Details

sample149.0ms

Algorithm

intervals

Results

66.0ms	87×	body	1280	valid
37.0ms	22×	body	2560	valid
23.0ms	57×	body	640	valid
8.0ms	30×	body	320	valid
4.0ms	48×	body	80	valid
2.0ms	12×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize8.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (tan (+ x eps)) (tan x))
2.5b	(tan (+ x eps))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`tan-quot` `add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `tan-sum` `frac-sub` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 25

Calls

2 calls:

8.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series142.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(- (tan (+ x eps)) (tan x))
55.0ms	(tan (+ x eps))

simplify77.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (22.0ms)

Iter	Nodes	Cost
0	134	211
1	295	202
2	757	200
3	2482	199
4	5001	199

prune86.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(* (tan x) (tan eps))
2.9b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3--` `flip3-+` `frac-add` `associate-/r/` `flip--` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

3.0ms	(+ (tan x) (tan eps))
11.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
43.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series747.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+ (tan x) (tan eps))
211.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
91.0ms	(* (tan x) (tan eps))
356.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify51.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	397	1050
1	1432	1005
2	5001	995

prune286.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (tan x) (tan eps))
0.1b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.9b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
45×	`tan-quot`
21×	`frac-times`
20×	`add-exp-log` `add-cbrt-cube`
19×	`pow-prod-down`
15×	`associate-*r/`
14×	`associate-*l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`frac-sub`
4×	`pow-sqr` `pow-prod-up`
3×	`*-commutative`
2×	`flip3-+` `pow-plus` `associate--l+` `flip-+` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `swap-sqr` `flip--`

Counts

4 → 110

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
20.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
10.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (tan x) (tan eps))
92.0ms	(* (tan x) (tan eps))
113.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
907.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify80.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	599	1352
1	3021	1220
2	5001	1220

prune370.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 13.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.3b	(log (exp (* (tan x) (tan eps))))
2.9b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (log (exp (* (tan x) (tan eps)))))) (tan x))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

46×	`pow1`
41×	`tan-quot`
20×	`frac-times`
18×	`add-exp-log` `pow-prod-down` `add-cbrt-cube`
14×	`associate-*r/`
13×	`associate-*l/`
9×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
7×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`frac-sub`
4×	`associate-r` `associate-l` `pow-sqr` `pow-prod-up`
3×	`log-prod` `log-pow`
2×	`flip3-+` `pow-plus` `associate--l+` `*-commutative` `flip-+`
1×	`pow2` `distribute-rgt-in` `sub-neg` `exp-prod` `flip3--` `exp-to-pow` `distribute-lft-in` `diff-log` `swap-sqr` `rem-log-exp` `flip--` `unswap-sqr`

Counts

4 → 103

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
24.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.0ms	(log (exp (* (tan x) (tan eps))))
12.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (log (exp (* (tan x) (tan eps)))))) (tan x))

series1.4s

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (tan x) (tan eps))
108.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
276.0ms	(log (exp (* (tan x) (tan eps))))
897.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (log (exp (* (tan x) (tan eps)))))) (tan x))

simplify83.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	609	1453
1	2951	1231
2	5002	1229

prune304.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 13.6b

regimes237.0ms

Accuracy

81.5% (1.4b remaining)

Error of 15.8b against oracle of 14.5b and baseline of 21.8b

bsearch205.0ms

Steps

Iters	Range		Point
9	3.629416761052502e-123	1.276114475802425e-115	2.1114736186435238e-119
9	-3.988411557623274e-08	-4.1946683250978935e-14	-4.2497976182633953e-14

simplify16.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	69
1	71	69
2	76	69
3	86	69
4	100	69
5	128	69
6	133	69
7	142	69
8	158	69
9	183	69
10	206	69
11	236	69
12	261	69
13	273	69
14	292	69
15	305	69
16	316	69
17	324	69
18	330	69
19	335	69
20	342	69
21	342	69

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.5s	3343×	body	1280	valid
1.1s	650×	body	2560	valid
715.0ms	1733×	body	640	valid
223.0ms	795×	body	320	valid
105.0ms	1127×	body	80	valid
62.0ms	352×	body	160	valid

Iter	Nodes	Cost
0	65	69
1	71	69
2	76	69
3	86	69
4	100	69
5	128	69
6	133	69
7	142	69
8	158	69
9	183	69
10	206	69
11	236	69
12	261	69
13	273	69
14	292	69
15	305	69
16	316	69
17	324	69
18	330	69
19	335	69
20	342	69
21	342	69

Iter	Nodes	Cost
0	65	69
1	71	69
2	76	69
3	86	69
4	100	69
5	128	69
6	133	69
7	142	69
8	158	69
9	183	69
10	206	69
11	236	69
12	261	69
13	273	69
14	292	69
15	305	69
16	316	69
17	324	69
18	330	69
19	335	69
20	342	69
21	342	69

Iter	Nodes	Cost
0	65	69
1	71	69
2	76	69
3	86	69
4	100	69
5	128	69
6	133	69
7	142	69
8	158	69
9	183	69
10	206	69
11	236	69
12	261	69
13	273	69
14	292	69
15	305	69
16	316	69
17	324	69
18	330	69
19	335	69
20	342	69
21	342	69