
2	5001	384

prune304.0ms

Filtered

125 candidates to 66 candidates (52.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	125	10	135

Merged error: 0.0b

Counts

135 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.3b	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
30×	`add-cube-cbrt` `*-un-lft-identity`
24×	`times-frac`
19×	`pow1` `log-pow`
18×	`exp-prod`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
7×	`difference-of-squares`
6×	`swap-sqr` `associate-r` `associate-l`
4×	`associate-/r/` `associate-/l*` `add-log-exp`
3×	`log-prod` `associate-/r*`
2×	`pow2` `frac-times` `flip3-+` `pow-plus` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `div-inv` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `exp-diff` `div-exp` `rem-log-exp` `clear-num` `flip--`

Counts

4 → 123

Calls

4 calls:

6.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
9.0ms	(* (tan x) (tan x))
8.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

series261.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
33.0ms	(* (tan x) (tan x))
33.0ms	(* (tan x) (tan x))
98.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

simplify49.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	362	1207
1	1191	1116
2	5001	1100

prune316.0ms

Filtered

135 candidates to 93 candidates (68.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	130	5	135
Fresh	5	3	8
Picked	1	0	1
Done	0	1	1
Total	136	9	145

Merged error: 0.0b

Counts

145 → 9

regimes166.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	13
1	12	13

end0.0ms

sample932.0ms

Algorithm

intervals

Results

361.0ms	1441×	body	1280	valid
206.0ms	1263×	body	640	valid
160.0ms	4380×	body	80	valid
68.0ms	595×	body	320	valid
26.0ms	321×	body	160	valid